Patent Publication Number: US-2019186746-A1

Title: Jet engine with plasma-assisted afterburner having Ring of Resonators and Resonator with Fuel Conduit

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application hereby incorporates by reference U.S. Pat. Nos. 5,361,737; 7,721,697; 8,783,220; 8,887,683; 9,551,315; 9,624,898; and 9,638,157. The present application also hereby incorporates by reference U.S. Patent Application Pub. Nos. 2009/0194051; 2011/0146607; 2011/0175691; 2014/0283780; 2014/0283781; 2014/0327357; 2015/0287574; 2017/0082083; 2017/0085060; 2017/0175697; and 2017/0175698. In addition, the present application hereby incorporates by reference International Patent Application Pub. Nos. WO 2011/112786; WO 2011/127298; WO 2015/157294; and WO 2015/176073. Further, the present application hereby incorporates by reference the following U.S. Patent Applications, each filed on the same date as the present application: “Plasma-Distributing Structure in a Resonator System” (identified by attorney docket number 17-1501); “Magnetic Direction of a Plasma Corona Provided Proximate to a Resonator” (identified by attorney docket number 17-1502); “Fuel Injection Using a Dielectric of a Resonator” (identified by attorney docket number 17-1505); “Jet Engine Including Resonator-based Diagnostics” (identified by attorney docket number 17-1506); “Power-generation Turbine Including Resonator-based Diagnostics” (identified by attorney docket number 17-1507); “Electromagnetic Wave Modification of Fuel in a Jet Engine” (identified by attorney docket number 17-1508); “Electromagnetic Wave Modification of Fuel in a Power-generation Turbine” (identified by attorney docket number 17-1509); “Jet Engine with Plasma-assisted Combustion” (identified by attorney docket number 17-1510); “Jet Engine with Fuel Injection Using a Conductor of a Resonator” (identified by attorney docket number 17-1511); “Jet Engine with Fuel Injection Using a Dielectric of a Resonator” (identified by attorney docket number 17-1512); “Jet Engine with Fuel Injection Using a Conductor of At Least One of Multiple Resonators” (identified by attorney docket number 17-1513); “Jet Engine with Fuel Injection Using a Dielectric of At Least One of Multiple Resonators” (identified by attorney docket number 17-1514); “Plasma-Distributing Structure in a Jet Engine” (identified by attorney docket number 17-1515); “Power-generation Gas Turbine with Plasma-assisted Combustion” (identified by attorney docket number 17-1516); “Power-generation Gas Turbine with Fuel Injection Using a Conductor of a Resonator” (identified by attorney docket number 17-1517); “Power-generation Gas Turbine with Fuel Injection Using a Dielectric of a Resonator” (identified by attorney docket number 17-1518); “Power-generation Gas Turbine with Plasma-assisted Combustion Using Multiple Resonators” (identified by attorney docket number 17-1519); “Power-generation Gas Turbine with Fuel Injection Using a Conductor of At Least One of Multiple Resonators” (identified by attorney docket number 17-1520); “Power-generation Gas Turbine with Fuel Injection Using a Dielectric of At Least One of Multiple Resonators” (identified by attorney docket number 17-1521); “Plasma-Distributing Structure in a Power Generation Turbine” (identified by attorney docket number 17-1522); “Jet Engine with Plasma-assisted Combustion and Directed Flame Path” (identified by attorney docket number 17-1523); “Jet Engine with Plasma-assisted Combustion Using Multiple Resonators and a Directed Flame Path” (identified by attorney docket number 17-1524); “Plasma-Distributing Structure and Directed Flame Path in a Jet Engine” (identified by attorney docket number 17-1525); “Power-generation Gas Turbine with Plasma-assisted Combustion and Directed Flame Path” (identified by attorney docket number 17-1526); “Power-generation Gas Turbine with Plasma-assisted Combustion Using Multiple Resonators and a Directed Flame Path” (identified by attorney docket number 17-1527); “Plasma-Distributing Structure and Directed Flame Path in a Power Generation Turbine” (identified by attorney docket number 17-1528); “Jet engine with plasma-assisted afterburner” (identified by attorney docket number 17-1529); “Jet engine with plasma-assisted afterburner having Resonator with Fuel Conduit” (identified by attorney docket number 17-1530); “Jet engine with plasma-assisted afterburner having Resonator with Fuel Conduit in Dielectric” (identified by attorney docket number 17-1531); “Jet engine with plasma-assisted afterburner having Ring of Resonators” (identified by attorney docket number 17-1532); “Jet engine with plasma-assisted afterburner having Ring of Resonators and Resonator with Fuel Conduit in Dielectric” (identified by attorney docket number 17-1534); and “Plasma-Distributing Structure in an Afterburner of a Jet Engine” (identified by attorney docket number 17-1535). 
    
    
     BACKGROUND 
     Resonators are devices and/or systems that can produce a large response for a given input when excited at a resonance frequency. Resonators are used in various applications, including acoustics, optics, photonics, electromagnetics, chemistry, particle physics, etc. For example, electromagnetic resonators can be used as antennas or as energy transmission devices. Further, resonators can concentrate a large amount of energy in a relatively small location (for example, as in the electromagnetic waves radiated by a laser). 
     Aircraft, including jets, can be used to transport cargo and/or passengers from one location to another at high velocities. By providing thrust using a jet engine or a propeller, aircraft can generate lift based on Bernoulli&#39;s principle. One way of powering a jet engine or a propeller includes combusting hydrocarbon fuel. 
     SUMMARY 
     In a first implementation, a system is provided. The system includes an afterburner including an afterburner duct that defines an afterburner channel. The afterburner is configured to receive input gas from a turbine of a jet engine into the afterburner channel and to output an exhaust gas resulting from combustion of fuel within the afterburner channel. The system also includes a plurality of resonators configured to be electromagnetically coupled to at least one radio-frequency power source. Each resonator has a resonant wavelength. Each resonator includes a first conductor, a second conductor, and a dielectric between the first conductor of that resonator and the second conductor of that resonator. Each resonator is configured such that, when that resonator is excited by the at least one radio-frequency power source with a signal having a wavelength proximate to an odd-integer multiple of one-quarter (¼) of the resonant wavelength of that resonator, that resonator provides within the afterburner at least one of electromagnetic waves or a plasma corona proximate to that resonator. A first resonator of the plurality of resonators further includes a fuel conduit having a first fuel outlet that is configured to output fuel for mixing with the input gas from the turbine of the jet engine. 
     In a second implementation, a method is provided. The method includes receiving input gas from a turbine of a jet engine into an afterburner channel defined by an afterburner duct of an afterburner. The method also includes outputting fuel into the afterburner channel for mixing with the input gas from the turbine of the jet engine. The method also includes exciting a plurality of resonators electromagnetically coupled to at least one radio-frequency power source. Each resonator has a resonant wavelength and includes a first conductor, a second conductor, and a dielectric between the first conductor of that resonator and the second conductor of that resonator. Furthermore, the method includes, in response to exciting each resonator of the plurality of resonators, providing within the afterburner at least one of electromagnetic waves or a plasma corona proximate to that resonator. Furthermore still, the method includes outputting, from the afterburner channel, an exhaust gas resulting from combustion of the fuel within the afterburner channel. 
     Other implementations will become apparent to those of ordinary skill in the art by reading the following detailed description, with reference where appropriate to the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1A  illustrates a cross-sectional view of an internal combustion engine. 
         FIG. 1B  illustrates an isometric view of an example quarter-wave coaxial cavity resonator (QWCCR) structure, according to example implementations. 
         FIG. 1C  illustrates a cutaway side view of a QWCCR structure, according to example implementations. 
         FIG. 1D  illustrates a cross-sectional view of a QWCCR structure, according to example implementations. 
         FIG. 1E  is a cross-sectional illustration of an electromagnetic mode in a QWCCR structure, according to example implementations. 
         FIG. 1F  is a cross-sectional illustration of an electromagnetic mode in a QWCCR structure, according to example implementations. 
         FIG. 1G  is a plot of a quarter-wave resonance condition of a QWCCR structure, according to example implementations. 
         FIG. 2  illustrates a system that includes a coaxial resonator, according to example implementations. 
         FIG. 3A  illustrates a system that includes a coaxial resonator, according to example implementations. 
         FIG. 3B  illustrates a system that includes a coaxial resonator, according to example implementations. 
         FIG. 4A  illustrates a system that includes a coaxial resonator, according to example implementations. 
         FIG. 4B  illustrates a controller, according to example implementations. 
         FIG. 5  illustrates a cutaway side view of a QWCCR structure connected to a fuel pump and a fuel tank, according to example implementations. 
         FIG. 6  illustrates a cross-sectional view of an example coaxial resonator connected to a direct-current (DC) power source through an additional resonator assembly acting as a radio-frequency (RF) attenuator, according to example implementations. 
         FIG. 7  illustrates a cross-sectional view of an example coaxial resonator connected to a DC power source through an additional resonator assembly acting as an RF attenuator, according to example implementations. 
         FIG. 8  illustrates an aircraft having a jet engine, according to example implementations. 
         FIG. 9  illustrates a jet engine, according to example implementations. 
         FIG. 10A  illustrates a combustor, according to example implementations. 
         FIG. 10B  illustrates a combustor, according to example implementations. 
         FIG. 10C  illustrates a combustor, according to example implementations. 
         FIG. 10D  illustrates a combustor, according to example implementations. 
         FIG. 10E  illustrates a combustor, according to example implementations. 
         FIG. 10F  illustrates a combustor, according to example implementations. 
         FIG. 11  illustrates a partial view of a combustor, according to example implementations. 
         FIG. 12  illustrates air flow paths through a combustor, according to example implementations. 
         FIG. 13  illustrates a jet engine including an afterburner, according to example implementations. 
         FIG. 14  illustrates a jet engine including an afterburner, according to example implementations. 
         FIG. 15A  is a perspective view of an afterburner duct and casing, according to example implementations. 
         FIG. 15B  is a perspective view of an afterburner duct and casing, according to example implementations. 
         FIG. 16A  is an elevation view of an afterburner duct and casing, according to example implementations. 
         FIG. 16B  is a cross-sectional view of the afterburner duct and casing shown in  FIG. 16A . 
         FIG. 17A  illustrates a torch igniter, according to example implementations. 
         FIG. 17B  illustrates a torch igniter, according to example implementations. 
         FIG. 18  illustrates a system of an afterburner, according to example implementations. 
         FIG. 19A  is a cross-sectional view of a fueling section of an afterburner, according to example implementations. 
         FIG. 19B  is a cross-sectional view of the fueling section shown in  FIG. 19A . 
         FIG. 19C  is a cross-sectional view of a fueling section of an afterburner, according to example implementations. 
         FIG. 19D  is a cross-sectional view of the fueling section shown in  FIG. 19C . 
         FIG. 20A  is a cross-sectional view of a resonator section of an afterburner, according to example implementations. 
         FIG. 20B  is a cross-sectional view of the resonator section shown in  FIG. 20A . 
         FIG. 20C  is a cross-sectional view of a resonator section of an afterburner, according to example implementations. 
         FIG. 20D  is a cross-sectional view of the resonator section shown in  FIG. 20C . 
         FIG. 21A  is a cross-sectional view of a resonator section of an afterburner, according to example implementations. 
         FIG. 21B  is a cross-sectional view of the resonator section shown in  FIG. 21A . 
         FIG. 21C  is a cross-sectional view of a resonator section of an afterburner, according to example implementations. 
         FIG. 21D  is a cross-sectional view of the resonator section shown in  FIG. 21C . 
         FIG. 22A  is a cross-sectional view of a resonator section of an afterburner, according to example implementations. 
         FIG. 22B  is a cross-sectional view of the resonator section shown in  FIG. 22A . 
         FIG. 22C  is a cross-sectional view of a resonator section of an afterburner, according to example implementations. 
         FIG. 22D  is a cross-sectional view of the resonator section shown in  FIG. 22C . 
         FIG. 23A  is a cross-sectional view of a resonator section of an afterburner, according to example implementations. 
         FIG. 23B  is a cross-sectional view of the resonator section shown in  FIG. 23A . 
         FIG. 23C  is a cross-sectional view of a resonator section of an afterburner, according to example implementations. 
         FIG. 23D  is a cross-sectional view of the resonator section shown in  FIG. 23C . 
         FIG. 24A  is a cross-sectional view of a resonator section of an afterburner, according to example implementations. 
         FIG. 24B  is a cross-sectional view of the resonator section shown in  FIG. 24A . 
         FIG. 24C  is a cross-sectional view of a resonator section of an afterburner, according to example implementations. 
         FIG. 24D  is a cross-sectional view of the resonator section shown in  FIG. 24C . 
         FIG. 25A  is a cross-sectional view of a resonator section of an afterburner, according to example implementations. 
         FIG. 25B  is a cross-sectional view of the resonator section shown in  FIG. 25A . 
         FIG. 25C  is a cross-sectional view of a resonator section of an afterburner, according to example implementations. 
         FIG. 25D  is a cross-sectional view of the resonator section shown in  FIG. 25C . 
         FIG. 26A  is a cross-sectional view of a resonator section of an afterburner, according to example implementations. 
         FIG. 26B  is a cross-sectional view of the resonator section shown in  FIG. 26A . 
         FIG. 26C  is a cross-sectional view of a resonator section of an afterburner, according to example implementations. 
         FIG. 26D  is a cross-sectional view of the resonator section shown in  FIG. 26C . 
         FIG. 27A  is a cross-sectional view of a resonator section of an afterburner, according to example implementations. 
         FIG. 27B  is a cross-sectional view of the resonator section shown in  FIG. 27A . 
         FIG. 27C  is a cross-sectional view of a resonator section of an afterburner, according to example implementations. 
         FIG. 27D  is a cross-sectional view of the resonator section shown in  FIG. 27C . 
         FIG. 28  illustrates a strut, according to example implementations. 
         FIG. 29  illustrates a strut, according to example implementations. 
         FIG. 30  illustrates a strut, according to example implementations. 
         FIG. 31  illustrates a resonator structure having a fuel conduit connected to a fuel pump and a fuel tank, according to example implementations. 
         FIG. 32  illustrates a resonator structure having a fuel conduit connected to a fuel pump and a fuel tank, according to example implementations. 
         FIG. 33A  is an elevational view of a conductor and fuel conduit of a resonator, according to example implementations. 
         FIG. 33B  is a cross-sectional view of the conductor and fuel conduit shown in  FIG. 33A . 
         FIG. 33C  is an elevational view of a conductor and fuel conduit of a resonator, according to example implementations. 
         FIG. 33D  is a cross-sectional view of the conductor and fuel conduit shown in  FIG. 33C . 
         FIG. 34A  is an elevational view a resonator structure having a fuel conduit, according to example implementations. 
         FIG. 34B  is a cross-sectional view of the resonator shown in  FIG. 34A . 
         FIG. 35  illustrates a cross-sectional view of a resonator having a fuel conduit within a conductor, according to example implementations. 
         FIG. 36A  is an elevation view of a conductor that can be used as an inner conductor of a resonator including a fuel conduit, according to example implementations. 
         FIG. 36B  is a cross-sectional view of the conductor and fuel conduit shown in  FIG. 36A . 
         FIG. 36C  is an elevation view of a conductor that can be used as an inner conductor of a resonator including a fuel conduit, according to example implementations. 
         FIG. 36D  is a cross-sectional view of the conductor and fuel conduit shown in  FIG. 36C . 
         FIG. 37  illustrates a resonator structure having a fuel conduit connected to a fuel pump and a fuel tank, according to example implementations. 
         FIG. 38  is a cutaway side view of a portion of a resonator section and other afterburner components, according to example implementations. 
         FIG. 39  is a flow chart depicting operations of a representative method, according to example implementations. 
     
    
    
     DETAILED DESCRIPTION 
     Example methods, devices, and systems are presently disclosed. It should be understood that the word “example” is used in the present disclosure to mean “serving as an instance or illustration.” Any implementation or feature presently disclosed as being an “example” is not necessarily to be construed as preferred or advantageous over other implementations or features. Other implementations can be utilized, and other changes can be made, without departing from the scope of the subject matter presented in the present disclosure. 
     Thus, the example implementations presently disclosed are not meant to be limiting. Components presently disclosed and illustrated in the figures can be arranged, substituted, combined, separated, and designed in a wide variety of different configurations, all of which are contemplated in the present disclosure. 
     Further, unless context suggests otherwise, the features illustrated in each of the figures can be used in combination with one another. Thus, the figures should be generally viewed as components of one or more overall implementations, with the understanding that not all illustrated features are necessary for each implementation. 
     In the context of this disclosure, various terms can refer to locations where, as a result of a particular configuration, and under certain conditions of operation, a voltage component can be measured as close to non-existent. For example, “voltage short” can refer to any location where a voltage component can be close to non-existent under certain conditions. Similar terms can equally refer to this location of close-to-zero voltage (for example, “virtual short circuit,” “virtual short location,” or “voltage null”). In examples, “virtual short” can be used to indicate locations where the close-to-zero voltage is a result of a standing wave crossing zero. “Voltage null” can be used to refer to locations of close-to-zero voltage for a reason other than as result of a standing wave crossing zero (for example, voltage attenuation or cancellation). Moreover, in the context of this disclosure, each of these terms that can refer to locations of close-to-zero voltage are meant to be non-limiting. 
     In an effort to provide technical context for the present disclosure, the information in this section can broadly describe various components of the implementations presently disclosed. However, such information is provided solely for the benefit of the reader and, as such, does not expressly limit the claimed subject matter. Further, components shown in the figures are shown for illustrative purposes only. As such, the illustrations are not to be construed as limiting. As is understood, components can be added, removed, or rearranged without departing from the scope of this disclosure. 
     I. Overview 
     A resonator can be configured to provide a plasma corona and/or electromagnetic waves in response to being excited by a radio-frequency power source. This present disclosure describes such a resonator with respect to an afterburner. The afterburner can be configured to connect to a turbine of a jet engine and/or can be part of a jet engine. The afterburner can further be configured to be disconnected from a jet engine to perform service to the jet engine and/or the afterburner. The afterburner can include an afterburner duct that defines an afterburner channel. The afterburner is arranged to combust fuel in the afterburner channel. 
     In an example implementation, a plurality of resonators or some portion of the plurality of resonators can be disposed within the afterburner channel. The plurality of resonators can be arranged as a ring of resonators. In some implementations, the resonators of a ring of resonators can be attached to a bracket and/or the afterburner duct. The resonators can be configured to provide the plasma corona within the afterburner channel while a gas from the turbine, mixed with fuel, is flowing through the afterburner channel. The plasma corona provided by the resonators may ignite the fuel and initiate further combustion of fuel within the afterburner channel. The electromagnetic waves may reform fuel to be combusted by the afterburner. In another example implementation, the resonator(s) or some portion of the resonator(s) can be disposed within a treatment chamber for pretreating fuel with the electromagnetic waves. In some of those implementations, the treatment chamber is disposed within the afterburner channel, while in some other implementations; the treatment chamber is disposed outside of the afterburner channel, such as on a casing of the afterburner. 
     A ring of resonators can include a resonator that includes first and second conductors and a dielectric between the first and second conductors. Furthermore, that resonator can include a fuel conduit within the first or second conductor. The fuel conduit is fluidly connectable to a fuel supply line. The fuel conduit can include one or more fuel outlets. A fuel pump can move fuel through the fuel supply so as to supply fuel to the fuel conduit and out the one or more fuel outlets. In some implementations, the electromagnetic waves provided by the resonator can affect the fuel moving through the fuel conduit. 
     The ring of resonators can include multiple resonators that are attached to the afterburner duct and/or a bracket. The bracket can be supported by struts. The struts can include passages for routing fuel supply lines and electrical circuitry to the ring of resonators. 
     Each resonator in a ring of resonators has a resonant wavelength. In some implementations, the resonant wavelength can be the same for all resonators in the ring. In other implementations, two or more resonators of the ring may have different resonant wavelengths. In some implementations, a single radio-frequency power source can provide the signals to excite each resonator in the ring. In other implementations, multiple radio-frequency power sources can provide the signals to excite the resonators in the ring. 
     In an example implementation, a resonator in the afterburner and/or a ring of resonators can include a first conductor and a second conductor, which could be separated by a dielectric insulator such as a ceramic material. The resonator can provide excitation energy and a plasma corona to enhance combustion in the afterburner. In some implementations, the resonator can also be configured to provide fuel into a combustion environment or other type of environment in which fuel may be desired. 
     In an example implementation, the resonator can provide fuel through the first conductor. For instance, the first conductor can include one or more fuel conduits, through which fuel can pass. These conduits can terminate at one or more fuel outlets out of which the fuel can be expelled into the environment and/or into another portion of the resonator. The first conductor can be an inner, center conductor, and at least a portion of the first conductor can be disposed within a cavity defined by the second conductor. Alternatively, the first conductor can be an outer conductor that defines a cavity, and at least a portion of the second conductor can be disposed within the cavity defined by the first conductor. 
     Using a resonator configured in this manner in an afterburner can be advantageous in a variety of ways. For example, the resonator can be used as a substitute or supplement for a separate fuel injector component, possibly even eliminating a need for such a component. As another example, passing the fuel through the first conductor can expose the fuel to resonator-generated electromagnetic waves, which can result in a reformation of the fuel before the resonator provides the fuel into the afterburner channel and/or ignites the fuel. And in addition, outlets of the fuel conduit can be oriented towards the location where the resonator will excite a plasma corona, thereby providing the fuel proximate to the ignition source (particularly, toward/through the plasma corona), which can improve the resulting combustion. 
     Furthermore, in some implementations, a resonator configured in this manner can be used together with additional resonators within the afterburner channel. Optionally, one or more of the additional resonators can also be configured such that fuel passes through a first conductor respectively of each of one or more of the additional resonators and is exposed to electromagnetic waves. Advantageously, when multiple resonators are configured such that fuel passes through a first conductor of each of the resonators, a greater amount of fuel can be reformed before entering the combustion chamber of the afterburner channel as opposed to an amount of fuel that can be reformed when only a single resonator includes a fuel conduit. Additionally or alternatively, one or more of the additional resonators can be controlled so as to provide a plasma corona. When multiple resonators are controlled so as to provide multiple plasma coronas within the afterburner channel, fuel introduced into the combustion chamber may combust at multiple ignition points, thereby increasing the probability of fuel being combusted before exiting the afterburner channel. Increasing the probability of fuel being combusted may improve various operating characteristics of the afterburner, including fuel efficiency and emissions, for example. 
     Furthermore still, in some implementations, one or more of the plurality of resonators can assume a dual role. For instance, providing the at least one plasma corona can include causing a given resonator of the plurality of resonators to provide a plasma corona. Moreover, in that implementation, the given resonator can be excited prior to formation of the plasma corona, such that the given resonator provides electromagnetic waves for pre-treating fuel that is input through the given resonator and/or fuel that is within the afterburner channel. 
     Similarly, in some implementations, a first set of resonators of a plurality of resonators can provide plasma coronas and a second set of resonators of the plurality of resonators need not provide respective plasma coronas. The first set of resonators could include one or more resonators of the plurality of resonators, and the second set of resonators could include one or more other resonators of the plurality of resonators. With this arrangement, after initiating combustion, rather than providing plasma coronas, the second set of resonators could instead enhance an already present combustion process by providing electromagnetic waves that can reform fuel that is being input to the afterburner channel and/or already in the afterburner channel. In one example, the resonators of the second set of resonators could be controlled so as to initially provide plasma coronas and then, after initiating combustion, to stop providing plasma coronas. Alternatively, resonators of the second set of resonators might never provide plasma coronas, but only provide electromagnetic waves for pre-treating or reforming fuel. 
     Furthermore still, the resonator in the afterburner channel can be one of multiple resonators disposed in the afterburner channel. Each of those resonators can be configured to provide electromagnetic waves and/or a plasma corona. In some implementations, the multiple resonators can be disposed within the afterburner channel and separated from each other so that the electromagnetic waves provided by those resonators are able to influence fuel within a large zone in the afterburner channel, such as a cross-section of the afterburner channel in which the resonators are disposed. The electromagnetic waves within that zone can provide a large electric field within the afterburner channel such that a fuel flow rate within the afterburner channel can increase as compared to when the resonators are not providing the electromagnetic waves. Additionally or alternatively, the multiple resonators spread throughout the zone of the afterburner channel can provide the plasma corona though a large portion of the zone to increase combustion efficiency within the afterburner. 
     II. Example Combustion 
     Igniters can be used to ignite a mixture of air and fuel (for example, within a combustion chamber of an internal combustion engine  101 , such as that illustrated in cross-section in  FIG. 1A ). For example, igniters can be configured as gap spark igniters, similar to an automotive spark plug. However, gap spark igniters might not be desirable in some applications and/or under some conditions. For example, a gap spark igniter might not be capable of igniting and initiating combustion of fuel mixtures that have fuel-to-air ratios below a certain threshold. Further, lean mixtures of fuel and air might have significant environmental and economic benefits by making combustion (for example, within a combustor or an afterburner) more efficient, and thus, using a gap spark igniter might preclude achieving such benefits. In addition, higher thermal efficiencies can be achieved by operating at higher power densities and pressures. However, using more energetic or powerful gap spark igniters reduces overall ignition efficiency because the higher energy levels can be detrimental to the gap spark igniter&#39;s lifetime. Higher energy levels might also contribute to the formation of undesirable pollutants and can reduce overall engine efficiency. 
     While gap spark igniters are described above, other types of igniters can generally include glow plugs (for example, in diesel-fueled internal combustion engines), open flame sources (for example, cigarette lighters, friction spark devices, etc.), and other heat sources. 
     A variety of fuels (for example, hydrocarbon fuels) can be combusted to yield energy within an internal combustion engine, within a power-generation turbine, within a jet engine, or within various other applications. For example, kerosene (also known as paraffin or lamp oil), gasoline (also known as petrol), fractional distillates of petroleum fuel oil (for example, diesel fuel), crude oil, Fischer-Tropsch synthesized paraffinic kerosene, natural gas, and coal are all hydrocarbon fuels that, when combusted, liberate energy stored within chemical bonds of the fuel. Jet fuel, specifically, can be classified by its “jet propellant” (JP) number. The “jet propellant” (JP) number can correspond to a classification system utilized by the United States military. For example, JP-1 can be a pure kerosene fuel, JP-4 can be a 50% kerosene and 50% gasoline blend, JP-9 can be another kerosene-based fuel, JP-9 can be a gas turbine fuel (for example, including tetrahydrodimethylcyclopentadiene) specifically used in missile applications, and JP-10 can be a fuel similar to JP-9 that includes endo-tetrahydrodicyclopentadiene, exo-tetrahydrodicyclopentadiene, and adamantane. Other forms of jet fuel include zip fuel (for example, high-energy fuel that contains boron), SYNTROLEUM® FT-fuel, other kerosene-type fuels (for example, Jet A fuel and Jet A-1 fuel), and naphtha-type fuels (for example, Jet B fuel). It is understood that other fuels can be combusted as well. Further, the fuel type used can depend upon the application. For example, jet engines, internal combustion engines, and power-generation turbines may each burn different types of fuels. 
     When fuel (for example, hydrocarbon fuel) interacts with electromagnetic radiation, the fuel can change chemical composition. For example, when hydrocarbon fuel interacts with (for example, is irradiated by) microwaves, some of the hydrogen atoms can be ionized and/or one or more hydrogen atoms can be liberated from a hydrocarbon chain. The processes of liberating hydrogen within fuel, ionizing hydrogen within fuel, or otherwise changing the chemical composition of fuel are collectively referred to in the present disclosure as “reforming” the fuel. Reforming the fuel can include exciting the hydrocarbon fuel at one or more of its natural resonant frequencies (for example, acoustic and/or electromagnetic resonant frequencies) to break one or more of the carbon-hydrogen (or other) bonds within the hydrocarbon chain. When hydrogen within a hydrocarbon fuel becomes ionized and/or is liberated from the hydrocarbon chain, the resulting hydrocarbon fuel can require less energy to burn. Thus, a leaner fuel/air mixture that includes reformed fuel can achieve the same output power (for example, within a combustion chamber of a jet engine or a power-generation turbine) as compared to a more rich fuel/air mixture that includes non-reformed fuel, since the reformed fuel can combust more quickly and thoroughly. Analogously, when comparing equal fuel-to-air ratios, less input energy can be required to combust a mixture that includes reformed fuel when compared to a mixture that includes non-reformed fuel. 
     In addition to reforming fuels, electromagnetic radiation can alter an energy state of fuel and/or of a fuel mixture. In an example implementation, altering the energy state of fuel can include exciting electrons within the valence band of the hydrocarbon chain to higher energy levels. In such scenarios, raising the energy state can also include reorienting polar molecules (for example, water and/or polar hydrocarbon chains) within a fuel/air mixture due to electromagnetic fields applying a torque on polar molecules. Reorienting polar molecules can result in molecular motion, thereby increasing an effective temperature and/or kinetic energy of the molecule, which raises the energy state of fuel. By raising the energy state of fuel, the activation energy for combustion of the fuel can be reduced. When the activation energy for combustion is reduced, the energy supplied by the ignition source can also be decreased, thereby conserving energy during ignition. 
     Presently disclosed are ignition systems with resonators (for example, QWCCR structures) that use both RF power and DC power. The presently disclosed RF ignition systems provide an alternative to other types of igniters. For example, the QWCCR structure can be used as an igniter (for example, in place of an automotive gap spark plug) in the internal combustion engine  101 . Such RF ignition systems can excite plasma (for example, within a corona). If an igniter is configured as one of the RF ignition systems presently disclosed, then more efficient, leaner, cleaner combustion can be achieved. Such increased combustion efficiency can be achieved at decreased air pressures and temperatures when compared with a gap spark igniter (for example, if the RF ignition system is used in a jet engine). Further, such increased combustion efficiency can be achieved at higher air pressures and temperatures when compared with a gap spark igniter. It is understood throughout this disclosure that where reference is made to “RF” or to microwaves, in alternate implementations, other wavelengths of electromagnetic waves outside of the RF range can be used alternatively or in addition to RF electromagnetic waves. 
     As described above, RF ignition systems can excite plasma. Plasma is one of the four fundamental states of matter (in addition to solid, liquid, and gas). Further, plasmas are mixtures of positively charged gas ions and negatively charged electrons. Because plasmas are mixtures of charged particles, plasmas have associated intrinsic electric fields. In addition, when the charged particles in the mixture move, plasmas also produce magnetic fields (for example, according to Ampere&#39;s law). Given the electromagnetic nature of plasmas, plasmas interact with, and can be manipulated by, external electric and magnetic fields. For example, placing a ferromagnetic material (for example, iron, cobalt, nickel, neodymium, samarium-cobalt, etc.) near a plasma can cause the plasma to be attracted to or repelled from the ferromagnetic material (for example, causing the plasma to move). 
     Plasmas can be formed in a variety of ways. One way of forming a plasma can include heating gases to a sufficiently high temperature (for example, depending on ambient pressure). Additionally or alternatively, forming a plasma can include exposing gases to a sufficiently strong electromagnetic field. Lightning is an environmental phenomenon involving plasma. One application of plasma can include neon signs. Further, because plasma is responsive to applied electromagnetic fields, plasma can be directed according to specific patterns. Hence, plasmas can also be used in technologies such as plasma televisions or plasma etching. 
     Plasmas can be characterized according to their temperature and electron density. For example, one type of plasma can be a “microwave-generated plasma” (for example, ranging from 5 eV to 15 eV in energy). Such a plasma can be generated by a QWCCR structure, for example. 
     III. Example Resonator 
     An example implementation of a QWCCR structure  100  is illustrated in  FIGS. 1B-1D . As illustrated, the QWCCR structure  100  can include an outer conductor  102 , an inner conductor  104  with an associated electrode  106 , a base conductor  110 , and a dielectric  108 . Also as illustrated, the QWCCR structure  100  can be shaped as concentric circular cylinders. The inner conductor  104  can have radius ‘a’, the outer conductor  102  can have inner radius ‘b’, and the outer conductor  102  can have outer radius ‘c’, as illustrated in cross-section in  FIG. 1D . In alternate implementations, the QWCCR structure  100  can have other shapes (for example, concentric ellipsoidal cylinders or concentric, enclosed, elongated volumes with square or rectangular cross-sections). The inner conductor  104 , the outer conductor  102  (or just the inner surface of the outer conductor  102 ), the electrode  106 , and the base conductor  110  can be made of various conductive materials (for example, steel, gold, silver, platinum, nickel, or alloys thereof). Further, in some implementations, the inner conductor  104 , the outer conductor  102 , and the base conductor  110  can be made of the same conductive materials, while in other implementations, the inner conductor  104 , the outer conductor  102 , and the base conductor  110  can be made of different conductive materials. Additionally, in some implementations, the inner conductor  104 , the outer conductor  102 , and/or the base conductor  110  can include a dielectric material coated in a conductor (for example, a metal-plated ceramic). In such implementations, the conductive coating can be thicker than a skin-depth of the conductor at a given excitation frequency of the QWCCR structure  100  such that electricity is conducted throughout the conductive coating. 
     As illustrated, an electrode  106  can be disposed at a distal end of the inner conductor  104 . The electrode  106  can be made of a conductive material as described above (for example, the same conductive material as the inner conductor  104 ). For example, the electrode  106  can be machined with the inner conductor  104  as a single piece. In some implementations, as illustrated, the base conductor  110 , the outer conductor  102 , the inner conductor  104 , and the electrode can be shorted together. For example, the base conductor  110  can short the outer conductor  102  to the inner conductor  104 , in some implementations. When shorted together, these components can be directly electrically coupled to one another such that each of these components is at the same electric potential. 
     Further, in implementations where the base conductor  110 , the outer conductor  102 , and the inner conductor  104  (including the electrode  106 ) are shorted together, the base conductor  110 , the outer conductor  102 , and the inner conductor  104  (including the electrode  106 ) can be machined as a single piece. In addition, the electrode  106  can include a concentrator (for example, a tip, a point, or an edge), which can concentrate and enhance the electric field at one or more locations. Such an enhanced electric field can create conditions that promote the excitation of a plasma corona near the concentrator (for example, through a breakdown of a dielectric, such as air, that surrounds the concentrator). The concentrator can be a patterned or shaped portion of the electrode  106 , for example. The electrode  106 , including the concentrator, can be electromagnetically coupled to the inner conductor  104 . In the present disclosure and claims, the electrode  106  and/or the concentrator can be described as being “configured to electromagnetically couple to” the inner conductor  104 . This language is to be interpreted broadly as meaning that the electrode  106  and/or the concentrator: are presently electromagnetically coupled to the inner conductor  104 , are always electromagnetically coupled to the inner conductor  104 , can be selectively electromagnetically coupled to the inner conductor  104  (for example, using a switch), are only electromagnetically coupled to the inner conductor  104  when a power source is connected to the inner conductor  104 , and/or are able to be electromagnetically coupled to the inner conductor  104  if one or more components are repositioned relative to one another. For example, the electrode  106  can be “configured to electromagnetically couple to” the inner conductor  104  if the electrode  106  is machined as a single piece with the inner conductor  104 , if the electrode  106  is connected to the inner conductor  104  using a wire or other conducting mechanism, or if the electrode  106  is disposed sufficiently close to the inner conductor  104  such that the electrode  106  electromagnetically couples to one or more evanescent waves excited by the inner conductor  104  when the inner conductor  104  is connected to a power source. 
     As illustrated in  FIG. 1C , the electrode  106  and/or a concentrator of the electrode  106  can extend beyond the distal end of the outer conductor  102  and/or the distal end of the dielectric  108 . In alternate implementations, the electrode  106  and/or a concentrator of the electrode  106  can be flush with the distal end of the outer conductor  102  and/or the distal end of the dielectric  108 . In alternate implementations, the electrode  106  and/or a concentrator of the electrode  106  can be shorter than the outer conductor  102 , such that no portion of the electrode  106  and/or concentrator is flush with the distal end of the outer conductor  102  and no portion extends beyond the distal end of the outer conductor  102 . The QWCCR structure  100  can be excited at resonance, in some implementations. The resonance can generate a standing voltage quarter-wave within the QWCCR structure  100 . If the concentrator, the distal end of the outer conductor  102 , and the distal end of the dielectric  108  are each flush with one another, the electromagnetic field can quickly collapse outside of the QWCCR structure  100 , thereby concentrating the majority of the electromagnetic energy at the concentrator. In still other implementations, the distal end of the outer conductor  102  and/or the distal end of the dielectric  108  can extend beyond the electrode  106  and/or a concentrator of the electrode  106 . The electrode  106  can effectively modify the physical length of the inner conductor  104 , which can modify the resonance conditions of the QWCCR structure  100  (for example, can modify the electrical length of the QWCCR structure  100 ). Various resonance conditions can thus be achieved across a variety of QWCCR structures  100  by varying the geometry of the electrode  106  and/or a concentrator of the electrode  106 . 
     Further, as illustrated in  FIG. 1C , the base conductor  110  can be electrically coupled to the outer conductor  102  and the inner conductor  104 . In alternate implementations, the inner conductor  104  can be electrically insulated from the outer conductor  102  (rather than shorted together through the base conductor  110 ). 
     Plasmas (for example, plasma coronas generated by the QWCCR structure  100 ) can be used to ignite mixtures of air and fuel (for example, hydrocarbon fuel for use in a combustion process). Plasma-assisted ignition (for example, using a QWCCR structure  100 ) is fundamentally different from ignition using a gap spark plug. For example, efficient electron-impact excitation, dissociation of molecules, and ionization of atoms, which might not occur in ignition using gap spark plugs, can occur in plasma-assisted ignition. Further, in plasmas, an external electric field can accelerate the electrons and/or ions. Thus, using electric fields, energy within the plasma (for example, thermal energy) can be directed to specific locations (for example, within a combustion chamber). 
     There are a variety of mechanisms by which plasma can impart the energy necessary to ignite mixtures of air and fuel. For example, electrons can impart energy to molecules during collisions. However, this singular energy exchange might be relatively minor (for example, because an electron&#39;s mass is orders of magnitude less than a molecule&#39;s mass). So long as the rate at which electrons are imparting energy to the molecules is higher than the rate at which molecules are undergoing relaxation, a population distribution of the molecules (for example, a population distribution that differs from an initial Boltzmann distribution of the molecules) can arise. The molecules having higher energy, along with the dissociation and ionization processes, can emit ultraviolet (UV) radiation (for example, when undergoing relaxation) that affects mixtures of fuel and air. Further, gas heating and an increase in system reactivity can increase the likelihood of ignition and flame propagation. In addition, when the average electron energy within a plasma (for example, within a combustion chamber) exceeds 10 eV, gas ionization can be the predominant mechanism by which plasma is formed (over electron-impact excitation and dissociation of molecules). 
     Plasma-assisted ignition can have a variety of benefits over ignition using a gap spark plug. For example, in plasma-assisted ignition, a plasma corona that is generated can be physically larger (for example, in length, width, radius, and/or overall volumetric extent) than a typical spark from a gap spark plug. This can allow a more lean fuel mixture (also known as lower fuel-to-air ratio) to be burned once combustion occurs as compared with alternative ignition, for example. Also, because a larger energy can be energized in plasma-assisted ignition, stoichiometric ratio fuels can be combusted more fully, thereby creating fewer regulated pollutants (for example, creating less NO x  to be expelled as exhaust) and/or leaving less unspent fuel. 
     Dielectric breakdown of air or another dielectric material near the electrode  106  of the QWCCR structure  100  can be a mechanism by which a plasma corona is excited near the concentrator of the QWCCR structure  100 . Factors that impact the breakdown of a dielectric, such as dielectric breakdown of air, include free-electron population, electron diffusion, electron drift, electron attachment, and electron recombination. Free electrons in the free-electron population can collide with neutral particles or ions during ionization events. Such collisions can create additional free electrons, thereby increasing the likelihood of dielectric breakdown. Oppositely, electron diffusion and attachment can each be mechanisms by which free electrons recombine and are lost, thereby reducing the likelihood of dielectric breakdown. 
     As presently described, a plasma corona can be provided “proximate to” a distal end of the QWCCR structure  100 , the electrode  106 , and/or a concentrator of the QWCCR structure  100 . In other words, the plasma corona could be described as being provided “nearby” or “at” a distal end of the QWCCR structure  100 , the electrode  106 , and/or a concentrator of the QWCCR structure  100 . Further, this terminology is not to be viewed as limiting. For example, while the plasma corona is provided “proximate to” the QWCCR structure  100 , this does not limit the plasma corona from extending away from the QWCCR structure  100  and/or from being moved to other locations that are farther from the QWCCR structure  100  after being provided “proximate to” the QWCCR structure  100 . 
     When used to describe a relationship between a plasma corona and a distal end of the QWCCR structure  100 , a relationship between a plasma corona and the electrode  106 , a relationship between a plasma corona and a concentrator of the electrode  106 , or similar relationships, the term “proximate” can describe the physical separation between the plasma corona and the other component. In various implementations, the physical separation can include different ranges. For example, a plasma corona provided “proximate to” the concentrator can be separated from the concentrator (in other words, can “stand off from” the concentrator) by less than 1.0 nanometer, by 1.0 nanometer to 10.0 nanometers, by 10.0 nanometers to 100.0 nanometers, by 100.0 nanometers to 1.0 micrometer, by 1.0 micrometer to 10.0 micrometers, by 10.0 micrometers to 100.0 micrometers, or by 100.0 micrometers to 1.0 millimeter. Additionally or alternatively, a plasma corona provided “proximate to” the concentrator can be separated from the concentrator by 0.01 times a width of the plasma corona to 0.1 times a width of the plasma corona, by 0.1 times a width of the plasma corona to 1.0 times the width of the plasma corona, or by 1.0 times a width of the plasma corona to 10.0 times a width of the plasma corona. Even further, a plasma corona provided “proximate to” the concentrator can be separated from the concentrator by 0.01 times a radius of the concentrator to 0.1 times a radius of the concentrator, by 0.1 times a radius of the concentrator to 1.0 times a radius of the concentrator, or by 1.0 times a radius of the concentrator to 10.0 times a radius of the concentrator. 
     It is understood that in various implementations, the plasma corona can emit light entirely within the visible spectrum, partially within the visible spectrum and partially outside the visible spectrum, or completely outside the visible spectrum. In other words, even if the plasma corona is “invisible” to the human eye and/or to optics that only sense light within the visible spectrum, it is not necessarily the case that the plasma corona is not being provided. 
     IV. Mathematical Description of Example Resonator 
     In order for dielectric breakdown to occur, an electric field within the dielectric must be greater than or equal to an electric field breakdown threshold. An electric field generated by an alternating current (AC) source can be described by a root-mean-square (rms) value for electric field (E rms ). The rms value for electric field (E rms ) can be calculated according the following equation: 
     
       
         
           
             
               E 
               rms 
             
             = 
             
               
                 
                   1 
                   
                     
                       T 
                       2 
                     
                     - 
                     
                       T 
                       1 
                     
                   
                 
                  
                 
                   
                     ∫ 
                     
                       T 
                       1 
                     
                     
                       T 
                       2 
                     
                   
                    
                   
                     
                       E 
                       2 
                     
                      
                     dt 
                   
                 
               
             
           
         
       
     
     where T 2 −T 1  represents the period over which the electric field is oscillating (for example, corresponding to the period of the AC source generating the electric field). As described mathematically above, the rms value for electric field (E rms ) represents the quadratic mean of the electric field. Using the rms value for electric field, an effective electric field (E eff ) can be calculated that is approximately frequency independent (for example, by removing phase lag effects from the oscillating electric field): 
     
       
         
           
             
               E 
               eff 
               2 
             
             = 
             
               
                 E 
                 rms 
                 2 
               
                
               
                 
                   v 
                   c 
                   2 
                 
                 
                   
                     ω 
                     2 
                   
                   + 
                   
                     v 
                     c 
                     2 
                   
                 
               
             
           
         
       
     
     where ω represents the angular frequency of the electric field (for example, 
     
       
         
           
             
               ω 
               = 
               
                 
                   2 
                    
                   π 
                 
                 
                   
                     T 
                     2 
                   
                   - 
                   
                     T 
                     1 
                   
                 
               
             
             ) 
           
         
       
     
     and ν c  represents the effective momentum collision frequency of the electrons and neutral particles. The angular frequency (ω) of the electric field can correspond to the frequency of an excitation source used to excite the electric field (for example, the QWCCR structure  100 ). Using this effective electric field (E eff ), DC breakdown voltages for various gases (and potentially other dielectrics) can be related to AC breakdown values for uniform electric fields. For air, ν c ≈5·10 9 ×p, where p represents the pressure (in torr). At atmospheric pressure (for example, around 760 torr) or above and excitation frequencies of below 1 THz, the effective momentum collision frequency of the electrons and neutral particles (ν c ) will dominate the denominator of the fractional coefficient of E rms   2 . Therefore, an approximation of the rms breakdown field (E b ) can be used. The rms breakdown field (E b ), in V/cm, of a uniform microwave field in the collision regime can be given by: 
     
       
         
           
             
               E 
               b 
             
             = 
             
               
                 30 
                 · 
                 297 
               
                
               
                 ( 
                 
                   p 
                   T 
                 
                 ) 
               
             
           
         
       
     
     where T is the temperature in Kelvin. 
     An analytical description of the electromagnetics of the QWCCR structure  100  follows. 
     If fringing electromagnetic fields are assumed to be small, the lowest quarter-wave resonance in a coaxial cavity is a transverse electromagnetic mode (TEM mode) (as opposed to a transverse electric mode (TE mode) or a transverse magnetic mode (TM mode)). The TEM mode is the dominant mode in a coaxial cavity and has no cutoff frequency (ω c ). In the TEM mode (as illustrated in  FIG. 1E ), because neither the electric field nor the magnetic field have any components in the z-direction (coordinate system illustrated in  FIG. 1D ), the electric and magnetic fields can be written, respectively, as: 
     
       
         
           
             H 
             = 
             
               
                 
                   H 
                   ϕ 
                 
                  
                 
                   
                     a 
                     ^ 
                   
                   ϕ 
                 
               
               = 
               
                 
                   
                     I 
                     0 
                   
                   
                     2 
                      
                     π 
                      
                     
                         
                     
                      
                     r 
                   
                 
                  
                 
                   cos 
                    
                   
                     ( 
                     
                       β 
                        
                       
                           
                       
                        
                       z 
                     
                     ) 
                   
                 
                  
                 
                     
                 
                  
                 
                   
                     a 
                     ^ 
                   
                   ϕ 
                 
               
             
           
         
       
       
         
           
             E 
             = 
             
               
                 
                   E 
                   r 
                 
                  
                 
                   
                     a 
                     ^ 
                   
                   r 
                 
               
               = 
               
                 
                   
                     V 
                     0 
                   
                   
                     2 
                      
                     π 
                      
                     
                         
                     
                      
                     r 
                   
                 
                  
                 
                   sin 
                    
                   
                     ( 
                     
                       β 
                        
                       
                           
                       
                        
                       z 
                     
                     ) 
                   
                 
                  
                 
                     
                 
                  
                 
                   
                     a 
                     ^ 
                   
                   r 
                 
               
             
           
         
       
     
     where H is a phasor representing the magnetic field vector, E is a phasor representing the electric field vector, â φ  represents a unit vector in the φ direction (labeled in  FIG. 1D ), â r  represents a unit vector in the r direction (labeled in  FIG. 1D ), β represents the wave number (canonically defined as 
     
       
         
           
             
               β 
               = 
               
                 
                   2 
                    
                   π 
                 
                 λ 
               
             
             , 
           
         
       
     
     where λ is the wavelength), I 0  represents the maximum current in the cavity, V 0  represents the maximum voltage in the cavity, and z represents a distance along the QWCCR structure  100  in the z direction (labeled in  FIG. 1D ). 
     In various implementations, various electromagnetic modes of the QWCCR structure  100  can be excited in order to achieve various electromagnetic properties. In some implementations, for instance, a single electromagnetic mode can be excited, whereas in alternate implementations, a plurality of electromagnetic modes can be excited. For example, in some implementations, the TE 01  mode (as illustrated in  FIG. 1F ) can be excited. 
     Quality factor (Q) can be defined as: 
     
       
         
           
             Q 
             = 
             
               
                 
                   
                     ω 
                     · 
                     U 
                   
                   
                     P 
                     L 
                   
                 
                 → 
                 U 
               
               = 
               
                 
                   
                     P 
                     L 
                   
                   · 
                   Q 
                 
                 ω 
               
             
           
         
       
     
     where ω is the angular frequency, U is the time-average energy, and P L  is the time-average power loss. Quality factor (Q) can be used to measure goodness of a resonator cavity. Other formulations of goodness measurement can also be used (for example, based on full-width, half-max (FWHM) or a 3 decibel (dB) bandwidth of cavity resonance). In some implementations, the quality factor (Q) can be maximized when the ratio of the inner radius of the outer conductor ‘b’ to the radius of the inner conductor ‘a’ is approximately equal to 4. However, it will be understood that many other ways to adjust and/or maximize quality factor (Q) are possible and contemplated in the present disclosure. 
     At resonance, the stored energy of the QWCCR structure  100  oscillates between electrical energy (U e ) (within the electric field) and magnetic energy (U m ) (within the magnetic field). Time-average stored energy in the QWCCR structure  100  can be calculated using the following: 
     
       
         
           
             U 
             = 
             
               
                 
                   U 
                   m 
                 
                 + 
                 
                   U 
                   e 
                 
               
               = 
               
                 
                   
                     1 
                     4 
                   
                    
                   
                     
                       ∫ 
                       vol 
                     
                      
                     
                       μ 
                        
                       
                         
                            
                           H 
                            
                         
                         2 
                       
                     
                   
                 
                 + 
                 
                   ɛ 
                    
                   
                     
                        
                       E 
                        
                     
                     2 
                   
                 
               
             
           
         
       
     
     where μ is magnetic permeability and E is dielectric permittivity. By inserting the values for electric field and magnetic field from above, and integrating over the entire volume of the QWCCR structure  100 , the following expression can be obtained: 
     
       
         
           
             U 
             = 
             
               
                 
                   
                     ln 
                      
                     
                       ( 
                       
                         b 
                         a 
                       
                       ) 
                     
                   
                   · 
                   λ 
                 
                 
                   64 
                    
                   π 
                 
               
                
               
                 ( 
                 
                   
                     μ 
                     · 
                     
                       I 
                       0 
                       2 
                     
                   
                   + 
                   
                     ɛ 
                     · 
                     
                       V 
                       0 
                       2 
                     
                   
                 
                 ) 
               
             
           
         
       
     
     where b represents the inner radius of the outer conductor  102  of the QWCCR structure  100  (as illustrated in  FIG. 1D ), a represents the radius of the inner conductor  104  of the QWCCR structure  100  (as illustrated in  FIG. 1D ), and represents the wavelength of the source (for example, AC source) used to excite the QWCCR structure  100 . Because the magnetic energy at maximum is the same as the electric energy at maximum, μ·I 0   2  can be replaced with ε·V 0   2 , thus resulting in: 
     
       
         
           
             U 
             = 
             
               
                 
                   
                     ln 
                      
                     
                       ( 
                       
                         b 
                         a 
                       
                       ) 
                     
                   
                   · 
                   λ 
                 
                 
                   32 
                    
                   π 
                 
               
                
               
                 ( 
                 
                   ɛ 
                   · 
                   
                     V 
                     0 
                     2 
                   
                 
                 ) 
               
             
           
         
       
     
     Now, by equating the two above expressions for U, the following relationship can be expressed: 
     
       
         
           
             
               
                 
                   P 
                   L 
                 
                 · 
                 Q 
               
               ω 
             
             = 
             
               
                 
                   
                     
                       
                         ln 
                          
                         
                           ( 
                           
                             b 
                             a 
                           
                           ) 
                         
                       
                       · 
                       λ 
                     
                     
                       32 
                        
                       π 
                     
                   
                    
                   
                     ( 
                     
                       ɛ 
                       · 
                       
                         V 
                         0 
                         2 
                       
                     
                     ) 
                   
                 
                 → 
                 
                   V 
                   0 
                 
               
               = 
               
                 
                   
                     32 
                      
                     
                       π 
                       · 
                       Q 
                       · 
                       
                         P 
                         L 
                       
                     
                   
                   
                     ω 
                     · 
                     ɛ 
                     · 
                     
                       ln 
                        
                       
                         ( 
                         
                           b 
                           a 
                         
                         ) 
                       
                     
                     · 
                     λ 
                   
                 
               
             
           
         
       
     
     Further, in recognizing that 
     
       
         
           
             
               ω 
               = 
               
                 
                   2 
                    
                   π 
                    
                   
                       
                   
                    
                   f 
                 
                 = 
                 
                   
                     2 
                      
                     π 
                      
                     
                         
                     
                      
                     c 
                   
                   λ 
                 
               
             
             , 
           
         
       
     
     where c is the speed of light; 
     
       
         
           
             
               
                 c 
                 = 
                 
                   
                     1 
                     
                       μ 
                       · 
                       ɛ 
                     
                   
                 
               
               ; 
               
                 
                   and 
                    
                   
                       
                   
                    
                   η 
                 
                 = 
                 
                   
                     μ 
                     ɛ 
                   
                 
               
             
             , 
           
         
       
     
     where η is the impedance of the dielectric between the inner conductor  104  and the outer conductor  102  of the QWCCR structure  100 , the following relationship for the peak potential (V 0 ) can be identified: 
     
       
         
           
             
               V 
               0 
             
             = 
             
               4 
                
               
                 
                   
                     η 
                     · 
                     Q 
                     · 
                     
                       P 
                       L 
                     
                   
                   
                     ln 
                      
                     
                       ( 
                       
                         b 
                         a 
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
     Given that electric field decays as the distance from the peak potential (V 0 ) increases, the largest value of electric field corresponding to the peak potential (V 0 ) occurs exactly at the surface of the inner conductor (for example, at radius a, as illustrated in  FIG. 1D ). Using the above equation for phasor electric field (E), the peak value of electric field (E a ) can be expressed as: 
     
       
         
           
             
               E 
               a 
             
             = 
             
               
                 
                   V 
                   0 
                 
                 
                   2 
                    
                   π 
                    
                   
                       
                   
                    
                   a 
                 
               
               = 
               
                 
                   2 
                   
                     π 
                      
                     
                         
                     
                      
                     a 
                   
                 
                  
                 
                   
                     
                       η 
                       · 
                       Q 
                       · 
                       
                         P 
                         L 
                       
                     
                     
                       ln 
                        
                       
                         ( 
                         
                           b 
                           a 
                         
                         ) 
                       
                     
                   
                 
               
             
           
         
       
     
     If the above peak value of electric field (E a ) meets or exceeds the above-described rms breakdown field (E b ), a dielectric breakdown can occur. For example, a dielectric breakdown of the air surrounding the tip of the QWCCR structure  100  can result in a plasma corona being excited. As indicated in the above equation for peak electric field (E a ), the smaller the radius a of the inner conductor  104 , the smaller the inner radius b of outer conductor  102 , the higher the quality factor (Q) of the QWCCR structure  100 , and the larger the time-average power loss (P L ), the more likely it is that breakdown can occur (for example, because the peak value of electric field (E a ) is larger). A larger excitation power can correspond to a larger time-average power loss (P L ) in the QWCCR structure  100 , for example. 
     The power loss (P L ) can include ohmic losses (P σ ) on conductive surfaces (for example, the surface of the outer conductor  102 , the surface of the inner conductor  104 , and/or the surface of the base conductor  110 , as illustrated in  FIG. 1C ), dielectric losses (P σ     e   ) in the dielectric  108 , and radiation losses (P rad ) from a radiating end of the QWCCR structure  100  (for example, the distal end of the QWCCR structure  100 ). Each of the conductors can have a corresponding surface resistance (R S ). The surface resistance (R S ) can be the same for one or more of the conductors if the corresponding conductors are made of the same conductive materials. The corresponding surface resistance for each conductor can be expressed as 
     
       
         
           
             
               
                 R 
                 S 
               
               = 
               
                 
                   
                     ω 
                     · 
                     
                       μ 
                       c 
                     
                   
                   
                     2 
                     · 
                     
                       σ 
                       c 
                     
                   
                 
               
             
             , 
           
         
       
     
     where μ c  is the magnetic permeability of the respective conductor and σ c  is the conductivity of the respective conductor. The power lost by each conductor can be calculated according to the following: 
     
       
         
           
             
               P 
               σ 
             
             = 
             
               
                 1 
                 2 
               
                
               
                 
                   ∫ 
                   A 
                 
                  
                 
                   
                     R 
                     S 
                   
                    
                   
                     
                        
                       
                         H 
                         // 
                       
                        
                     
                     2 
                   
                 
               
             
           
         
       
     
     where H //  is the magnetic field parallel to the surface of the conductor. Thus, the total power loss in all conductors can be represented by: 
     
       
         
           
             
               P 
               σ 
             
             = 
             
               
                 
                   P 
                   inner 
                 
                 + 
                 
                   P 
                   outer 
                 
                 + 
                 
                   P 
                   base 
                 
               
               = 
               
                 
                   
                     
                       R 
                       S 
                     
                     · 
                     
                       I 
                       0 
                       2 
                     
                   
                   
                     4 
                      
                     π 
                   
                 
                  
                 
                   [ 
                   
                     
                       λ 
                       
                         8 
                         · 
                         a 
                       
                     
                     + 
                     
                       λ 
                       
                         8 
                         · 
                         b 
                       
                     
                     + 
                     
                       ln 
                        
                       
                         ( 
                         
                           b 
                           a 
                         
                         ) 
                       
                     
                   
                   ] 
                 
               
             
           
         
       
     
     Further, if the dielectric  108  is an isotropic, low-loss dielectric, the dielectric  108  can be characterized by its dielectric constant (ε) and its loss tangent (tan(δ e )), where the loss tangent (tan(δ e )) represents conductivity and alternating molecular dipole losses. Using dielectric constant (E) and loss tangent (tan(δ e )), an effective dielectric conductivity (σ e ) can be approximately defined as: 
       σ e ≈ω·ε·tan(δ e )
 
     Based on the above, the power dissipated in the dielectric can be calculated according to the following: 
     
       
         
           
             
               P 
               
                 σ 
                 e 
               
             
             = 
             
               
                 
                   1 
                   2 
                 
                  
                 
                   
                     ∫ 
                     vol 
                   
                    
                   
                     
                       σ 
                       e 
                     
                      
                     
                       
                          
                         E 
                          
                       
                       2 
                     
                   
                 
               
               = 
               
                 
                   
                     
                       σ 
                       e 
                     
                     · 
                     η 
                     · 
                     
                       I 
                       0 
                       2 
                     
                   
                   
                     4 
                      
                     π 
                   
                 
                  
                 
                   ( 
                   
                     
                       
                         ln 
                          
                         
                           ( 
                           
                             b 
                             a 
                           
                           ) 
                         
                       
                       · 
                       λ 
                     
                     8 
                   
                   ) 
                 
               
             
           
         
       
     
     In order to combine all quality factors of the QWCCR structure  100  into a total internal quality factor (Q int ), the following relationship can be used: 
     
       
         
           
             
               Q 
               int 
             
             = 
             
               1 
               
                 ( 
                 
                   
                     Q 
                     inner 
                     
                       - 
                       1 
                     
                   
                   + 
                   
                     Q 
                     outer 
                     
                       - 
                       1 
                     
                   
                   + 
                   
                     Q 
                     base 
                     
                       - 
                       1 
                     
                   
                   + 
                   
                     Q 
                     
                       σ 
                       e 
                     
                     
                       - 
                       1 
                     
                   
                 
                 ) 
               
             
           
         
       
     
     where Q inner   −1 , Q outer   −1 , Q base   −1 , and Q σ     e     −1  are the quality factors of the inner conductor  104 , the outer conductor  102 , the base conductor  110 , and the dielectric  108 , respectively. Using the above expression for quality factor (Q) in terms of time-average power loss (P L ), angular frequency (ω), and time-average energy (U), the following expression for internal quality factor (Q int ) can be determined: 
     
       
         
           
             
               Q 
               int 
             
             = 
             
               
                 ( 
                 
                   
                     
                       
                         R 
                         S 
                       
                       
                         2 
                         · 
                         π 
                         · 
                         η 
                       
                     
                      
                     
                       [ 
                       
                         
                           
                             ( 
                             
                               
                                 b 
                                 a 
                               
                               + 
                               1 
                             
                             ) 
                           
                           
                             
                               b 
                               a 
                             
                             · 
                             
                               ln 
                                
                               
                                 ( 
                                 
                                   b 
                                   a 
                                 
                                 ) 
                               
                             
                           
                         
                         + 
                         8 
                       
                       ] 
                     
                   
                   + 
                   
                     tan 
                      
                     
                       ( 
                       
                         δ 
                         e 
                       
                       ) 
                     
                   
                 
                 ) 
               
               
                 - 
                 1 
               
             
           
         
       
     
     Based on the definitions of the individual quality factors above, the individual contribution of the outer conductor quality factor (Q outer ) to the internal quality factor (Q int ) can be greater than the individual contribution of the inner conductor quality factor (Q inner ). Thus, to increase the internal quality factor (Q int ), a material with higher conductivity can be used for the inner conductor  104  than is used for the outer conductor  102 . Further, the base conductor  110  quality factor (Q base ) and the dielectric  108  quality factor (Q σ     e   ) can be unaffected by the geometry of the QWCCR structure  100  (both in terms of 
     
       
         
           
             b 
             a 
           
         
       
     
     and in terms of 
     
       
         
           
             
               
                 b 
                 λ 
               
               ) 
             
             . 
           
         
       
     
     The QWCCR structure  100  can also radiate electromagnetic waves (for example, from a distal, non-closed end opposite the base conductor  110 ). For example, if the QWCCR structure  100  is being excited by an RF power source (for example, a signal generator oscillating at radio frequencies), the QWCCR structure  100  can radiate microwaves from a distal end (for example, from an aperture of the distal end) of the QWCCR structure  100 . Such radiation can lead to power losses, which can be approximated using admittance. Assuming that the transverse dimensions of the QWCCR structure  100  are significantly smaller than the wavelength (λ) being used to excite the QWCCR structure  100  (in other words, a&lt;&lt;λ and b&lt;&lt;λ), the real part (G r ) and imaginary part (B r ) of admittance can be represented by: 
     
       
         
           
             
               G 
               r 
             
             ≈ 
             
               
                 4 
                 · 
                 
                   π 
                   5 
                 
                 · 
                 
                   
                     [ 
                     
                       
                         
                           ( 
                           
                             
                               ( 
                               
                                 b 
                                 λ 
                               
                               ) 
                             
                             
                               ( 
                               
                                 b 
                                 a 
                               
                               ) 
                             
                           
                           ) 
                         
                         2 
                       
                       - 
                       
                         
                           ( 
                           
                             b 
                             λ 
                           
                           ) 
                         
                         2 
                       
                     
                     ] 
                   
                   2 
                 
               
               
                 3 
                 · 
                 η 
                 · 
                 
                   
                     ln 
                     2 
                   
                    
                   
                     ( 
                     
                       b 
                       a 
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             
               B 
               r 
             
             ≈ 
             
               
                 
                   16 
                   · 
                   π 
                   · 
                   
                     ( 
                     
                       
                         
                           ( 
                           
                             b 
                             λ 
                           
                           ) 
                         
                         
                           ( 
                           
                             b 
                             a 
                           
                           ) 
                         
                       
                       - 
                       
                         ( 
                         
                           b 
                           λ 
                         
                         ) 
                       
                     
                     ) 
                   
                 
                 
                   η 
                   · 
                   
                     
                       ln 
                       2 
                     
                      
                     
                       ( 
                       
                         b 
                         a 
                       
                       ) 
                     
                   
                 
               
               · 
               
                 [ 
                 
                   
                     E 
                     ( 
                     
                       
                         2 
                          
                         
                           
                             b 
                             a 
                           
                         
                       
                       
                         1 
                         + 
                         
                           b 
                           a 
                         
                       
                     
                     ) 
                   
                   - 
                   1 
                 
                 ] 
               
             
           
         
       
     
     where E(x) is the complete elliptical integral of the second kind. Namely: 
     
       
         
           
             
               E 
                
               
                 ( 
                 x 
                 ) 
               
             
             = 
             
               
                 ∫ 
                 0 
                 
                   π 
                   2 
                 
               
                
               
                 
                   
                     
                       1 
                       - 
                       
                         
                           x 
                           2 
                         
                         · 
                         
                           
                             sin 
                             2 
                           
                            
                           
                             ( 
                             θ 
                             ) 
                           
                         
                       
                     
                   
                   · 
                   d 
                 
                  
                 
                     
                 
                  
                 θ 
               
             
           
         
       
     
     Further, the line integral of the electric field from the inner conductor  104  to the outer conductor  102  can be used to determine the potential difference (V ab ) across the shunt admittance corresponding to the electromagnetic waves radiated. 
     
       
         
           
             
               
                 V 
                 ab 
               
                
               
                  
                 
                   
                     β 
                      
                     
                         
                     
                      
                     z 
                   
                   = 
                   
                     π 
                     4 
                   
                 
               
             
             = 
             
               
                 
                   ∫ 
                   
                     a 
                     → 
                     b 
                   
                 
                  
                 
                   E 
                   r 
                 
               
               = 
               
                 
                   
                     V 
                     0 
                   
                    
                   
                       
                   
                    
                   
                     ln 
                      
                     
                       ( 
                       
                         b 
                         a 
                       
                       ) 
                     
                   
                 
                 
                   2 
                    
                   π 
                 
               
             
           
         
       
     
     Using the potential difference (V ab ) across the shunt admittance corresponding to the electromagnetic waves radiated, the power going to radiation (P rad ) can be represented by: 
     
       
         
           
             
               P 
               rad 
             
             = 
             
               
                 
                   1 
                   2 
                 
                  
                 
                   G 
                   r 
                 
                  
                 
                   V 
                   ab 
                   2 
                 
               
               = 
               
                 
                   
                     V 
                     0 
                   
                    
                   
                     
                       
                         
                           
                             π 
                             3 
                           
                            
                           
                             ( 
                             
                               b 
                               λ 
                             
                             ) 
                           
                         
                         4 
                       
                        
                       
                         [ 
                         
                           
                             
                               ( 
                               
                                 b 
                                 a 
                               
                               ) 
                             
                             2 
                           
                           - 
                           1 
                         
                         ] 
                       
                     
                     2 
                   
                 
                 
                   6 
                    
                   
                     
                       η 
                        
                       
                         ( 
                         
                           b 
                           a 
                         
                         ) 
                       
                     
                     4 
                   
                 
               
             
           
         
       
     
     In addition, using the potential difference (V ab ) across the shunt admittance corresponding to the electromagnetic waves radiated, the energy stored during radiation (U rad ) can be represented by: 
     
       
         
           
             
               U 
               rad 
             
             = 
             
               
                 
                   1 
                   4 
                 
                  
                 
                   ( 
                   
                     
                       B 
                       r 
                     
                     ω 
                   
                   ) 
                 
                  
                 
                   V 
                   ab 
                   2 
                 
               
               = 
               
                 
                   
                     ɛ 
                      
                     
                         
                     
                      
                     
                       V 
                       0 
                       2 
                     
                      
                     
                       
                         λ 
                          
                         
                           ( 
                           
                             b 
                             λ 
                           
                           ) 
                         
                       
                        
                       
                         [ 
                         
                           
                             
                               ( 
                               
                                 b 
                                 a 
                               
                               ) 
                             
                             
                               - 
                               1 
                             
                           
                           + 
                           1 
                         
                         ] 
                       
                     
                   
                   
                     2 
                      
                     
                       π 
                       2 
                     
                   
                 
                 [ 
                 
                   
                     E 
                     ( 
                     
                       
                         2 
                          
                         
                           
                             b 
                             a 
                           
                         
                       
                       
                         1 
                         + 
                         
                           b 
                           a 
                         
                       
                     
                     ) 
                   
                   - 
                   1 
                 
                 ] 
               
             
           
         
       
     
     Based on the above, the overall quality factor of the QWCCR structure  100  (Q QWCCR ) can be described by the following: 
     
       
         
           
             
               Q 
               QWCCR 
             
             = 
             
               
                 ω 
                  
                 
                   ( 
                   U 
                   ) 
                 
               
               
                 
                   P 
                   inner 
                 
                 + 
                 
                   P 
                   outer 
                 
                 + 
                 
                   P 
                   base 
                 
                 + 
                 
                   P 
                   
                     σ 
                     e 
                   
                 
                 + 
                 
                   P 
                   rad 
                 
               
             
           
         
       
     
     If the energy stored during radiation (U rad ) is small compared with the energy stored in the interior of the QWCCR structure  100  (U), the radiation power (P rad ) can be treated similarly to the other losses. Further, the energy stored during radiation (U rad ) can be neglected in the above equation: 
     
       
         
           
             Q 
             ≈ 
             
               
                 ω 
                  
                 
                   ( 
                   U 
                   ) 
                 
               
               
                 
                   P 
                   inner 
                 
                 + 
                 
                   P 
                   outer 
                 
                 + 
                 
                   P 
                   base 
                 
                 + 
                 
                   P 
                   
                     σ 
                     e 
                   
                 
                 + 
                 
                   P 
                   rad 
                 
               
             
           
         
       
     
     Still further, the quality factor of the radiation component (Q rad ) can be described using the above relationship for quality factors: 
     
       
         
           
             
               Q 
               rad 
             
             = 
             
               
                 
                   ω 
                    
                   
                       
                   
                    
                   U 
                 
                 
                   P 
                   rad 
                 
               
               = 
               
                 
                   3 
                    
                   
                     
                       ( 
                       
                         b 
                         λ 
                       
                       ) 
                     
                     4 
                   
                    
                   
                       
                   
                    
                   
                     ln 
                      
                     
                       ( 
                       
                         b 
                         a 
                       
                       ) 
                     
                   
                 
                 
                   8 
                    
                   
                     
                       
                         
                           
                             π 
                             3 
                           
                            
                           
                             ( 
                             
                               b 
                               λ 
                             
                             ) 
                           
                         
                         4 
                       
                        
                       
                         [ 
                         
                           
                             
                               ( 
                               
                                 b 
                                 a 
                               
                               ) 
                             
                             2 
                           
                           - 
                           1 
                         
                         ] 
                       
                     
                     2 
                   
                 
               
             
           
         
       
     
     Even further, using the above-referenced quality factors, the total quality factor of the QWCCR structure  100  (Q QWCCR ) can be approximated by: 
     
       
         
           
             
               Q 
               QWCCR 
             
             ≈ 
             
               
                 ( 
                 
                   
                     
                       8 
                        
                       
                         
                           
                             
                               
                                 π 
                                 3 
                               
                                
                               
                                 ( 
                                 
                                   b 
                                   λ 
                                 
                                 ) 
                               
                             
                             4 
                           
                            
                           
                             [ 
                             
                               
                                 
                                   ( 
                                   
                                     b 
                                     a 
                                   
                                   ) 
                                 
                                 2 
                               
                               - 
                               1 
                             
                             ] 
                           
                         
                         2 
                       
                     
                     
                       3 
                        
                       
                         
                           ( 
                           
                             b 
                             a 
                           
                           ) 
                         
                         4 
                       
                        
                       
                         ln 
                          
                         
                           ( 
                           
                             b 
                             a 
                           
                           ) 
                         
                       
                     
                   
                   + 
                   
                     
                       
                         R 
                         S 
                       
                       
                         2 
                          
                         πη 
                       
                     
                      
                     
                       [ 
                       
                         
                           
                             ( 
                             
                               
                                 ( 
                                 
                                   b 
                                   a 
                                 
                                 ) 
                               
                               + 
                               1 
                             
                             ) 
                           
                           
                             
                               ( 
                               
                                 b 
                                 λ 
                               
                               ) 
                             
                              
                             
                               ln 
                                
                               
                                 ( 
                                 
                                   b 
                                   a 
                                 
                                 ) 
                               
                             
                           
                         
                         + 
                         8 
                       
                       ] 
                     
                   
                   + 
                   
                     tan 
                      
                     
                       ( 
                       
                         δ 
                         e 
                       
                       ) 
                     
                   
                 
                 ) 
               
               
                 - 
                 1 
               
             
           
         
       
     
     Based on the above relationships, it can be shown that one method of minimizing losses due to radiation of electromagnetic waves by the QWCCR structure  100  is to minimize the inner radius b of the outer conductor  102  with respect to the excitation wavelength (λ). Another way of minimizing losses due to radiation of electromagnetic waves is to select an inner radius b of the outer conductor  102  that is close in dimension to the radius a of the inner conductor  104 . 
     Various physical quantities and dimensions of the QWCCR structure  100  can be adjusted to modify performance of the QWCCR structure  100 . For example, physical quantities and dimensions can be modified to maximize and/or optimize the total quality factor of the QWCCR structure  100  (Q QWCCR ). In some implementations, different dielectrics can be inserted into the QWCCR structure  100 . In one implementation, the dielectric  108  can include a composite of multiple dielectric materials. For example, a half of the dielectric  108  near a proximal end of the QWCCR structure  100  can include alumina ceramic while a half of the dielectric  108  near a distal end of the QWCCR structure  100  can include air. The resonant frequency can be based on the dimensions and the fabrication materials of the QWCCR structure  100 . Hence, modification of the dielectric  108  can modify a resonant frequency of the QWCCR structure  100 . In some implementations, the resonant frequency can be 2.45 GHz based on the dimensions of the QWCCR structure  100 . In other implementations, the resonant frequency of the QWCCR structure  100  could be within an inclusive range between 1 GHz to 100 GHz. In still other implementations, the resonant frequency of the QWCCR structure  100  could be within an inclusive range of 100 MHz to 1 GHz or an inclusive range of 100 GHz to 300 GHz. However, other resonant frequencies are contemplated within the context of the present disclosure. 
     An RF power source exciting the QWCCR structure  100  can generate a standing electromagnetic wave within the QWCCR structure  100 . In some implementations, the resonant frequency of the QWCCR structure  100  can be designed to match the frequency of an RF power source that is exciting the QWCCR structure  100  (for example, to maximize power transferred to the QWCCR structure  100 ). For example, if a desired excitation frequency corresponds to a wavelength of λ 0 , dimensions of the QWCCR structure  100  can be modified such that the electrical length of the QWCCR structure  100  is an odd-integer multiple of quarter wavelengths (for example, ¼λ 0 , ¾λ 0 , 5/4λ 0 , 7/4λ 0 , 9/4λ 0 , 11/4λ 0 , 13/4λ 0 , etc.). The electrical length is a measure of the length of a resonator in terms of the wavelength of an electromagnetic wave used to excite the resonator. The QWCCR structure  100  can be designed for a given resonant frequency based on the dimensions of the QWCCR structure  100  (for example, adjusting dimensions of the inner conductor  104 , the outer conductor  102 , or the dielectric  108 ) or the materials of the QWCCR structure  100  (for example, adjusting materials of the inner conductor  104 , the outer conductor  102 , or the dielectric  108 ). 
     In other implementations, the resonant frequency of the QWCCR structure  100  can be designed or adjusted such that its resonant frequency does not match the frequency of an RF power source that is exciting the QWCCR structure  100  (for example, to reduce power transferred to the QWCCR structure  100 ). Analogously, the frequency of an RF power source can be de-tuned relative to the resonant frequency of a QWCCR structure  100  that is being excited by the RF power source. Additionally or alternatively, the physical quantities and dimensions of the QWCCR structure  100  can be modified to enhance the amount of energy radiated (for example, from the distal end) in the form of electromagnetic waves (for example, microwaves) from the QWCCR structure  100 . As an example, one or more elements of the QWCCR structure  100  could be movable or otherwise adjustable so as to modify the resonant properties of the QWCCR structure  100 . Enhancing the amount of energy radiated might be done at the expense of maximizing the electric field at a concentrator of the electrode  106  at the distal end of the inner conductor  104 . For example, some implementations can include slots or openings in the outer conductor  102  to increase the amount of radiated energy despite possibly reducing a quality factor of the QWCCR structure  100 . 
     In still other implementations, the physical quantities and dimensions of the QWCCR structure  100  can be designed in such a way so as to enhance the intensity of an electric field at a concentrator of the electrode  106  of the QWCCR structure  100 . Enhancing the electric field at a concentrator of the electrode  106  of the QWCCR structure  100  can result in an increase in plasma corona excitation (for example, an increase in dielectric breakdown near the concentrator), when the QWCCR structure  100  is excited with sufficiently high RF power/current. To increase electric field at a concentrator of the electrode  106  of the QWCCR structure  100 , a radius of the concentrator can be minimized (for example, configured as a very sharp structure, such as a tip). Additionally or alternatively, to increase the electric field at a tip of the QWCCR structure  100  (for example, thereby increasing the intensity and/or size of an excited plasma corona), the intrinsic impedance (η) of the dielectric  108  can be increased, the power used to excite the QWCCR structure  100  can be increased, and the total quality factor of the QWCCR structure  100  (Q QWCCR ) can be increased (for example, by increasing the volume energy storage (U) of the cavity or by minimizing the surface and radiation losses). 
     Further, the shunt capacitance (C) of a circular coaxial cavity (for example, in farads/meter, and neglecting fringing fields) can be expressed as follows: 
     
       
         
           
             C 
             = 
             
               
                 2 
                  
                 
                   πɛ 
                   0 
                 
                  
                 
                   ɛ 
                   r 
                 
               
               
                 ln 
                  
                 
                   ( 
                   
                     b 
                     a 
                   
                   ) 
                 
               
             
           
         
       
     
     where ε 0  represents the permittivity of free space, ε r  represents the relative dielectric constant of the dielectric  108  between the inner conductor  104  and the outer conductor  102 , b is the inner radius of the outer conductor  102 , and a is the radius of the inner conductor  104  (as illustrated in  FIG. 1D ). 
     Similarly, the shunt inductance (L) of a circular coaxial cavity (for example, in henrys/meter) can be expressed as follows: 
     
       
         
           
             L 
             = 
             
               
                 
                   
                     μ 
                     0 
                   
                    
                   
                     μ 
                     r 
                   
                 
                 
                   2 
                    
                   π 
                 
               
                
               
                 ln 
                  
                 
                   ( 
                   
                     b 
                     a 
                   
                   ) 
                 
               
             
           
         
       
     
     where μ 0  represents the permeability of free space, μ r  represents the relative permeability of the dielectric  108  between the inner conductor  104  and the outer conductor  102 , b is the inner radius of the outer conductor  102 , and a is the radius of the inner conductor  104  (as illustrated in  FIG. 1D ). 
     Based on the above, the complex impedance (Z) of a circular coaxial cavity (for example, in ohms, Ω) can be expressed as follows: 
     
       
         
           
             Z 
             = 
             
               
                 
                   R 
                   + 
                   
                     j 
                      
                     
                         
                     
                      
                     ω 
                      
                     
                         
                     
                      
                     L 
                   
                 
                 
                   G 
                   + 
                   
                     j 
                      
                     
                         
                     
                      
                     ω 
                      
                     
                         
                     
                      
                     C 
                   
                 
               
             
           
         
       
     
     where G represents the conductance per unit length of the dielectric between the inner conductor and the outer conductor, R represents the resistance per unit length of the QWCCR structure  100 , j represents the imaginary unit (for example, √{square root over (−1)}), ω represents the frequency at which the QWCCR structure  100  is being excited, L represents the shunt inductance of the QWCCR structure  100 , and C represents the shunt capacitance of the QWCCR structure  100 . 
     At very high frequencies (for example, GHz frequencies) the complex impedance (Z) can be approximated by: 
     
       
         
           
             
               Z 
               0 
             
             = 
             
               
                 L 
                 C 
               
             
           
         
       
     
     where Z 0  represents the characteristic impedance of the QWCCR structure  100  (in other words, the complex impedance (Z) of the QWCCR structure  100  at high frequencies). 
     As described above, the shunt inductance (L) and the shunt capacitance (C) of the QWCCR structure  100  depend on the relative permeability (μ r ) and the relative dielectric constant (ε r ), respectively, of the dielectric  108  between the inner conductor  104  and the outer conductor  102 . Thus, any modification to either the relative permeability (μ r ) or the relative dielectric constant (ε r ) of the dielectric  108  between the inner conductor  104  and the outer conductor  102  can result in a modification of the characteristic impedance (Z 0 ) of the QWCCR structure  100 . Such modifications to impedance can be measured using an impedance measurement device (for example, an oscilloscope, a spectrum analyzer, and/or an AC volt meter). 
     The above characteristic impedance (Z 0 ) represents an impedance calculated by neglecting fringing fields. In some applications and implementations, the fringing fields can be non-negligible (for example, the fringing fields can significantly impact the impedance of the QWCCR structure  100 ). Further, in such implementations, the composition of the materials surrounding the QWCCR structure  100  can affect the characteristic impedance (Z 0 ) of the QWCCR structure  100 . Measurements of such changes to characteristic impedance (Z 0 ) can provide information regarding the environment (for example, a combustion chamber) surrounding the QWCCR structure  100  (for example, the temperature, pressure, or atomic composition of the environment). A change in the characteristic impedance (Z 0 ) can coincide with a change in the cutoff frequency, resonant frequency, short-circuit condition, open-circuit condition, lumped-circuit model, mode distribution, etc. of the QWCCR structure  100 . 
       FIG. 1G  illustrates a quarter-wave resonance condition of the QWCCR structure  100 . The y-axis of the plot corresponds to a power of electromagnetic waves radiated from a distal end of the QWCCR structure  100  and the x-axis corresponds to an excitation frequency (w) (for example, from a radio-frequency power source that is electromagnetically coupled to the QWCCR structure  100 ) used to excite the QWCCR structure  100 . As illustrated, the shape of the curve can be a Lorentzian. 
     As illustrated in  FIG. 1G  the curve has a maximum power at a quarter-wave (λ/4) resonance. This resonance can correspond to excitation frequency (ω) that has an associated excitation wavelength that is four times the length of the QWCCR structure  100 . In other words, at the resonant frequency (ω 0 ) the QWCCR structure  100  is being excited by a standing wave, where one-quarter of the length of the standing wave is equal to the length of the QWCCR structure  100 . Although not illustrated, it is understood that the QWCCR structure  100  could experience additional resonances (for example, at odd-integer multiples of the resonant wavelength: ¼λ 0 , ¾λ 0 , 5/4λ 0 , 7/4λ 0 , 9/4λ 0 , 11/4λ 0 , 13/4λ 0 ,). Each of the additional resonances could look similar to the resonance illustrated in  FIG. 1G  (for example, could have a Lorentzian shape). 
     As illustrated, the power of the electromagnetic waves radiated from the distal end of the QWCCR structure  100  decreases exponentially the further the excitation frequency (ω) is from the resonant frequency (ω 0 ). However, the power of the electromagnetic waves is not necessarily zero as soon as you move away from resonance. Hence, it is understood that even when excited near the quarter-wave resonance condition (in other words, proximate to the quarter-wave resonance condition), rather than exactly at the resonance condition, the QWCCR structure  100  can still radiate electromagnetic waves with non-zero power and/or provide a plasma corona, depending on arrangement. 
     When the QWCCR structure  100  is being excited such that it provides a plasma corona proximate to the distal end (for example, at the electrode  106 ), a plot with a shape similar to that of  FIG. 1G  could be provided. In such a scenario, a plot of voltage at the electrode  106  versus excitation frequency (ω) could include a Gaussian shape, rather than a Lorentzian shape. In other words, the voltage at the electrode  106  may reach a peak when excited by a resonant frequency. The voltage at the electrode  106  may fall off exponentially according to a Gaussian shape as the excitation frequency moves away from the resonant frequency. It will be understood that the Gaussian and Lorentzian shapes presently described may be based on one or more characteristics of the QWCCR structure  100 , such as its shape, quality factor, bias conditions, or other factors. 
     It is understood that when the term “proximate” is used to describe a relationship between a wavelength of a signal (for example, a signal used to excite the QWCCR structure  100 ) and a resonant wavelength of a resonator (for example, the QWCCR structure  100 ), the term “proximate” can describe a difference in length. For example, if the wavelength of the signal is “proximate to an odd-integer multiple of one-quarter of the resonant wavelength,” the wavelength of the signal can be equal to, within 0.001% of, within 0.01% of, within 0.1% of, within 1.0% of, within 5.0% of, within 10.0% of, within 15.0% of, within 20.0% of, and/or within 25.0% of one-quarter of the resonant wavelength. Additionally or alternatively, if the wavelength of the signal is “proximate to an odd-integer multiple of one-quarter of the resonant wavelength,” the wavelength of the signal can be within 0.1 nm, within 1.0 nm, within 10.0 nm, within 0.1 micrometers, within 1.0 micrometers, within 10.0 micrometers, within 0.1 millimeters, within 1.0 millimeters, and/or within 1.0 centimeters of one-quarter of the resonant wavelength, depending on context (for example, depending on the resonant wavelength). Still further, if the wavelength of the signal is “proximate to an odd-integer multiple of one-quarter of the resonant wavelength,” the wavelength of the signal can be a multiple of one-quarter of the resonant wavelength that is an odd number plus or minus 0.5, an odd number plus or minus 0.1, an odd number plus or minus 0.01, an odd number plus or minus 0.001, and/or an odd number plus or minus 0.0001. 
     The quality factor of the QWCCR structure  100  (Q QWCCR ), described above, can be used to describe the width and/or the sharpness of the resonance (in other words, how quickly the power drops off as you excite the QWCCR structure  100  further and further from the resonance condition). For example, a square root of the quality factor can correspond to the voltage modification experienced at the electrode  106  of the QWCCR structure  100  when the QWCRR structure  100  is excited at the quarter-wave resonant condition. Additionally, the quality factor may be equal to the resonant frequency (ω 0 ) divided by full width at half maximum (FWHM). The FWHM is equal to the width of the curve in terms of frequency between the two points on the curve where the power is equal to 50% of the maximum power, as illustrated. The 50% power maximum point can also be referred to as the −3 decibel (dB) point, because it is the point at which the maximum voltage at the distal end of the QWCCR structure  100  decreases by 3 dB (or 29.29% for voltage) and the maximum power radiated by the QWCCR structure  100  decreases by 3 dB (or 50% for power). In various implementations, the FWHM of the QWCCR structure  100  could have various values. For example, the FWHM could be between 5 MHz and 10 MHz, between 10 MHz and 20 MHz, between 20 MHz and 40 MHz, between 40 MHz and 60 MHz, between 60 MHz and 80 MHz, or between 80 MHz and 100 MHz. Other FWHM values are also possible. 
     Further, the quality factor of the QWCCR structure  100  (Q QWCCR ) can also take various values in various implementations. For example, the quality factor could be between 25 and 50, between 50 and 75, between 75 and 100, between 100 and 125, between 125 and 150, between 150 and 175, between 175 and 200, between 200 and 300, between 300 and 400, between 400 and 500, between 500 and 600, between 600 and 700, between 700 and 800, between 800 and 900, between 900 and 1000, or between 1000 and 1100. Other quality factor values are also possible. 
     It is understood that, in alternate implementations, alternate structures (for example, alternate quarter-wave structures) can be used to emit electromagnetic radiation and/or excite plasma coronas (for example, other structures that concentrate electric field at specific locations using points or tips with sufficiently small radii). For example, other quarter-wave resonant structures, such as a coaxial-cavity resonator (sometimes referred to as a “coaxial resonator”), a dielectric resonator, a crystal resonator, a ceramic resonator, a surface-acoustic-wave resonator, an yttrium-iron-garnet resonator, a rectangular-waveguide cavity resonator, a parallel-plate resonator, a gap-coupled microstrip resonator, etc. can be used to excite a plasma corona. 
     Further, it is understood that wherever in this disclosure the terms “resonator,” “QWCCR,” “QWCCR structure,” and “coaxial resonator,” are used, any of the structures enumerated in the preceding paragraph could be used, assuming appropriate modifications are made to a corresponding system. In addition, the terms “resonator,” “QWCCR,” “QWCCR structure,” and “coaxial resonator” are not to be construed as inclusive or all-encompassing, but rather as examples of a particular structure that could be included in a particular implementation. Still further, when a “QWCCR structure” is described, the QWCCR structure can correspond to a coaxial resonator, a coaxial resonator with an additional base conductor, a coaxial resonator excited by a signal with a wavelength that corresponds to an odd-integer multiple of one-quarter (¼) of a length of the coaxial resonator, and other structures, in various implementations. 
     Additionally, whenever any “QWCCR,” “QWCCR structure,” “coaxial resonator,” “resonator,” or any of the specific resonators in this disclosure or in the claims are described as being “configured such that, when the resonator is excited by the radio-frequency power source with a signal having a wavelength proximate to an odd-integer multiple of one-quarter (¼) of the resonant wavelength, the resonator provides at least one of a plasma corona or electromagnetic waves,” some or all of the following are contemplated, depending on context. First, the corresponding resonator could be configured to provide a plasma corona when excited by the radio-frequency power source with a signal having a wavelength proximate to an odd-integer multiple of one-quarter (¼) of a resonant wavelength of the resonator. Second, the corresponding resonator could be configured to provide electromagnetic waves when excited by the radio-frequency power source with a signal having a wavelength proximate to an odd-integer multiple of one-quarter (¼) of a resonant wavelength of the resonator. Third, the corresponding resonator could be configured to provide, when excited by the radio-frequency power source with a signal having a wavelength proximate to an odd-integer multiple of one-quarter (¼) of a resonant wavelength of the resonator, both a plasma corona and electromagnetic waves. 
     V. Example Resonator Systems 
     In some implementations, the coaxial resonator  201  can be used as an antenna (for example, instead of or in addition to generating a plasma corona). As an antenna, the coaxial resonator  201  can radiate electromagnetic waves. The electromagnetic waves can consequently influence charged particles. As illustrated in the system  200  of  FIG. 2 , such electromagnetic waves can be radiated when the coaxial resonator  201  is excited by a signal generator  202 . For example, the signal generator  202  can be coupled to the coaxial resonator  201  in order to excite the coaxial resonator  201  (for example, to excite a plasma corona and to produce electromagnetic waves). Such a coupling can include inductive coupling (for example, using an induction feed loop), parallel capacitive coupling (for example, using a parallel plate capacitor), or non-parallel capacitive coupling (for example, using an electric field applied opposite a non-zero voltage conductor end). Further, the electrical distance between the signal generator  202  and the coaxial resonator  201  can be optimized (for example, minimized or adjusted based on wavelength of an RF signal) in order to minimize the amount of energy lost to heating and/or to maximize a quality factor. Further, in some implementations, the coaxial resonator  201  can radiate acoustic waves when excited (for example, at resonance). The acoustic waves produced can induce motion in nearby particles, for example. 
     The signal generator  202  can be a device that produces periodic waveforms (for example, using an oscillator circuit). In various implementations, the signal generator  202  can produce a sinusoidal waveform, a square waveform, a triangular waveform, a pulsed waveform, or a sawtooth waveform. Further, the signal generator  202  can produce waveforms with various frequencies (for example, frequencies between 1 Hz and 1 THz). The electromagnetic waves radiated from the coaxial resonator  201  can be based on the waveform produced by the signal generator  202 . For example, if the waveforms produced by the signal generator  202  are sinusoidal waves having frequencies between 300 MHz and 300 GHz (for example, between 1 GHz and 100 GHz), the electromagnetic waves radiated by coaxial resonator  201  can be microwaves. In various implementations, the signal generator  202  can, itself, be powered by an AC power source or a DC power source. 
     Depending on the signal used by the signal generator  202  to excite the coaxial resonator  201 , the coaxial resonator  201  can additionally excite one or more plasma coronas. For example, if a large enough voltage is used to excite the coaxial resonator  201 , a plasma corona can be excited at the distal end of the electrode  106  (for example, at a concentrator of the electrode  106 ). In some implementations, a voltage step-up device can be electrically coupled between the signal generator  202  and the coaxial resonator  201 . In such scenarios, the voltage step-up device can be operable to increase an amplitude of the AC voltage used to excite the coaxial resonator  201 . 
     In some implementations, the signal generator  202  can include one or more of the following: an internal power supply; an oscillator (for example, an RF oscillator, a surface acoustic wave resonator, or an yttrium-iron-garnet resonator); and an amplifier. The oscillator can generate a time-varying current and/or voltage (for example, using an oscillator circuit). The internal power supply can provide power to the oscillator. In some implementations, the internal power supply can include, for example, a DC battery (for example, a marine battery, an automotive battery, an aircraft battery, etc.), an alternator, a generator, a solar cell, and/or a fuel cell. In other implementations, the internal power supply can include a rectified AC power supply (for example, an electrical connection to a wall socket passed through a rectifier). The amplifier can magnify the power that is output by the oscillator (for example, to provide sufficient power to the coaxial resonator  201  to excite plasma coronas). For example, the amplifier can multiply the current and/or the voltage output by the oscillator. Additionally, in some implementations, the signal generator  202  can include a dedicated controller that executes instructions to control the signal generator  202 . 
     Additionally or alternatively, as illustrated in the system  300  of  FIG. 3A , the coaxial resonator  201  can be electrically coupled (for example, using a wired connection or wirelessly) to a DC power source  302 . Further, in some implementations, an RF cancellation resonator (not shown) can prevent RF power (for example, from the signal generator  202 ) from reaching, and potentially interfering with, the DC power source  302 . The RF cancellation resonator can include resistive elements, lumped-element inductors, and/or a frequency cancellation circuit. 
     In some implementations, the DC power source  302  can include a dedicated controller that executes instructions to control the DC power source  302 . The DC power source  302  can provide a bias signal (for example, corresponding to a DC bias condition) for the coaxial resonator  201 . For example, a DC voltage difference between the inner conductor  104  and the outer conductor  102  of the coaxial resonator  201  in  FIG. 3A  can be established by the DC power source  302  by increasing the DC voltage of the inner conductor  104  and/or decreasing the DC voltage of the outer conductor  102  (given the orientation of the positive terminal and negative terminal of the DC power source  302 ). In other implementations, a DC voltage difference between the inner conductor  104  and the outer conductor  102  can be established by the DC power source  302  by decreasing the DC voltage of the inner conductor  104  and/or increasing the DC voltage of the outer conductor  102  (if the orientation of the positive terminal and negative terminal of the DC power source  302  in  FIG. 3A  were reversed). The bias signal (for example, the voltage of the bias signal and/or the current of the bias signal) output by the DC power source  302  can be adjustable. 
     By providing the coaxial resonator  201  with a bias signal, an increased voltage can be presented at a concentrator of the electrode  106 , thereby yielding an increased electric field at the concentrator of the electrode  106 . The total electric field at the concentrator can thus be a sum of the electric field from the bias signal of the DC power source  302  and the electric field from the signal generator  202  exciting the coaxial resonator  201  at a resonance condition (for example, exciting the coaxial resonator  201  at a quarter-wave resonance condition so the electric field of the signal from the signal generator  202  reaches a maximum at the distal end of the coaxial resonator  201 ). Because of this increased total electric field, an excitation of a plasma corona near the concentrator can be more probable. 
     As an alternative, rather than using a bias signal, the signal generator  202  can simply excite the coaxial resonator  201  using a higher voltage. However, this might use considerably more power than providing a bias signal and augmenting that bias signal with an AC voltage oscillation. 
     In some implementations, the DC power source  302  can be switchable (for example, can generate the bias signal when switched on and not generate the bias signal when switched off). As such, the DC power source  302  can be switched on when a plasma corona output is desired from coaxial resonator  201  and can be switched off when a plasma corona output is not desired from coaxial resonator  201 . For example, the DC power source  302  can be switched on during an ignition sequence (for example, a sequence where fuel is being ignited within a combustion chamber to begin combustion), but switched off during a reforming sequence (for example, a sequence in which electromagnetic radiation is being used to chemically modify fuel). Further, in some implementations, the electric field at the concentrator of the electrode  106  used to initiate the plasma corona can be larger than the electric field at the concentrator used to sustain the plasma corona. Hence, in some implementations, the DC power source  302  can be switched on in order to excite the plasma corona, but switched off while the plasma corona is maintained by the signal from the signal generator  202 . 
     In alternate implementations, the system  200  of  FIG. 2  and/or the system  300  of  FIG. 3A  can include a plurality of coaxial resonators  201 . If the system  200  of  FIG. 2  includes a plurality of coaxial resonators  201 , the plurality of coaxial resonators  201  can each be electrically coupled to the same signal generator (for example, such that each of the plurality of coaxial resonators  201  is excited by the same signal), can each be electrically coupled to a respective signal generator (for example, such that each of the plurality of coaxial resonators  201  is independently excited, thereby allowing for unique excitation frequency, power, etc. for each of the plurality of coaxial resonators  201 ), or one set of the plurality of coaxial resonators  201  can be connected to a common signal generator and another set of the plurality of coaxial resonators  201  can be connected to one or more other signal generators, which could be similar or different from signal generator  202 . In implementations of the system  300  that include a plurality of coaxial resonators  201 , each of the coaxial resonators  201  can be attached to a respective DC power source (for example, multiple instances of DC power source  302 ) and a common signal generator (for example, such that a bias signal can be independently switchable and/or adjustable for each coaxial resonator  201 , while maintaining a common excitation waveform across all coaxial resonators  201  in the system  300 ), different signal generators and a common DC power source (for example, such that a bias signal can be jointly switchable across all coaxial resonators  201  in the system  300 , while maintaining an independent excitation waveform for each coaxial resonator  201 ), or different DC power sources and different signal generators (for example, such that the bias signal is independently switchable for each coaxial resonator  201 , while maintaining an independent excitation waveform for each coaxial resonator  201 ). 
       FIG. 3B  illustrates a circuit diagram of the system  300  of  FIG. 3A , which includes the signal generator  202 , the DC power source  302 , and the coaxial resonator  201  (illustrated in vertical cross-section). As illustrated, similar to the QWCCR structure  100 , the coaxial resonator  201  includes an outer conductor  322 , an inner conductor  324  (including an electrode  326 ), and a dielectric  328 . In addition, when the DC power source  302  is switched off, the circuit illustrated in  FIG. 3B  may not be an open-circuit. Instead, the signal generator  202  can simply be shorted to the inner conductor  324  when the DC power source  302  is switched off. As illustrated, the outer conductor  322  can be electrically coupled to ground. Further, the signal generator  202  and the DC power source  302  can be connected in series, with their negative terminals connected to ground. The positive terminals of the signal generator  202  and the DC power source  302  can be electrically coupled to the inner conductor  324 . Consequently, the electrode  326  can also be electrically coupled to the positive terminals through an electrical coupling between the inner conductor  324  and the electrode  326 . 
     In alternate implementations, the negative terminals of the signal generator  202  and the DC power source  302  can instead be connected to the inner conductor  324  and the positive terminals can be connected to the outer conductor  322 . In this way, the signal generator  202  and the DC power source  302  can instead apply a negative voltage (relative to ground) to the electrode  326  and/or inner conductor  324 , rather than a positive voltage (relative to ground). Further, in some implementations, the negative terminals of the DC power source  302  and the signal generator  202  and/or the inner conductor  324  might not be grounded. 
     As stated above, the DC power source  302  can be switchable. In this way a positive bias signal or a negative bias signal can be selectively applied to the inner conductor  324  and/or the electrode  326  relative to the outer conductor  322 . When the DC power source  302  is switched on, a bias condition can be present, and when the DC power source  302  is switched off, a bias condition might not be present. A bias signal provided by the DC power source  302  can increase the electric potential, and thus the electric field, at the electrode  326  (for example, at a concentrator of the electrode  106 , such as a tip, edge, or blade). By increasing the electric field at the electrode  326 , dielectric breakdown and potentially plasma excitation can be more prevalent. Thus, by switching on the DC power source  302 , the amount of plasma excited at a plasma corona can be enhanced. 
     In some implementations, the voltage of the DC power source  302  can range from +1 kV to +100 kV. Alternatively, the voltage of the DC power source  302  can range from −1 kV to −100 kV. Even further, the voltage of the DC power source  302  can be adjustable in some implementations. Furthermore, the voltage of the DC power source  302  can be pulsed, ramped, etc. For example, the voltage can be adjusted by a controller connected to the DC power source  302 . In such implementations, the voltage of the DC power source  302  can be adjusted by the controller according to sensor data (for example, sensor data corresponding to temperature, pressure, fuel composition, etc.). 
     As illustrated in  FIG. 4A , an example system  400  can include a controller  402 . In various implementations, the controller  402  can include a variety of components. For example, the controller  402  can include a desktop computing device, a laptop computing device, a server computing device (for example, a cloud server), a mobile computing device, a microcontroller (for example, embedded within a control system of a power-generation turbine, an automobile, or an aircraft), and/or a microprocessor. As illustrated, the controller  402  can be communicatively coupled to the signal generator  202 , the DC power source  302 , an impedance sensor  404 , and one or more other sensors  406 . Through the communicative couplings, the controller  402  can receive signals/data from various components of the system  400  and control/provide data to various components of the system  400 . For example, the controller  402  can switch the DC power source  302  in order to provide a time-modulated bias signal to the coaxial resonator  201  (for example, during an ignition sequence within a combustion chamber adjacent to, coupled to, or surrounding the coaxial resonator  201 ). 
     Further, a “communicative coupling,” as presently disclosed, is understood to cover a broad variety of connections between components, based on context. “Communicative couplings” can include direct and/or indirect couplings between components in various implementations. In some implementations, for example, a “communicative coupling” can include an electrical coupling between two (or more) components (for example, a physical connection between the two (or more) components that allows for electrical interaction, such as a direct wired connection used to read a sensor value from a sensor). Additionally or alternatively, a “communicative coupling” can include an electromagnetic coupling between two (or more) components (for example, a connection between the two (or more) components that allows for electromagnetic interaction, such as a wireless interaction based on optical coupling, inductive coupling, capacitive coupling, or coupling though evanescent electric and/or magnetic fields). In addition, a “communicative coupling” can include a connection (for example, over the public internet) in which one or more of the coupled components can transmit signals/data to and/or receive signals/data from one or more of the other coupled components. In various implementations, the “communicative coupling” can be unidirectional (in other words, one component sends signals and another component receives the signals) or bidirectional (in other words, both components send and receive signals). Other directionality combinations are also possible for communicative couplings involving more than two components. One example of a communicative coupling could be the controller  402  communicatively coupled to the coaxial resonator  201 , where the controller  402  reads a voltage and/or current value from the resonator directly. Another example of a communicative coupling could be the controller  402  communicating with a remote server over the public Internet to access a look-up table. Additional communicative couplings are also contemplated in the present disclosure. 
     In some implementations, the controller  402  can control one or more settings of the signal generator  202  (for example, waveform shape, output frequency, output power amplitude, output current amplitude, or output voltage amplitude) or the DC power source  302  (for example, switching on or off or adjusting the level of the bias signal). For example, the controller  402  can control the bias signal of the DC power source  302  (for example, a voltage of the bias signal) based on a calculated voltage used to excite a plasma corona (for example, based on conditions within a combustion chamber). The calculated voltage can account for the voltage amplitude being output by the signal generator  202 , in some implementations. The calculated voltage can ensure, for example, that the bias signal has a small effect on any standing electromagnetic wave formed within the coaxial resonator  201  based on an output of the signal generator  202 . 
     The controller  402  can be located nearby the signal generator  202 , the DC power source  302 , the impedance sensor  404 , and/or the one or more other sensors  406 . For example, the controller  402  may be connected by a wire connection to the signal generator  202 , the DC power source  302 , the impedance sensor  404 , and/or the one or more other sensors  406 . Alternatively, the controller  402  can be remotely located relative to the signal generator  202 , the DC power source  302 , the impedance sensor  404 , and/or the one or more other sensors  406 . For example, the controller  402  can communicate with the signal generator  202 , the DC power source  302 , the impedance sensor  404 , and/or the one or more other sensors  406  over BLUETOOTH®, over BLUETOOTH LOW ENERGY (BLE)®, over the public Internet, over WIFI® (IEEE 802.11 standards), over a wireless wide area network (WWAN), etc. 
     In some implementations, the controller  402  can be communicatively coupled to fewer components within the system  400  (for example, only communicatively coupled to the DC power source  302 ). Further, in implementations that include fewer components than illustrated in the system  400  (for example, in implementations, having only the coaxial resonator  201 , the signal generator  202 , and the controller  402 ), the controller  402  can interact with fewer components of the system  400 . For instance, the controller can interact only with the signal generator  202 . 
     The impedance sensor  404  can be connected to the coaxial resonator  201  (for example, one lead to the inner conductor  324  of the coaxial resonator  201  and one lead to the outer conductor  322  of the coaxial resonator  201 ) to measure an impedance of the coaxial resonator  201 . In some implementations, the impedance sensor  404  can include an oscilloscope, a spectrum analyzer, and/or an AC volt meter. The impedance measured by the impedance sensor  404  can be transmitted to the controller  402  (for example, as a digital signal or an analog signal). In some implementations, the impedance sensor  404  can be integrated with the controller  402  or connected to the controller  402  through a printed circuit board (PCB) or other mechanism. The impedance data can be used by the controller  402  to perform calculations and to adjust control of the signal generator  202  and/or the DC power source  302 . 
     Similarly, the other sensors  406  can also transmit data to the controller  402 . Analogous to the impedance sensor  404 , in some implementations, the other sensors  406  can be integrated with the controller  402  or connected to the controller  402  through a PCB or other mechanism. The other sensors  406  can include a variety of sensors, such as one or more of: a fuel gauge, a tachometer (for example, to measure revolutions per minute (RPM)), an altimeter, a barometer, a thermometer, a sensor that measures fuel composition, a gas chromatograph, a sensor measuring fuel-to-air ratio in a given fuel/air mixture, an anemometer, a torque sensor, a vibrometer, an accelerometer, or a load cell. 
     In some implementations, the controller  402  can be powered by the DC power source  302 . In other implementations, the controller  402  can be independently powered by a separate DC power source or an AC power source (for example, rectified within the controller  402 ). 
     As an example, a possible implementation of the controller  402  is illustrated in  FIG. 4B . As illustrated, the controller  402  can include a processor  452 , a memory  454 , and a network interface  456 . The processor  452 , the memory  454 , and the network interface  456  can be communicatively coupled over a system bus  450 . The system bus  450 , in some implementations, can be defined within a PCB. 
     The processor  452  can include one or more central processing units (CPUs), such as one or more general purpose processors and/or one or more dedicated processors (for example, application-specific integrated circuits (ASICs), digital signal processors (DSPs), or network processors). The processor  452  can be configured to execute instructions (for example, instructions stored within the memory  454 ) to perform various actions. Rather than a processor  452 , some implementations can include hardware logic (for example, one or more resistor-inductor-capacitor (RLC) circuits, flip-flops, latches, etc.) that performs actions (for example, based on the inputs from the impedance sensor  404  or the other sensors  406 ). 
     The memory  454  can store instructions that are executable by the processor  452  to carry out the various methods, processes, or operations presently disclosed. Alternatively, the method, processes, or operations can be defined by hardware, firmware, or any combination of hardware, firmware, or software. Further, the memory  454  can store data related to the signal generator  202  (for example, control signals), the DC power source  302  (for example, switching signals), the impedance sensor  404  (for example, look-up tables related to changes in impedance and/or a characteristic impedance of the coaxial resonator  201  based on certain environmental factors), and/or the other sensors  406  (for example, a look-up table of typical wind speeds based on elevation). 
     The memory  454  can include non-volatile memory. For example, the memory  454  can include a read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), a hard drive (for example, hard disk), and/or a solid-state drive (SSD). Additionally or alternatively, the memory  454  can include volatile memory. For example, the memory  454  can include a random-access memory (RAM), flash memory, dynamic random-access memory (DRAM), and/or static random-access memory (SRAM). In some implementations, the memory  454  can be partially or wholly integrated with the processor  452 . 
     The network interface  456  can enable the controller  402  to communicate with the other components of the system  400  and/or with outside computing device(s). The network interface  456  can include one or more ports (for example, serial ports) and/or an independent network interface controller (for example, an Ethernet controller). In some implementations, the network interface  456  can be communicatively coupled to the impedance sensor  404  or one or more of the other sensors  406 . Additionally or alternatively, the network interface  456  can be communicatively coupled to the signal generator  202 , the DC power source  302 , or an outside computing device (for example, a user device). Communicative couplings between the network interface  456  and other components can be wireless (for example, over WIFI®, BLUETOOTH®, BLUETOOTH LOW ENERGY (BLE)®, or a WWAN) or wireline (for example, over token ring, t-carrier connection, Ethernet, a trace in a PCB, or a wire connection). 
     In some implementations, the controller  402  can also include a user-input device (not shown). For example, the user-input device can include a keyboard, a mouse, a touch screen, etc. Further, in some implementations, the controller  402  can include a display or other user-feedback device (for example, one or more status lights, a speaker, a printer, etc.) (not shown). That status of the controller  402  can alternatively be provided to a user device through the network interface  456 . For example, a user device such as a personal computer or a mobile computing device can communicate with the controller  402  through the network interface  456  to retrieve the values of one or more of the other sensors  406  (for example, to be displayed on a display of the user device). 
     VI. Resonators with Fuel Injection 
     As illustrated in  FIG. 5 , in some implementations, the QWCCR structure  100  (or the coaxial resonator  201 ) can be attached to a fuel tank  502 . The fuel tank  502  can provide a fuel source for a combustion chamber or other environment, for example. The fuel tank  502  can contain or be connected to a fuel pump  504  through a fuel-supply line (for example, a hose or a pipe). The fuel pump  504  can transfer fuel from the fuel tank  502  into the fuel-supply line and propel the fuel through a fuel conduit  506  defined by or disposed within the inner conductor  104  of the QWCCR structure  100 . For example, the fuel pump  504  can include a mechanical pump (for example, gear pump, rotary vane pump, diaphragm pump, screw pump, peristaltic pump) or an electrical pump. In some implementations, the fuel tank  502  can include various sensors (for example, a pressure sensor, a temperature sensor, or a fuel-level sensor). Such sensors can be electrically connected to the controller  402  in order to provide data regarding the status of the fuel tank  502  to the controller  402 , for example. Additionally or alternatively, the fuel pump  504  can be connected to the controller  402 . Through such a connection, the controller  402  could control the fuel pump  504  (for example, to switch the fuel pump on and off, set a fuel injection rate, etc.). 
     In some implementations, the fuel conduit  506  can inject fuel (for example, into a combustion chamber) at one or more outlets  508  defined within the electrode  106  (for example, within a concentrator of the electrode  106 ). By conveying fuel through the fuel conduit  506  and out one or more outlets  508 , fuel can be introduced proximate to a source of ignition energy (for example, proximate to a plasma corona generated near a concentrator of the electrode  106 ), which can allow for efficient combustion and ignition. In alternate implementations, one or more outlets can be defined with other locations of the fuel conduit  506  (for example, so as not to interfere with the electric field at the concentrator of the electrode  106 ). 
     In some implementations, the fuel conduit  506  can act, at least in part, as a Faraday cage (for example, by encapsulating the fuel within a conductor that makes up the fuel conduit  506 ) to prevent electromagnetic radiation in the QWCCR structure  100  from interacting with the fuel while the fuel is transiting the fuel conduit  506 . In other structures, the fuel conduit  506  can allow electromagnetic radiation to interact with (for example, reform) the fuel within the fuel conduit  506 . 
     In some implementations, the QWCCR structure  100  can include multiple fuel conduits  506  (for example, multiple fuel conduits running from the proximal end of the QWCCR structure  100  to the distal end of the QWCCR structure  100 ). Additionally or alternatively, one or more fuel conduits  506  can be positioned within the dielectric  108  or within the outer conductor  102 . As described above, the outlet(s)  508  of the fuel conduit(s)  506  can be oriented in such as a way as to expel fuel toward concentrators (for example, tips, edges, or points) of one or more electrodes  106  (for example, toward regions where plasma coronas are likely to be excited). 
     VII. Additional Resonator Implementations 
       FIG. 6  illustrates a cross-sectional view of an example alternative coaxial resonator  600  connected to a DC power source through an additional resonator assembly acting as an RF attenuator, in accordance with example implementations. The coaxial resonator  600  is an assembly of two quarter-wave coaxial cavity resonators that are coupled together. More specifically, the coaxial resonator  600  includes a first resonator  602  and a second resonator  604  electrically coupled in a series arrangement along a longitudinal axis  606 . In some implementations, the coaxial resonator  600  includes a DC bias condition established at a node of the voltage standing wave (for example, between quarter-wave segments). In such implementations, there may be no impedance mismatch. Because there is no impedance mismatch, the diameters of the inner conductor and the outer conductor of the first resonator  602  can be different than the diameters of the inner conductor and the outer conductor of the second resonator  604 , respectively, without impacting the quality factor (Q). In such a way, the DC bias condition might not affect or interact with the AC signal coming from a signal generator. 
     The first resonator  602  and the second resonator  604  are defined by a common outer conductor wall structure  608 . The outer conductor wall structure  608  includes a first cylindrical wall  610  and a second cylindrical wall  612  centered on the longitudinal axis  606 . The first cylindrical wall  610  is constructed of a conducting material and surrounds a first cylindrical cavity  614  centered on the longitudinal axis  606 . The first cylindrical cavity  614  is filled with a dielectric  616  having a relative dielectric constant approximately equal to four (ε r ≈4), for example. 
     In the example implementation of  FIG. 6 , the first resonator  602  and the second resonator  604  adjoin one another in a connection plane  618  that is perpendicular to the longitudinal axis  606 . In other examples, the connection plane  618  might not be perpendicular to the longitudinal axis  606 , and can instead be designed with a different configuration that maintains constant impedance between the first resonator  602  and the second resonator  604 . 
     The second cylindrical wall  612  is constructed of a conducting material and surrounds a second cylindrical cavity  620  that is also centered on the longitudinal axis  606 . The second cylindrical cavity  620  is coaxial with the first cylindrical cavity  614 , but can have a greater physical length. The second cylindrical wall  612  provides the second cylindrical cavity  620  with a distal end  622  spaced along the longitudinal axis  606  from a proximal end  624  of the second cylindrical cavity  620 . 
     A center conductor structure  626  is supported within the conductor wall structure  608  of the coaxial resonator  600  by the dielectric  616 . The center conductor structure  626  includes a first center conductor  628 , a second center conductor  630 , and a radial conductor  632 . 
     The first center conductor  628  reaches within the first cylindrical cavity  614  along the longitudinal axis  606 . In the example implementation shown in  FIG. 6 , the first center conductor  628  has a proximal end  634  adjacent a proximal end  636  of the first cylindrical cavity  614 , and has a distal end  638  adjacent the distal end  624  of the first cylindrical cavity  614 . The radial conductor  632  projects radially from a location adjacent the distal end  638  of the first center conductor  628 , across the first cylindrical cavity  614 , and outward through an aperture  640 . 
     The second center conductor  630  has a proximal end  642  at the distal end  638  of the first center conductor  628 . The second center conductor  630  projects along the longitudinal axis  606  to a distal end  644  configured as an electrode tip located at or in close proximity to the distal end  622  of the second cylindrical cavity  620 . 
     To reduce any mismatch in impedances between the first resonator  602  and the second resonator  604 , the relative radial thicknesses between both the cylindrical walls  610 ,  612  and the respective center conductors  628 ,  630  are defined in relation to the relative dielectric constant of the dielectric  616  and the dielectric constant of the air or gas that fills the second cylindrical cavity  620 . In the example implementation of  FIG. 6 , the physical length of the second center conductor  630  along the longitudinal axis  606  is approximately twice the physical length of the first center conductor  628  along the longitudinal axis  606 . However, based at least in part on the dielectric  616  having a relative dielectric constant approximately equal to four, the electrical lengths of the two center conductors  628  and  630  are approximately equal. 
     In example implementations, any gaps between any of the center conductors  628 ,  630  and any outer conductor could be filled with a dielectric and/or the gap (for example, the second cylindrical cavity  620 ) could be large enough to reduce arcing (in other words, large enough such that the electric field is not of sufficient intensity to result in a dielectric breakdown of air or the intervening dielectric). As further shown in  FIG. 6 , the dielectric  616  fills the first cylindrical cavity  614  around the first center conductor  628  and the radial conductor  632 . 
     In the illustrated example, a DC power source  646  is connected to the center conductor structure  626  through the radial conductor  632  connected adjacent to a virtual short-circuit point of the DC power source  646 . 
     An RF control component, specifically, an RF frequency cancellation resonator assembly  648  is disposed between the radial conductor  632  and the DC power source  646  to restrict RF power from reaching the DC power source  646 . The RF frequency cancellation resonator assembly  648  is an additional resonator assembly having a center conductor  650 . The center conductor  650  has a first portion  652  and a second portion  654 , each of which has the same electrical length “X” illustrated in  FIG. 6  (and the same electrical length as the first center conductor  628  and the second center conductor  630 ). 
     In an example implementation, the electrical length “X” depicted in  FIG. 6  can be sized such that the center conductor  650  is an odd-integer multiple of half wavelengths (for example, ¼λ 0 , ¾λ 0 , 5/4λ 0 , 7/4λ 0 , 9/4λ 0 , 11/4λ 0 , 13/4λ 0 , etc.) out of phase (in other words, 180° out of phase) with the outer conducting wall  656  and the outer conducting wall  658 , simultaneously, where λ 0  is the resonant wavelength, and where the resonant wavelength λ 0  is inversely related to the frequency of the RF power. In alternative implementations, a similar “folded” structure to the electrical length “X” could be located within the cylindrical cavity  614  to achieve a similar phase shift between the inner conductor and the outer conductor. 
     The RF frequency cancellation resonator assembly  648  also has a short outer conducting wall  656  and a long outer conducting wall  658 . The short outer conducting wall  656  has first and second ends on opposite ends of the RF frequency cancellation resonator assembly  648 . The long outer conducting wall  658  also has first and second ends on opposite ends of the RF frequency cancellation resonator assembly  648 . The first and second ends of the short outer conducting wall  656  are each on the opposite side of the RF frequency cancellation resonator assembly  648  from the corresponding first and second ends of the long outer conducting wall  658 . 
     In an example implementation, the difference in electrical length between the short outer conducting wall  656  and the long outer conducting wall  658  is substantially equal to the combined electrical length of the first portion  652  and the second portion  654 . In this example, the combined electrical length of the first portion  652  and the second portion  654  is substantially equal to twice the electrical length of the first center conductor  628 . 
     In an example implementation, the short outer conducting wall  656  and the long outer conducting wall  658  surround a cavity  660  filled with a dielectric. In operation, with this example implementation, electric current running along the outer conductor of the RF frequency cancellation resonator assembly  648  primarily follows the shortest path and run along the short outer conducting wall  656 . Accordingly, electric current on the outer conductor of the RF frequency cancellation resonator assembly  648  travels two fewer quarter-wavelengths than current running along the center conductor  650  of the RF frequency cancellation resonator assembly  648 . 
     In examples, the RF frequency cancellation resonator assembly  648  can also have an internal conducting ground plane  662  disposed within the cavity  660  and between the first portion  652  and the second portion  654  of the center conductor  650 . Based on the geometry of the cancellation resonator assembly  648 , this configuration provides a frequency cancellation circuit connected between the DC power source  646  and the radial conductor  632 . 
     Further, in examples, the RF frequency cancellation resonator assembly  648  is configured to shift a voltage supply of RF energy 180 degrees out of phase relative to the ground plane  662  of the coaxial resonator  600  due to the difference in electrical length between the short outer conducting wall  656  and the center conductor  650  of the RF frequency cancellation resonator assembly  648 . 
       FIG. 7  illustrates a cross-sectional view of another example alternative coaxial resonator  700  connected to a DC power source through an additional resonator assembly acting as an RF attenuator, in accordance with an example implementation. The coaxial resonator  700  includes a first resonator portion  702  and a second resonator portion  704  electrically coupled in a series arrangement along a longitudinal axis  706 . 
     As depicted in  FIG. 7 , the first resonator portion  702  and the second resonator portion  704  are defined by a common outer conductor wall structure  708 . The wall structure  708  includes a first cylindrical wall portion  710  and a second cylindrical wall portion  712  centered on the longitudinal axis  706 . The first cylindrical wall portion  710  is constructed of a conducting material and surrounds a first cylindrical cavity  714  centered on the longitudinal axis  706 . In this example implementation, the first cylindrical cavity  714  is filled with a dielectric  716 . 
     An annular edge  718  of the first cylindrical wall portion  710  defines a proximal end  720  of the first cylindrical cavity  714 . A proximal end of the second cylindrical wall portion  712  adjoins a distal end  722  of the first cylindrical cavity  714 . 
     The coaxial resonator  700  further includes a first center conductor portion  724  and a second center conductor portion  726  (the center conductor portions  724 ,  726  represented by the densest cross-hatching in  FIG. 7 ). For illustration, the first center conductor portion  724  and the second center conductor portion  726  are separated by the vertical dashed line in  FIG. 7 . In some implementations, both the first center conductor portion  724  and the second center conductor portion  726  can correspond to an odd-integer multiple of quarter wavelengths based on the frequency of an RF power source used to excite the coaxial resonator  700 . The second center conductor portion  726  has a proximal end  728  adjoining a distal end  730  of the first center conductor portion  724 . The second center conductor portion  726  projects along the longitudinal axis  706  to a distal end configured as a concentrator  732  (for example, a tip) of an electrode located at or in close proximity to a distal end  734  of a second cylindrical cavity  736 . 
     The coaxial resonator  700  has an aperture  738  that reaches radially outward through the first cylindrical wall portion  710 . A radial conductor  740  extends out through the aperture  738  from the longitudinal axis  706  to be connected to an RF power source (for example, the signal generator  202 ) by an RF power input line. The end of the radial conductor  740  that is closer to the longitudinal axis  706  connects to a parallel plate capacitor  742  that is in a coupling arrangement to a center conductor structure  744 . The parallel plate capacitor  742  is also in a coupling arrangement to an inline folded RF attenuator  746 . The spacing between the parallel plate capacitor  742  and the center conductor structure  744  can depend on the materials used for fabrication (for example, the materials used to fabricate the parallel plate capacitor  742 , the center conductor structure  744 , and/or the dielectric  716 ). 
     In an example, the DC power source  646  described above is connected to the center conductor structure  744  at a proximal end  748  of the center conductor structure  744  with a DC power input line. The inline folded RF attenuator  746  is disposed between the second resonator portion  704  and the DC power source  646  to restrict RF power from reaching the DC power source  646 . 
     The inline folded RF attenuator  746  includes an interior center conductor portion  750  having a proximal end  752  and a distal end  754 . The inline folded RF attenuator  746  also includes an exterior center conductor portion  756  and a transition center conductor portion  758  that connects or couples the interior center conductor portion  750  and the exterior center conductor portion  756 . 
     The exterior center conductor portion  756  has a proximal end largely in the same plane as the proximal end  752 , and a distal end largely in the same plane as the distal end  754 . For example, in the cross-sectional illustration of  FIG. 7 , the plane of the proximal end  752  and the plane of the proximal end of the exterior center conductor portion  756  can be the plane of the cross-section that is illustrated. In this example implementation, the transition center conductor portion  758  is located proximal to the distal end  754 . The exterior center conductor portion  756  surrounds the interior center conductor portion  750 . 
     In this example, the exterior center conductor portion  756  resembles a cylindrical portion of conducting material surrounding the rest of the interior center conductor portion  750 . The longitudinal lengths of the interior center conductor portion  750  and the exterior center conductor portion  756  are substantially equal to the longitudinal length of the parallel plate capacitor  742  with which they are in a coupling arrangement. The electrical length between the proximal end  752  to the distal end  754 , for both the interior center conductor portion  750  and the exterior center conductor portion  756 , is substantially equal to one quarter-wavelength. The second center conductor portion  726  and the second cylindrical wall portion  712  are both configured to have an electrical length of one quarter-wavelength. 
     The wall structure  708  includes a short outer conducting portion  760  which has a proximal end largely in the same plane as the proximal end  752 , and a distal end largely in the same plane as the distal end  754 . An outer conducting path runs from the distal end of the wall structure  708  (that is substantially coplanar with the distal end  734  of the second cylindrical cavity  736 ), along the short outer conducting portion  760 , and stops at the proximal end  720  of the first cylindrical wall portion  710 . In this example, the outer conducting path has an electrical length of two quarter-wavelengths. 
     An inner conducting path runs from the concentrator  732  to the proximal end  728  of the second center conductor portion  726 , along the outside of the transition center conductor portion  758 , then along the outside from the distal end to the proximal end of the exterior center conductor portion  756 , then along an interior wall  762  of the exterior center conductor portion  756  from its proximal end to its distal end, then along the interior center conductor portion  750  from its distal end to its proximal end. In this example, the electrical length of this inner conducting path is four quarter-wavelengths, or two half wavelengths. The difference in electrical lengths between the inner conducting path and the outer conducting path is one half wavelength. 
     With this configuration, the inline folded RF attenuator  746  operates as a radio-frequency control component connected between the DC power source  646  and the voltage supply of RF energy. The inline folded RF attenuator  746  is configured to shift a voltage supply of RF energy 180 degrees out of phase relative to the ground plane of the coaxial resonator  700 . 
     The particular arrangement depicted in  FIG. 7  is not limiting with respect to the orientation of the inline folded RF attenuator  746 . In other examples, the entire arrangement depicted in  FIG. 7  can be “stretched,” with the inline folded RF attenuator  746  being disposed further away from the concentrator  732  and not directly coupled to the parallel plate capacitor  742 . For example, the inline folded RF attenuator  746  could be separated by one quarter-wavelength from the portion of the center conductor that would remain in direct coupling arrangement with the parallel plate capacitor  742 . The coaxial resonator  700  can achieve a maximize efficiency when (i) the inline folded RF attenuator  746  is an odd-integer multiple of quarter wavelengths from the concentrator  732 ; and (ii) the inline folded RF attenuator  746  is an odd-integer multiple of quarter wavelengths in electrical length. 
     In another example, the arrangement depicted in  FIG. 7  could be more compressed, with the exterior center conductor portions  756  of the inline folded RF attenuator  746  extending longitudinally as far as the parallel plate capacitor  742  and also surrounding the portion of center conductor exposed for plasma creation. This can be implemented by arranging the center conductor structure  744  in the middle so that the exterior center conductor portions  756  extends in either direction longitudinally. Any particular geometry of this arrangement can involve adjusting the various parameters of dielectrics to ensure impedance matching and full 180 degree phase cancellation. 
     In one example, the arrangements described with respect to  FIGS. 6 and 7  and the particular combination of components that provide the RF signal to the coaxial resonators are contained in a body dimensioned approximately the size of a gap spark igniter and adapted to mate with a combustor (for example, of an internal combustion engine). As an example for illustration, a microwave amplifier could be disposed at the resonator, and the resonator could be used as the frequency determining element in an oscillator amplifier arrangement. The amplifier/oscillator could be attached at the top or back of an igniter, and could have the high voltage supply also integrated in the module with diagnostics. This example permits the use of a single, low-voltage DC power supply for feeding the module along with a timing signal. 
     VIII. Jet Engines 
     The above coaxial resonators could be usefully employed in the context of a gas turbine such as a jet turbine configured to power an aircraft. For example, a coaxial cavity resonator similar to the coaxial resonator  201  illustrated in  FIG. 2  could be used in a gas turbine. While reference is made to “QWCCR,” “QWCCR structure,” and “coaxial resonator” elsewhere in the description, it will be understood that other types of resonators are possible and contemplated. 
     An example gas turbine includes a compressor coupled to a turbine through a shaft, and the gas turbine also includes a combustion chamber or area, called a combustor. In operation, atmospheric air flows through a compressor that brings the air to higher pressure. Energy is then added by spraying fuel into the air and igniting it so the combustion generates a high-temperature, high-pressure gas flow. The high-temperature, high-pressure gas enters a turbine, where it expands down to an exhaust pressure, producing a shaft work output at the shaft coupled to the turbine in the process. 
     The shaft work output is used to drive the compressor and other devices (for example, an electric generator) that can be coupled to the shaft. The energy that is not used for shaft work comes out in the exhaust gases that can include a high temperature and/or a high velocity. Gas turbines can be utilized to power aircraft, trains, ships, electrical generators, pumps, gas compressors, and tanks, among other machines. 
       FIG. 8  illustrates an aircraft  800  having a jet engine  802 , according to example implementations. To help propel the aircraft  800  through the air, the aircraft  800  includes a propulsion system operable to generate thrust. The jet engine  802  is a gas turbine engine that is part of the propulsion system of the aircraft  800 . The aircraft  800  can include several jet engines (for example, 2 or 4) similar to the jet engine  802  coupled to wings of the aircraft  800 , for example. The jet engine  802  includes several components of a gas turbine such as the compressor, the combustor, and the turbine. 
       FIG. 9  illustrates several components of the jet engine  802 , according to an example implementation. As illustrated, the jet engine  802  is configured as a gas turbine engine. Large amounts of surrounding air (free stream) are continuously brought into an inlet or intake  900 . At the rear of the intake  900 , the air enters a compressor  902  (axial, centrifugal, or both). The compressor  902  operates as many rows of airfoils, with each row producing an increase in pressure. At the exit of the compressor  902 , the air is at a much higher pressure than free stream at the intake  900 . 
     Fuel is mixed with the compressed air exiting the compressor  902 , and the fuel-compressed air mixture is burned in a combustor  904 , generating a flow of hot, high pressure gas. The hot, high pressure gas exiting the combustor  904  then passes through a turbine  906 , which extracts energy from the flow of gas by making turbine blades spin in the flow. The energy extracted by the turbine  906  is then used to turn the compressor  902  by coupling the compressor  902  and the turbine  906  by a central shaft  908 . 
     The turbine  906  transforms or converts some energy of the hot gas to drive the compressor  902 , but there is enough energy left over to provide thrust to the jet engine  802  by increasing velocity of the flow of gas through a nozzle  910  disposed adjacent the turbine  906 . Because the exit velocity is greater than the free stream velocity, thrust is created and the aircraft  800  is propelled. 
     Several variations could be made to the jet engine  802 . For instance, the jet engine  802  could be configured as a turbofan engine or a turboprop engine where additional components are added to the several components illustrated in  FIG. 9 . 
     The combustor  904 , which can also be referred to as a burner, combustion chamber, or flame holder, comprises the area of the jet engine  802  where combustion takes place. The combustor  904  is configured to contain and maintain stable combustion despite high air flow rates. As such, in examples, the combustor  904  is configured to mix the air and fuel, ignite the air-fuel mixture, and then mix in more air to complete the combustion process. 
       FIGS. 10A, 10B, 10C, 10D, 10E, 10F  illustrate example types of combustors, according to example implementations. In particular,  FIG. 10A  illustrates a partial perspective view of an annular combustor  1000 , and  FIG. 10B  illustrates a partial frontal view of the annular combustor  1000 .  FIG. 10C  illustrates a partial perspective view of a tubular or can combustor  1002 , and  FIG. 10D  illustrates a partial frontal view of the can combustor  1002 .  FIG. 10E  illustrates a partial perspective view of a can-annular combustor  1004 , and  FIG. 10F  illustrates a partial frontal view of the can-annular combustor  1004 . 
     The annular combustor  1000  shown in  FIGS. 10A-10B  has an annular cross section and has a liner sitting inside an outer casing, which has been peeled open in  FIG. 10A  for illustration. The annular combustor  1000  does not define separate combustion zones, but rather has a continuous liner and casing forming a ring  1006  (the annulus). 
     The can combustor  1002  shown in  FIGS. 10C and 10D  includes multiple combustion cans such as combustion cans  1008 ,  1010 , and  1012  arranged in a radial array about a central shaft. Each combustion can is a self-contained cylindrical combustion chamber that has both a liner and a casing. Each combustion can has its own fuel injector, igniter, liner, and casing. The primary air from the compressor  902  is guided into each individual combustion can, where it is decelerated, mixed with fuel, and then ignited. Secondary air also comes from the compressor  902 , where it is fed outside of the liner. The secondary air is then fed, for example, through slits in the liner, into the combustion zone to cool the liner using thin film cooling. 
     In example implementations, multiple combustion cans are arranged around the jet engine  802 , and their shared exhaust is fed to the turbine  906 . However, the can combustor  1002  can weigh more than other combustor configurations and can be characterized by higher pressure drop across the combustion cans than other combustor configurations. 
     The can-annular combustor  1004  shown in  FIGS. 10E-10F  includes an annular casing  1014  and can-shaped liners, such as liner  1016 . The can-annular combustor  1004  has discrete combustion zones contained in separate liners with their own fuel injectors. Unlike the can combustor  1002 , the combustion zones of the can-annular combustor  1004  share a common ring (annulus) casing (for example, annular casing  1014 ). Each combustion zone of the can-annular combustor  1004  does not operate as a separate pressure vessel; rather, the combustion zones “communicate” with each other through liner holes or connecting tubes that allow some air to flow circumferentially between the combustion zones. Further, rather than having separate igniters for each combustion can, once combustion takes place in one or two combustion cans of the can-annular combustor  1004  cans, combustion could spread to and ignite the other combustion cans due to communication between the combustion zones through the liner holes or connecting tubes. 
     Regardless of the type of combustor, the combustion process inside the combustor  904  can determine, at least partially, many of the operating characteristics of the jet engine  802 , such as fuel efficiency, levels of emissions, and transient response (the response to changing conditions such a fuel flow and air speed). Further, also regardless of the type of combustor, the combustor  904  has several components that can be used, and these several components are described below. 
       FIG. 11  illustrates a schematic diagram of a partial view of the combustor  904 , according to an example implementation. The combustor  904  includes a casing  1100  that is configured as an outer shell of the combustor  904 . The casing  1100  can be protected from thermal loads by the air flowing in it, and can operate as a pressure vessel that withstands the difference between the high pressures inside the combustor  904  and the lower pressure outside the combustor  904 . 
     The combustor  904  also includes a diffuser  1102  that is configured to slow the high speed, highly compressed air from the compressor  902  to a velocity optimal for the combustor  904 . Reducing the velocity results in a loss in total pressure, and the diffuser  1102  is configured to limit such loss of pressure. The diffuser  1102  is also configured to limit flow distortion by avoiding flow effects like boundary layer separation. 
     The combustor  904  further includes a liner  1104  that contains the combustion process and is configured to withstand extended high temperature cycles, and therefore can be made from superalloys. Furthermore, the liner  1104  is cooled with air flow. In some example implementations, in addition to air cooling, the combustor  904  can include thermal barrier coatings to further cool the liner  1104 . 
       FIG. 12  illustrates air flow paths through the combustor  904 , according to an example implementation. Primary air is the main combustion air and is highly compressed air from the compressor  902 . The primary air can be decelerated using the diffuser  1102  and is fed through primary air holes  1200 . This air is mixed with fuel, and then combusted in a combustion zone  1202 . 
     Intermediate air is the air injected into the combustion zone  1202  through intermediate air holes  1204 . The air injected through the intermediate air holes  1204  completes the combustion processes, cooling the air down and diluting concentrations of carbon monoxide (CO) and hydrogen (H 2 ). 
     Dilution air is air injected through dilution air holes  1206  in the liner  1104  at the end of the combustion zone  1202  to help cool the air to before it reaches the turbine  906 . The dilution air can be used to produce the uniform temperature profile desired in the combustor  904 . 
     Cooling air is air that is injected through cooling air holes  1208  in the liner  1104  to generate a layer (film) of cool air to protect the liner  1104  from the high combustion temperatures. The combustor  904  is configured such that the cooling air does not directly interact with the combustion air and combustion process. 
     Referring back to  FIG. 11 , the combustor  904  further includes a snout  1106 , which is an extension of a dome  1108 . The snout  1106  operates as an air splitter, separating the primary air from the secondary air flows (intermediate, dilution, and cooling air). 
     The dome  1108  and a swirler  1110  are the components of the combustor  904  through which the primary air flows as it enters the combustion zone  1202 . The dome  1108  and the swirler  1110  are configured to generate turbulence in the flow to rapidly mix the air with fuel. The swirler  1110  establishes a local low pressure zone that forces some of the combustion products to recirculate, creating high turbulence. However, the higher the turbulence, the higher the pressure loss is for the combustor  904 , so the dome  1108  and the swirler  1110  are configured to not generate more turbulence than is sufficient to mix the fuel and air. In some examples, with the resonators disclosed in the present disclosure, the combustor  904  can be configured without the dome  1108  and the swirler  1110 . In other examples, the dome  1108  and the swirler  1110  can be made smaller when the combustor resonators disclosed in the present disclosure are used because the flame front propagation can be faster than when a conventional igniter is used. 
     The combustor  904  further includes a fuel injector  1112  configured to introduce fuel to the combustion zone  1202  and, along with the swirler  1110 , is configured to mix the fuel and air. The fuel injector  1112  can be configured as any of several types of fuel injectors including: pressure-atomizing, air blast, vaporizing, and premix/prevaporizing injectors. 
     Pressure atomizing fuel injectors rely on high fuel pressures (as much as 1200 pounds per square inch (psi)) to atomize the fuel. When using this type of fuel injector, the fuel system is configured to be sufficiently robust to withstand such high pressures. The fuel tends to be heterogeneously atomized, resulting in incomplete or uneven combustion, which generates pollutants and smoke. 
     The air-blast injector “blasts” fuel with a stream of air, atomizing the fuel into homogeneous droplets, and can cause the combustor  904  to be smokeless. This air blast injector can operate at lower fuel pressures than the pressure atomizing fuel injector. 
     The vaporizing fuel injector is similar to the air-blast injector in that the primary air is mixed with the fuel as it is injected into the combustion zone  1202 . However, with the vaporizing fuel injector the fuel-air mixture travels through a tube within the combustion zone  1202 . Heat from the combustion zone  1202  is transferred to the fuel-air mixture, vaporizing some of the fuel to enhance the mixing before the mixture is combusted. This way, the fuel is combusted with low thermal radiation, which helps protect the liner  1104 . However, the vaporizer tube can have low durability because of the low fuel flow rate within it causing the tube to be less protected from the combustion heat. 
     The premixing/prevaporizing injector is configured to mix or vaporize the fuel before it reaches the combustion zone  1202 . This way, the fuel is uniformly mixed with the air, and emissions from the jet engine  802  can be reduced. However, fuel can auto-ignite or otherwise combust before the fuel-air mixture reaches the combustion zone  1202 , and the combustor  904  can thus be damaged. 
     In some example implementations, a resonator could be configured with fuel passages disposed within the resonator, such that the resonator integrates operations of the fuel injector  1112  with operations of an igniter described below. In these examples, the resonator could be configured to perform the atomization and vaporization of the fuel in addition to mixing and preparing the fuel for combustion. The fuel would then be passed through a formed plasma to ensure ignition. Further, the presence of electromagnetic waves radiated by the resonator could be used to energize the air-fuel mixture and stimulate combustion. 
     The combustor  904  also includes an igniter  1114  configured to ignite air-fuel mixture to cause combustion. In examples, the igniter  1114  can be configured as an electrical spark igniter, similar to an automotive spark plug. However, there are several disadvantages to such configuration as described below. The igniter  1114  is disposed proximate to the combustion zone  1202  where the fuel and air are already mixed, but is located upstream from the combustion location so that it is not damaged by the combustion itself. In example implementations, once combustion is initially started by the igniter  1114 , the combustion is self-sustaining and the igniter  1114  is no longer used. In the annular combustor  1000  and the can-annular combustor  1004 , the flame can propagate from one combustion zone to another, so igniters might not be used at each combustion zone. 
     However, in some examples, combustion can stop due to operating conditions that are not favorable to sustaining combustion. For example, the aircraft  800  can operate at high altitude with low air density, which might affect combustion. In another example, a speed of the aircraft  800  can be sufficiently low to stop the combustion process. Other operating conditions could cause the combustion to stop. In these examples, the igniter  1114  could also be used to restart combustion. 
     In some systems, ignition-assisting techniques can be used to restart combustion. One such method is oxygen injection, where oxygen is fed to the ignition area, helping the fuel to easily combust. This is particularly useful in some aircraft applications where the jet engine  802  may have to restart at high altitude. Further, described in the present disclosure are igniters and systems that could lower the probability of stopping and having to restart combustion. Particularly, the igniter  1114  could be configured as any of the resonators described in the present disclosure to enhance combustion. In some examples, if the igniter  1114  is configured as a coaxial resonator, the coaxial resonator could be used as a sensor to obtain real-time measurements of the conditions inside the combustor  904  and could be used to predict when combustion would stop (for example, when a flameout would occur). Once such a prediction is made, flameout can be precluded (or its likelihood reduced) by proactively performing operations such as adding more fuel, providing additional plasma, and/or increasing compression using the compressor  902 , among other possible operations. 
     In some example implementations of the jet engine  802 , combustion can take place in locations within the jet engine  802  other than the combustor  904 . For example, in order for an aircraft to fly faster than the speed of sound, the aircraft needs to generate a high thrust to overcome a sharp rise in drag near the speed of sound. To achieve such high thrust, an afterburner can be added to the jet engine. The afterburner can be considered another type of combustor. 
       FIG. 13  illustrates the jet engine  802  including an afterburner  1300  downstream of the turbine  906 , in accordance with an example implementation. As described above with respect to  FIG. 9 , some of the energy of the exhaust gas from the combustor  904  is used to turn the turbine  906 . The afterburner  1300  is used to add energy to generate more thrust by injecting fuel directly into the hot exhaust gas exiting the turbine  906 . 
     The nozzle  910  of the jet engine  802 , as illustrated in  FIG. 13 , is extended or moved downstream in the jet engine  802  to enable placing flame holders  1302  between the turbine  906  and the exit of the jet engine  802 . As shown in  FIG. 13 , the flame holders  1302  can include multiple hoops, such as hoops  1304 ,  1306 . In another arrangement, the flame holders  1302  can include multiple parallel gutters that extend across an afterburner channel  1308  and perpendicular to the engine axis. In yet another arrangement, the flame holders  1302  can include multiple gutters extending radially from the internal surface of the afterburner channel  1308  in a star pattern with respect to the engine axis. The gutters of the flame holders  1302  can be configured with a u- or v-shaped cross section that is open on a downstream side of the gutter. The flame holders  1302  provide a zone of low velocity air so as to retain gases during their combustion in the afterburner channel  1308 . 
     In some examples, when the afterburner  1300  is turned on, additional fuel is injected through, between, or around the flame holders  1302  and into the gas exiting the turbine  906 . In other examples, fuel is injected in the afterburner  1300  upstream of the flame holders  1302 . The fuel burns and produces additional thrust. 
     After passing the turbine  906 , the gas from the turbine  906  expands, thus losing temperature. The gas from the turbine  906  is an input gas to the afterburner  1300 . Fuel is injected into the input gas from the turbine  906  to produce a fuel-air mixture within an afterburner channel  1308 . Combustion of the fuel within the fuel-air mixture within the afterburner channel  1308  results in an exhaust gas from the afterburner  1300  having a temperature and pressure greater than a temperature and pressure, respectively, of the gas from the turbine  906 . The exhaust gas resulting from combustion within the afterburner channel  1308  passes through the nozzle  910  at a higher velocity, thereby generating additional thrust. 
     In some examples, ignition within the afterburner  1300  may be hard to achieve. In particular, because velocities and temperatures do not substantially change at the inlet of the afterburner  1300 , ignition in the afterburner  1300  may be difficult to achieve when the aircraft  800  is flying at high altitudes. The difficulty is associated with the low pressure in the afterburner  1300  that affects ignition directly. Therefore, it can be desirable to have a system that better prepares the fuel for easier ignition in the afterburner  1300  at higher altitude. 
     Further, the exhaust gas from the turbine  906  that enters the afterburner  1300  has reduced oxygen and is not highly compressed due to previous combustion at the combustor  904 . Therefore, combustion in the afterburner  1300  is generally fuel-inefficient compared with combustion in the combustor  904 . Thus, the afterburner  1300  increases thrust at the cost of increased fuel inefficiency, thereby limiting its practical use to short bursts or intermittent operation. As such, the afterburner  1300  is turned on selectively when the extra thrust is used, but is otherwise turned off. It can thus be desirable to have an afterburner that is more efficient to enable using the afterburner more often and more efficiently to enable persistent, as opposed to intermittent operation. 
     The combustion taking place at the combustor  904  and the combustion taking place in the afterburner  1300  of the jet engine  802  can affect many of the operating characteristics of the jet engine  802 . As examples, combustion determines fuel efficiency, thrust levels, and levels of emissions and transient response (the response to changing conditions such a fuel flow and air speed). It can thus be desirable to have an ignition system that prepares the fuel for efficient and thorough combustion, facilitates starting and restarting ignition when desired regardless of altitude, and enables combustion of a lean fuel mixture at high compression ratios to increase efficiency. 
     IX. Afterburners 
       FIG. 13  illustrates the jet engine  802  including an afterburner  1300  downstream of the turbine  906 , in accordance with an example implementation. As described above with respect to  FIG. 9 , some of the energy of the exhaust gas from the combustor  904  is used to turn the turbine  906 . The afterburner  1300  is used to add energy to generate more thrust by injecting fuel directly into the hot exhaust gas exiting the turbine  906 . 
     The nozzle  910  of the jet engine  802 , as illustrated in  FIG. 13 , is extended or moved downstream in the jet engine  802  to enable placing flame holders  1302  between the turbine  906  and the exit of the jet engine  802 . As shown in  FIG. 13 , the flame holders  1302  can include multiple hoops, such as hoops  1304 ,  1306 . In another arrangement, the flame holders  1302  can include multiple parallel gutters that extend across the afterburner channel  1308  and perpendicular to the engine axis. In yet another arrangement, the flame holders  1302  can include multiple gutters extending radially from the internal surface of the afterburner channel  1308  in a star pattern with respect to the engine axis. The gutters of the flame holders  1302  can be configured with a u- or v-shaped cross section that is open on a downstream side of the gutter. The flame holders  1302  provide a zone of low velocity air so as to retain gases during their combustion in the afterburner channel  1308 . 
     In some examples, when the afterburner  1300  is turned on, additional fuel is injected through, between, or around the flame holders  1302  and into the gas exiting the turbine  906 . In other examples, fuel is injected in the afterburner  1300  upstream of the flame holders  1302 . The fuel burns and produces additional thrust. 
     After passing the turbine  906 , the gas from the turbine  906  expands, thus losing temperature. The gas from the turbine  906  is an input gas to the afterburner  1300 . Fuel is injected into the input gas from the turbine  906  to produce a fuel-air mixture within the afterburner channel  1308 . Combustion of the fuel within the fuel-air mixture within the afterburner channel  1308  results in an exhaust gas from the afterburner  1300  having a temperature and pressure greater than a temperature and pressure, respectively, of the gas from the turbine  906 . The exhaust gas resulting from combustion within the afterburner channel  1308  passes through the nozzle  910  at a higher velocity, thereby generating additional thrust with respect to gas from the turbine  906  that flows through the afterburner channel  1308  when fuel is not being injected into the afterburner channel  1308 . 
     The fuel-air mixture produced by the injection process of fuel in the afterburner  1300  has a flame propagation velocity that is lower than the gas speed through the afterburner  1300 . Thus, unless sources of continuous ignition are present in the chamber, the burning gas ignited by a temporary process could be blown out of the jet engine  802  as soon as the ignition is stopped. 
     In examples, this ignition process can start the stabilization process of the flame and can then be turned off. Further, fuel can be added in sequence to a number of stream tubes in the afterburner  1300  to prevent pressure surges during afterburner ignition and to allow modulation of the thrust of the afterburner  1300 . Thus, once one region is “lit,” it can act as a source of ignition for adjacent regions when fuel is added to them. 
     Several ignition techniques could be used in the afterburner  1300  including: hot-streak, spark or arc ignition, and pilot burner techniques. In the hot-streak technique, fuel is injected for a short period into the gas resulting from the combustor  904  just upstream of the turbine  906 . The combustible flow formed by this process produces a hot stream of burning gas. Combustion occurs in this stream by auto-ignition because of the high temperatures present upstream of the turbine  906 . The hot streak can be maintained for a brief period to prevent thermal damage to the turbine  906 . 
     In the arc-ignition technique, ignition and initiation of the flame stabilization process can be started by producing a high-energy electric arc in a primary stream tube. In this example, ignition can be produced by placing the arc in a region of the wake of the flame holders that is sheltered and that can have its own fuel supply system. 
     The pilot-burner technique is similar to the arc-ignition technique and can use an arc to initiate combustion. In the pilot burner technique, in an example, a small can burner is located in the primary stream tube. A continuous source of hot combustion products is established and acts in a manner similar to the hot-streak technique to start the stabilization process once fuel injection is started. 
     In some examples, ignition may be hard to achieve. In particular, because velocities and temperatures do not substantially change at the inlet of the afterburner  1300 , ignition or “relighting” of the combustion process in the afterburner  1300  may be difficult to achieve when the aircraft  800  is flying at high altitudes. The difficulty is associated with the low pressure in the afterburner  1300  that affects both the preparation of the fuel (by the injector system) and the ignition process directly. Therefore, it can be desirable to have a system that better prepares the fuel for easier ignition in the afterburner  1300  at higher altitude. 
     Further, because the exhaust gas from the turbine  906  that enters the afterburner  1300  has reduced oxygen due to previous combustion at the combustor  904 , and because the fuel is not burning in a highly compressed air environment, the afterburner  1300  is generally inefficient compared with the combustor  904 . Efficiency of the afterburner  1300  can also decline as the inlet and tailpipe pressure decrease with increasing altitude. Thus, the afterburner  1300  significantly increases thrust at the cost of high fuel consumption and increased fuel inefficiency, thereby limiting its practical use to short bursts. As such, the afterburner  1300  is turned on selectively when the extra thrust is used, but is otherwise turned off. It can thus be desirable to have an afterburner that is more efficient to enable using the afterburner more often and more efficiently to enable persistent, as opposed to intermittent, supersonic flight. 
     The combustion taking place at the combustor  904  and the combustion taking place in the afterburner  1300  of the jet engine  802  can affect many of the operating characteristics of the jet engine  802 . As examples, combustion determines fuel efficiency, thrust levels, and levels of emissions and transient response (the response to changing conditions such a fuel flow and air speed). It can thus be desirable to have an ignition system that prepares the fuel for efficient and thorough combustion, facilitates starting and restarting ignition when desired regardless of altitude, and enables combustion of a lean fuel mixture at high compression ratios to increase efficiency. 
       FIG. 14  shows the jet engine  802  and additional details of the afterburner  1300 . In  FIG. 14 , the nozzle  910  is downstream from the turbine  906  to enable placing a fueling section  1422 , a resonator section  1426 , and a flame holders section  1424  between the turbine  906  and the nozzle  910 . The flame holders  1302  can be disposed within the flame holders section  1424 . 
     A torch igniter  1414  can, but need not necessarily, be disposed within the afterburner channel  1308 . In an example implementation, the torch igniter  1414  can be disposed between the fueling section  1422  and the flame holders section  1424 . The torch igniter  1414  can ignite fuel within the torch igniter  1414  to produce a flame that ignites fuel within the afterburner channel  1308 . 
     The afterburner  1300 , and particularly the fueling section  1422  and/or the resonator section  1426 , can include a resonator according to the example implementations. The resonator can be a coaxial-cavity resonator, similar to the coaxial resonator  201  illustrated in  FIG. 2 , for example. Alternatively, the resonator can be a dielectric resonator, a crystal resonator, a ceramic resonator, a surface-acoustic-wave resonator, an yttrium-iron-garnet resonator, a rectangular-waveguide cavity resonator, a parallel-plate resonator, or a gap-coupled microstrip resonator. While reference is made to “QWCCR,” “QWCCR structure,” and “coaxial resonator” elsewhere in the disclosure, it will be understood that other types of resonators are possible and contemplated. Furthermore, the afterburner  1300 , the fueling section  1422 , and/or the resonator section  1426 , can include at least one ring of resonators. Several examples of a ring of resonators are discussed below. 
     In the afterburner  1300 , the nozzle  910  can be configured as an adjustable nozzle to vary the amount of thrust provided by the jet engine  802 . Adjusting the nozzle  910  can include increasing or decreasing an aperture size of the nozzle  910 . Decreasing the aperture size of the nozzle  910  constricts airflow through the nozzle  910  to increase the thrust of the jet engine  802 . In an example implementation, the nozzle  910  is a component of the afterburner  1300 . In another example implementation, the nozzle is a component removably attachable to the afterburner  1300  or provided in another manner. 
     As shown in  FIG. 14 , the afterburner  1300  can include an afterburner duct  1400 , a casing  1402 , and the afterburner channel  1308 . The afterburner duct  1400  is a structure that defines the afterburner channel  1308 . For example, the afterburner duct  1400  can include a metallic structure that defines a shape and volume of the afterburner channel  1308 . As will be discussed below, a component of the afterburner  1300  can attach to and/or pass through the afterburner duct  1400 . As an example, a fuel supply line for transferring fuel from a fuel tank outsider of the afterburner duct  1400  to a fuel outlet in the afterburner channel  1308  can attach to and/or pass through the afterburner duct  1400 . In an example implementation, the afterburner duct  1400  can include a port for the fuel supply line to pass through the afterburner duct  1400 . A port can include a through-hole in the afterburner duct  1400 . 
     A fuel supply line can be made from one or more materials. As an example, the fuel supply line can comprise a steel tube or an aluminum tube. A fuel supply line can include multiple attachment fittings, such as multiple threaded fittings to connect a fuel supply line to fuel pump, a fuel storage tank, a resonator, another fuel supply line, a strut configured for transporting fuel, etc. A strut, for instance, can be one of multiple struts configured to support a bracket in the afterburner channel, such as a bracket in the center of the afterburner channel  1308  or proximate to the afterburner duct  1400 . Such struts can include one or more fuel outlets and can be connected to or part of a fuel supply line connected to a fuel pump or fuel storage tank. The fuel outlets can be disposed within the struts to output fuel in a fuel spray pattern for the afterburner  1300 . Further, a strut can include a tubular strut, having one or more passages that extend at least partially through a tube. 
     The afterburner duct  1400  includes an open end  1404 . For example implementations in which the afterburner  1300  is attached to the turbine  906 , the open end  1404  is in proximity to an exit  1428  of the turbine  906 . In those example implementations, the open end  1404  is open to the exit  1428  to permit a gas  1410  from the turbine  906  to enter into the afterburner channel  1308 . The gas  1410  can be referred to as an input gas from the turbine  906 , an exhaust gas from the turbine  906 , an input gas to the afterburner  1300 , and/or an input gas to the afterburner channel  1308 . 
     The afterburner duct  1400  includes another open end that is downstream and opposite the open end  1404 . In the example implementation in which the nozzle  910  is a component removably attachable to the afterburner  1300 , the other open end can be an open end that is upstream of the nozzle  910 , such as the open end  1406 . In the example implementation in which the nozzle  910  is a component of the afterburner  1300 , the other open end can be an open end at or within the nozzle  910 , such as the open end  1408 . The afterburner channel  1308  can extend from the open end  1404  to the open end  1406  or  1408 . 
     The gas  1410  that enters the afterburner channel  1308  at the open end  1404  can be mixed with fuel. Combustion of that gas and fuel mixture can occur within channel  1308 . An exhaust gas  1418  formed during combustion of the gas and fuel mixture within the afterburner channel  1308  can exit the afterburner  1300  through the open end  1406  or  1408 . 
     The casing  1402  can be configured to support the afterburner duct  1400  within the casing  1402 . One or more brackets (not shown) and/or fasteners (not shown) can be used for attaching the afterburner duct  1400  to the casing  1402 . The afterburner  1300  can include a cooling passage  1416  between the afterburner duct  1400  and the casing  1402 . A gas  1412  from the turbine  906  can flow into the cooling passage  1416 . The afterburner duct  1400  can include cooling ports (shown in  FIG. 16B ) so that at least some of the gas  1412  within the cooling passage  1416  can pass through the afterburner duct  1400  and into the afterburner channel  1308 . A gas within the cooling passage  1416  and/or a gas within the cooling ports can cool the afterburner duct  1400 . A gas  1420  can exit the cooling passage  1416  proximate the nozzle  910 . The gas  1420  can include a portion of the gas  1412 , such as a portion of the gas  1412  that did not pass through the cooling ports into the afterburner channel  1308 . 
     A shape of the casing  1402  or some portion of the casing  1402  can be any of a variety of shapes. For an example implementation in which the casing  1402  is attached to the aircraft  800 , the shape of the casing  1402  can depend on the shape of a portion of the aircraft  800  at which the casing  1402  attaches to the aircraft  800 . The shape of a portion of the casing  1402  can be a cylinder, a rectangular prism, a pyramid, a frustum, or some other shape. Likewise, the shape of the entire casing  1402  can be a cylinder, a rectangular prism, a pyramid, a frustum, some other shape, or a combination of two or more shapes. 
     A shape of the afterburner duct  1400  or a portion of the afterburner duct  1400  can also be any of a variety of shapes. The shape of the afterburner duct  1400  or the portion of the afterburner duct  1400  can depend on the shape(s) of the casing  1402 . The shape of a portion of the afterburner duct  1400  can be a cylinder, a rectangular prism, a pyramid, a frustum, or some other shape. And likewise, the shape of the entire duct  1400  can be a cylinder, a rectangular prism, a pyramid, a frustum, some other shape, or a combination of two or more shapes. For example purposes only,  FIGS. 15A and 15B  illustrate the afterburner duct  1400  and the casing  1402  both having cylindrical shapes. The afterburner duct  1400  and the casing  1402  do not necessarily have to have the same shapes. For example the afterburner duct  1400  can be cylindrical, and the casing can have a non-cylindrical shape, such as a rectangular prism. Furthermore, in some example implementations the afterburner duct  1400  may serve as the casing for the afterburner. 
       FIG. 15A  is a perspective view of the afterburner duct  1400  and the casing  1402  with a view of the open end  1404 .  FIG. 15A  shows a portion of the afterburner channel  1308 , and a portion of the cooling passage  1416 . The gas  1410  enters the afterburner channel  1308  through the open end  1404 . The gas  1412  enters the cooling passage  1416  proximate the open end  1404 . 
       FIG. 15B  is a perspective view of the afterburner duct  1400  and the casing  1402  with a view of the open end  1406  or  1408 .  FIG. 15B  shows a portion of the afterburner channel  1308 , and a portion of the cooling passage  1416 . The exhaust gas  1418  exits the afterburner channel  1308  through the open end  1406  or  1408 . The gas  1420  exits the cooling passage  1416  proximate the open end  1406  or  1408 . 
       FIG. 16A  is an elevation view of the afterburner duct  1400  and the casing  1402  from the side of the afterburner duct  1400  having the open end  1404 .  FIG. 16A  shows that the cooling passage  1416  is between the afterburner duct  1400  and the casing  1402 .  FIG. 16A  also shows the afterburner channel  1308  is within the afterburner duct  1400 . 
       FIG. 16B  is a cross-sectional view A-A of the afterburner duct  1400  and the casing  1402  shown in  FIG. 16A . As shown in  FIG. 16B , the casing  1402  has an outer surface  1434  and an inner surface  1436 . Similarly, the afterburner duct  1400  has an outer surface  1430  and an inner surface  1432 . The cooling passage  1416  can be formed by at least the outer surface  1430  in cooperation with the inner surface  1436 . The open end  1404  and the open end  1406  or  1408  extend between portions of the inner surface  1432  shown in  FIG. 16B . 
       FIG. 16B  also shows ports  1438 ,  1440 ,  1450  within the casing  1402 , and ports  1442 ,  1444 ,  1446 ,  144 ,  1452  within the afterburner duct  1400 . A port in the casing  1402  and a port in the afterburner duct  1400  can be aligned, such as the pair of ports  1438 ,  1442 , the pair of ports  1440 ,  1446 , and the pair of ports  1450 ,  1452 . A pair of aligned ports can provide a path for routing a fuel supply line, a strut, an electrical circuitry conduit, and/or a resonator, through the casing  1402  and the afterburner duct  1400 , into the afterburner channel  1308 . A port in the afterburner duct  1400 , such as the ports  1444 ,  1448  might not be aligned with a port in the casing  1402 . Those ports may be used as cooling ports and/or cooling air holes. Some of the gas  1412  flowing within the cooling passage  1416  can pass through the ports  1444 ,  1148  to reduce a temperature of the afterburner duct  1400 . 
     Returning to  FIG. 14 , the torch igniter  1414  could be used to initiate combustion of fuel within the afterburner channel  1308  when additional thrust by the jet engine  802  is requested. The torch igniter  1414  or another shield can shield a resonator from at least a portion of a force occurring in the channel due to a gas flowing through the afterburner channel  1308 . Shielding a resonator using the torch igniter  1414  or another shield in proximity to the resonator may permit the resonator to provide a plasma corona with a shape that improves combustion of the fuel within the channel. 
       FIG. 17A  illustrates details of the torch igniter  1414  in accordance with an example implementation. As shown in  FIG. 17A , the torch igniter  1414  includes a casing  1700 . A portion of the casing  1700  bounded by a broken line  1702  is cut away to show other portions of the torch igniter  1414 . The torch igniter  1414  includes a torch igniter channel  1704 , a torch igniter opening  1706 , a resonator  1708 , and an attachment bracket  1710  for attachment of the resonator  1708  within the torch igniter channel  1704 . 
     The torch igniter  1414  includes a fuel supply line  1712  and an electrical circuitry conduit  1716 . The fuel supply line  1712  includes an outlet  1714  for outputting fuel into the torch igniter channel  1704 . The fuel supply line  1712  can pass through a hole  1718  in the casing  1700  and through a pair of ports, such as the ports  1446 ,  1440 , so that the fuel within a fuel pump and/or fuel tank, outside of the casing  1402 , can be provided to outlet  1714 . A portion of the electrical circuitry conduit  1716  can pass through a hole  1720  in the casing  1700  and through a pair of ports, such as the ports  1452 ,  1450 , so that electrical circuitry can be routed within the electrical circuitry conduit  1716  from outside of the casing  1402  to the resonator  1708 . 
     The resonator  1708  can be arranged like any resonator discussed in this disclosure. Accordingly, the electrical circuitry conduit  1716  can include electrical conductors to and from a signal generator, such as the signal generator  202  shown in  FIG. 2 , or electrical conductors to and from a signal generator and a DC power source, such as the signal generator  202  and the DC power source shown in  FIGS. 3A, 3B, and 4A . 
     A fuel pump, such as the fuel pump  504 , can pump fuel through the fuel supply line  1712 . The fuel within the fuel supply line  1712  can be output through the outlet  1714  and into the torch igniter channel  1704 . The resonator  1708  can be excited with a signal carried on electrical conductors within the electrical circuitry conduit  1716  to generate a plasma corona. That plasma corona can cause combustion of the fuel output into the torch igniter channel  1704 . A flame generated by combustion of the fuel in the torch igniter channel  1704  can pass through the torch igniter opening  1706  in order to start combustion of fuel within the afterburner channel  1308 . 
       FIG. 17B  illustrates details of the torch igniter  1414  in accordance with another example implementation. As shown in  FIG. 17B , the torch igniter  1414  includes a casing  1730 . A portion of the casing  1730  bounded by a broken line  1732  is cut away to show other portions of the torch igniter  1414 . The torch igniter  1414  includes a torch igniter channel  1734 , a torch igniter opening  1736 , a resonator  1738 , and an attachment bracket  1740  for attachment of the resonator  1738  within the torch igniter channel  1734 . 
     The torch igniter  1414  includes a fuel supply line  1742  and an electrical circuitry conduit  1746 . The fuel supply line  1742  is removably connectable to a fuel conduit  1748  within the resonator  1738 . The fuel conduit  1748  includes an outlet  1750  for outputting fuel into the torch igniter channel  1734 . The fuel supply line  1742  can pass through a hole  1752  in the casing  1730  and through a pair of ports, such as the ports  1446 ,  1440 , so that the fuel within a fuel pump and/or fuel tank, outside of the casing  1402 , can be provided to outlet  1750 . A portion of the electrical circuitry conduit  1746  can pass through a hole  1754  in the casing  1730  and through a pair of ports, such as the ports  1452 ,  1450 , so that electrical circuitry can be routed within the electrical circuitry conduit  1746  from outside of the casing  1402  to the resonator  1738 . 
     The resonator  1738  can be arranged like any resonator discussed in this disclosure. Accordingly, the electrical circuitry conduit  1746  can include electrical conductors to and from a signal generator, such as the signal generator  202  shown in  FIG. 2 , or electrical conductors to and from a signal generator and a DC power source, such as the signal generator  202  and the DC power source shown in  FIGS. 3A, 3B, and 4A . 
     A fuel pump, such as the fuel pump  504 , can pump fuel through the fuel supply line  1742 . The fuel within the fuel supply line  1742  can be output through the outlet  1750  and into the torch igniter channel  1734 . The resonator  1738  can be excited with a signal carried on electrical conductors within the electrical circuitry conduit  1746  to generate a plasma corona. That plasma corona can cause combustion of the fuel output into the torch igniter channel  1734 . A flame generated by combustion of the fuel in the torch igniter channel  1734  can pass through the torch igniter opening  1736  in order to start combustion of fuel within the afterburner channel  1308 . In this example implementation, outputting the fuel in proximity to the plasma corona can help improve efficiency of combustion of the fuel. 
     As indicated above, the torch igniter  1414  can be used to initiate combustion of fuel within the afterburner channel  1308 . In other implementations, combustion of fuel within the afterburner channel  1308  can be initiated by a resonator or resonators that are not within the torch igniter  1414 . In still other implementations, combustion of fuel within the afterburner channel  1308  can be initiated by both the torch igniter  1414  and a resonator or resonators that are not within the torch igniter  1414 . 
     Returning to  FIG. 14 , the fueling section  1422  is a section of the afterburner  1300  that includes a fuel outlet for outputting fuel into the afterburner channel  1308 . The fuel outlet within the fueling section  1422  can be disposed within a component of the afterburner, such as a strut, a resonator, or a fuel injector. The fuel output by the fuel outlet can mix with the gas the afterburner  1300  receives from the turbine  906 . The fueling section  1422  can include a ring of resonators in which at least one resonator in the ring includes at least one fuel conduit and at least one fuel outlet. The afterburner  1300  can include multiple fueling sections having a separate ring of resonators in which at least one resonator in the ring includes at least one fuel conduit and at least one fuel outlet. Furthermore, a resonator in a ring of resonators in the fueling section  1422  does not necessarily have to include a fuel conduit and fuel outlet. A plasma corona provided by a resonator in the afterburner  1300  can cause combustion of the fuel output by the fueling section  1422  and/or by a resonator in the fueling section  1422 . 
     The resonator section  1426  is a section of the afterburner  1300  that includes one or more resonators. In some implementations, multiple resonators in the resonator section  1426  and/or otherwise within the afterburner are arranged as a ring of resonators. Furthermore, a resonator section that includes (i) one or more resonators, (ii) a fuel conduit within the resonator, and (iii) a fuel outlet within the fuel conduit, can also be considered a fueling section. Examples of a resonator section, such as the resonator section  1426 , are shown in  FIGS. 20A to 27D . 
     A resonator of the afterburner  1300  can be configured to be electromagnetically coupled to a radio-frequency power source, such as the signal generator  202 . A resonator of the afterburner  1300  can be configured to provide electromagnetic waves and/or a plasma corona when the resonator is excited by the radio-frequency power source. A resonator of the afterburner  1300  can be arranged like any resonator discussed in this disclosure. A resonator of the afterburner  1300  can be disposed outside of the afterburner channel  1308 , disposed within the afterburner channel  1308 , or partially disposed within the afterburner channel  1308  and partially disposed outside of the afterburner channel  1308 . 
       FIG. 18  is a block diagram showing additional features of the afterburner  1300  in accordance with an example implementation. As shown in  FIG. 18 , the afterburner  1300  includes a controller  1800 , a signal generator  1802 , a DC power source  1804 , a fuel tank  1806 , a fuel pump  1808 , fuel supply lines  1812 ,  1814 , ports  1816 ,  1818 , and ignition switch  1820 . A system bus, network or other connection mechanism  1810  can communicatively couple the controller  1800  to the signal generator  1802 , the DC power source  1804 , and/or the fuel pump  1808 . The ports  1816 ,  1818  can extend through the casing  1402  or through the casing  1402  and the afterburner duct  1400 . The ignition switch  1820  can be configured for changing a signal level, such as a voltage level, on an input line to the controller  1800  to signal that use of the afterburner  1300  is requested or that use of the afterburner  1300  is no longer requested. 
     The fuel pump  1808  can be installed within the fuel tank  1806  and/or can be attached to the fuel tank  1806  by the fuel supply line  1812 . The fuel tank  1806  and the fuel pump  1808  can be located outside of the casing  1402 . The fuel supply line  1814  is attached to the fuel pump  1808  and can be routed along the casing  1402  to the port  1816 , at which point the fuel supply line  1814  can pass through the casing  1402  to enter the afterburner  1300 . The fuel supply line  1814  can further pass through the afterburner duct  1400  so that a portion of the fuel supply line  1814  is disposed within the afterburner channel  1308 . The fuel supply line  1814  can include and/or connect to a strut, such as a tubular strut, that projects inward through the casing  1402 , through the afterburner duct  1400  and into the afterburner channel  1308 . 
     Electrical circuitry can be connected to the signal generator  1802  and/or the DC power source  1804 . The signal generator  1802  can be arranged like any signal generator discussed in this disclosure, such as the signal generator  202 . For instance, the signal generator  1802  can include a radio-frequency power source discussed in this disclosure. Moreover, the signal generator  1802  can include at least one signal generator (in other words, one or more signal generators), such as at least one radio-frequency power source. For the implementations in which the afterburner  1300  includes a plurality of resonators that are electromagnetically coupled to and/or configured to electromagnetically couple to the at least one radio-frequency power source, each resonator can be electromagnetically coupled to and/or configured to electromagnetically couple to a separate radio-frequency power source or to a radio-frequency power source electromagnetically coupled to and/or configured to electromagnetically couple to at least one other resonator of the plurality of resonators. 
     For some implementations, as discussed, the signal generator  1802  can include a single signal generator. That signal generator  1802  can provide one resonator with a signal to excite that resonator. Alternatively, that signal generator  1802  can, for example, provide multiple resonators with a signal to excite those multiple resonators. As an example, the signals can be provided by multiple signal outputs of the signal generator  1802 . As another example, the signals can be provided by a single signal output of the signal generator  1802  and travel to the multiple resonators via parallel electrical circuitry. 
     Furthermore, for some implementations, as discussed, the signal generator  1802  can include multiple signal generators. For some of those implementations, each signal generator  1802  can electromagnetically couple to a respective resonator of the multiple resonators. For some other implementations, one or more of the multiple signal generators can electromagnetically couple to two or more resonators. As an example, a first signal generator can electromagnetically couple to a set of one or more resonators configured for providing electromagnetic waves and a plasma corona, and a second signal generator can electromagnetically couple to a set of one or more resonators configured for providing electromagnetic waves, but not the plasma corona. 
     Furthermore, in some implementations, the signal provided by the signal generator  1802  to one or more resonators electromagnetically coupled to the signal generator  1802  can include a pulsed signal. In some of those implementations, the pulsed signal can, but need not necessarily, include a pulse train, a non-sinusoidal waveform, or a square wave. As an example, the pulsed signal provided by the signal generator  1802  can include a pulsed signal within the range of 100-1000 Hz. The frequency range of the pulsed signal can vary based on an amplifier used by and/or in conjunction with the signal generator  1802 . The pulsed signal has a duty cycle. The duty cycle can, but need not necessarily, be fifty percent on and fifty percent off. For instance, in some implementations, the duty cycle could be within the range twenty percent on and eighty percent off, to eighty percent on and twenty percent off. Increasing the duty cycle of the pulsed signal can result in transferring more energy to the resonator(s) receiving the pulsed signal. 
     The DC power source  1804  can be arranged like any DC power source discussed in this disclosure, such as the DC power source  302 . Moreover, the DC power source  1804  can include at least one DC power source (in other words, one or more DC power sources). For the implementations in which the afterburner  1300  includes a plurality of resonators, each resonator can be electromagnetically coupled to and/or configured to electromagnetically couple to a separate DC power source or to a DC power source electromagnetically coupled to and/or configured to electromagnetically couple to at least one other resonator of the plurality of resonators. 
     In an example implementation, the electrical circuitry connected to the signal generator  1802  and/or the DC power source  1804  can be routed along the outer surface  1434  of the casing  1402 . In another example implementation, the electrical circuitry connected to the signal generator  1802  and/or the DC power source  1804  can be routed to the port  1816 , at which point the electrical circuitry can pass through the casing  1402  to enter the afterburner  1300 . The electrical circuitry connected to the signal generator  1802  and/or the DC power source  1804  can also connect to a resonator of the afterburner  1300 , such as a resonator in a ring of resonators. As shown in  FIG. 18 , the electrical circuitry provided to the port  1818  can include an electrical circuit connected to the signal generator  1802  and an electrical circuit connected to the DC power source  1804 . In another implementation, two electrical circuits from the signal generator  1802  can be provided to the port  1818  for connection to a resonator disposed in the afterburner channel  1308 . 
     In an example implementation, the resonator of the afterburner  1300  can include a resonator completely disposed within the afterburner channel  1308 , a resonator partially disposed within the afterburner channel  1308  and partially disposed outside of the afterburner channel  1308 , and/or a resonator completely disposed outside of the afterburner channel  1308 . The resonator of the afterburner  1300  can include an electrode disposed within the afterburner channel  1308 . And the signal generator  1802  can be configured to excite the resonator of the afterburner  1300  with a radio frequency signal. Further, for implementations in which the resonator of the afterburner  1300  includes two conductors, the DC power source  1804  can be configured to provide a bias signal between those two conductors. 
     Exciting the resonator of the afterburner  1300  with the radio frequency signal can cause the resonator to provide electromagnetic waves and/or a plasma corona within the afterburner  1300 . In an example implementation in which the electrode of the resonator is disposed within the afterburner channel  1308 , that resonator can provide the electromagnetic waves and/or a plasma corona within the afterburner channel  1308 . In another example implementation, the resonator of the afterburner  1300  can provide the electromagnetic waves and/or a plasma corona within the torch igniter channel  1704 ,  1734 . In yet another example implementation, the resonator of the afterburner  1300  can provide the electromagnetic waves within a fuel supply line, such as the fuel supply line  1814 , a fuel supply line leading to a fuel outlet, and/or a fuel conduit within a resonator. 
     The fuel supply line  1814  can include and/or be fluidly coupled to a treatment chamber  1822 . In an example implementation, the treatment chamber  1822  can be within the afterburner channel  1308 . In another example implementation, the treatment chamber  1822  can be outside of the afterburner channel  1308 , such as a treatment chamber attached to the casing  1402 . At least a portion of a resonator  1824 , such as a distal end of the resonator  1824 , can be disposed within the treatment chamber  1822  and excited by a signal from the signal generator  1802  so that the electromagnetic waves can be used to modify the fuel in any of the ways presently discussed in order to “pretreat” the fuel within the treatment chamber  1822 . The fuel, after being exposed to electromagnetic waves in the treatment chamber  1822 , can flow through the fuel supply line  1814  to afterburner channel  1308  and/or a fuel outlet, such as a fuel outlet within a fuel conduit in a resonator. A portion of the fuel supply line  1814 , such as a portion between the treatment chamber  1822  and the afterburner channel  1308  and/or the fuel outlet can be made of a material, such as a metal or a rare earth magnetic material, that can insulate the electromagnetic effects of the pretreated fuel while the pretreated fuel is in transit within the fuel supply line  1814  from the treatment chamber  1822 . 
     The controller  1800  can be configured to perform a variety of operations. For example, the controller  1800  can be configured to cause fuel within a fuel tank, such as the fuel tank  1806 , to be pumped through a fuel supply line, such as fuel supply lines  1812 ,  1814 , and into the afterburner channel  1308  for mixing with a gas within the afterburner channel  1308 . The controller  1800  can be configured to cause fuel to be output through a fuel outlet, such as any fuel outlet discussed in this disclosure. As another example, the controller  1800  can be configured to cause the DC power source  1804  to switch from one operating state to another operating state, such as an operating state in which the DC power source  1804  is providing a bias signal between two conductors of a resonator of the afterburner  1300  to an operating state in which the DC power source  1804  is not providing the bias signal between those two conductors of the resonator. As another example, the controller  1800  can be configured to cause the signal generator  1802  to output a radio frequency signal. 
     The controller  1800  can control one or more DC power sources and/or one or more radio-frequency power sources connected to the resonators of a ring of resonators. In some implementations, the signal generator  1802  includes at least a first radio-frequency power source and a second radio-frequency power source, and the ring of resonators includes at least (i) a first resonator set having at least one resonator configured to be electromagnetically coupled to at least the first radio-frequency power source, and (ii) a second resonator set having at least one resonator configured to be electromagnetically coupled to at least the second radio-frequency power source. Each first radio-frequency power source is configured to provide the signal to at least one resonator of the first resonator set. Likewise, each second radio-frequency power source is configured to provide the signal to at least one resonator of the second resonator set. The DC power source  1804  can include one or more direct-current power source. Those direct-current power sources can provide a bias signal between the first conductor and the second conductor of each resonator in the ring of resonators. In some of the implementations, at least a portion of each resonator of the first ring of resonators is at least partially disposed in the afterburner channel  1308  upstream or downstream of the second ring of resonators. 
     The controller  1800  can include a processor, a memory, and a data transceiver. The processor can include one or more general purpose processors (for example, an INTEL® single core microprocessor or an INTEL® multicore microprocessor), and/or one or more special purpose processors (for example, a digital signal processor, a graphics processor, or an application specific integrated circuit (ASIC) processor). The processor can be configured to execute computer-readable program instructions. The processor can be configured to execute hard-coded functionality in addition to or instead of software-coded functionality. 
     The memory can include one or more memories. The memory can comprise a non-transitory memory or a transitory memory. The non-transitory memory can be located within or as part of the processor (for example, within a single integrated circuit chip) or can be separate and distinct from the processor. The non-transitory memory can include a volatile or non-volatile storage component, such as an optical, magnetic, organic or other memory or disc storage component. The non-transitory memory can include or be configured as a random-access memory (RAM), a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), or a compact disk read-only memory (CD-ROM). The RAM can include static RAM or dynamic RAM. 
     The data transceiver can include a receiver to receive data transmitted over a wired or wireless communication link, and a transmitter to transmit data over the wired or wireless communication link. In an example implementation, the controller  1800  can be arranged like the controller  402  shown in  FIG. 4B . 
     X. Resonator(s) in Afterburner Implementations 
       FIG. 19A  is a cross-sectional view of a fueling section  1900  for an example implementation in which a shape of at least a portion of the afterburner duct  1400  is annular. At least a portion of the casing  1402  can, but need not necessarily, have an annular shape. The fueling section  1900  is an example implementation of the fueling section  1422  shown in  FIG. 14 . 
     The fueling section  1900  includes a bracket  1902  within the afterburner channel  1308  and includes struts  1904 ,  1906 ,  1908 ,  1910 . The bracket  1902  can support the struts  1904 ,  1906 ,  1908 ,  1910 . A portion (not shown) of each of the struts  1904 ,  1906 ,  1908 ,  1910  can be disposed within a port in the afterburner duct  1400 . Portions  1916 ,  1918 ,  1920 ,  1922  of the struts  1904 ,  1906 ,  1908 ,  1910 , respectively, can be disposed within the cooling passage  1416 . A portion (not shown) of each of the struts  1904 ,  1906 ,  1908 ,  1910  can be disposed within a port in the casing  1402 . Further, a portion (not shown) of each of the struts  1904 ,  1906 ,  1908 ,  1910  can be disposed outside of the casing  1402  for attaching the struts  1904 ,  1906 ,  1908 ,  1910  to the casing  1402 . In some implementations, the struts  1904 ,  1906 ,  1908 ,  1910  are tubular struts with one or more passages. 
     In an example implementation, a strut supported by and/or attached to the bracket  1902  can be connected to a portion of a fuel supply line, such as the fuel supply line  1814 . A strut connected to the fuel supply line  1814  can include an outlet, such as an outlet  1912 , for outputting fuel into the afterburner channel  1308 . In another example implementation, a strut supported by and/or attached to the bracket  1902  can be connected to the fuel supply line  1814  and a resonator can be attached to the strut, such as a resonator  1914  attached to the strut  1904 . A strut connected to a fuel supply line can be part of that fuel supply line. 
     In another example implementation, a strut supported by and/or attached to the bracket  1902  can include a passage for electrical circuitry that is connected to the signal generator  1802  and/or the DC power source  1804 . In yet another example implementation, a strut supported by and/or attached to the bracket  1902  can include both a passage for the electrical circuitry and a portion of a fuel supply line. For the example implementations that include a strut supported by and/or attached to the bracket  1902 , the implementations can include a number of struts other than four struts as shown in  FIG. 19A . 
     The resonator  1914  can be configured as any resonator discussed in this disclosure. Electrical circuitry connected to the signal generator  1802  and/or the DC power source  1804  can connect to the resonator  1914 . In some example implementations, the resonator  1914  can include a fuel conduit. In accordance with those implementations, the fuel conduit can be fluidly coupled to a fuel passage within the strut  1904 . The resonator  1914  can be configured to provide electromagnetic waves and/or a plasma corona in response to being excited by a radio frequency signal from the signal generator  1802 . 
     Components, such as a fuel supply line and/or a fuel conduit, that are fluidly coupled are components connected together such that a fluid, such as a fuel, can flow from one component to the other component. In some implementations, two components can be fluidly coupled such that the fluid can flow from a first component to a second component and from the second component to the first component. In other implementations, two components can be fluidly coupled such that the fluid can flow from the first component to the second component, but not from the second component to the first component. Those other implementations can, for example, include a one-way check valve that prevents the fluid within the second component to flow into the first component. 
       FIG. 19B  is a cross-sectional view of the fueling section  1900 .  FIG. 19B  includes an arrow  1924  to indicate a direction that a gas could flow through the afterburner channel  1308  and the cooling passage  1416  within the fueling section  1900 . The vertical dashed lines in  FIG. 19B , as well as in  FIGS. 19D, 20B, 20D, 21B, 21D, 22B, 22D, 23B, and 23D  represent left and right ends of a section cut out of the afterburner  1300 , rather than any hidden feature show in those figures. 
       FIG. 19C  is a cross-sectional view of a fueling section  1930  for an example implementation in which a shape of at least a portion of the afterburner duct  1400  is annular. At least a portion of the casing  1402  can, but need not necessarily, have an annular shape The fueling section  1930  is an example implementation of the fueling section  1422  shown in  FIG. 14 , and is one of many possible variations of the fueling section  1900  shown in  FIG. 19A . This variation shows the fueling section  1930  with a resonator on multiple different struts. 
     The fueling section  1930  includes the bracket  1902  within the afterburner channel  1308  and includes the struts  1904 ,  1906 ,  1908 ,  1910 , as discussed above. The fueling section  1930  includes multiple resonators attached to the struts. As shown in  FIG. 19C , the resonator  1914  is attached to the r strut  1904 , and a resonator  1932  is attached to the strut  1908 . For the example implementations that include one or more struts in the fueling section  1930 , more than two resonators can be attached to the struts. Furthermore, more than one resonator can be attached to a single strut. 
     The resonator  1932  can be configured as any resonator discussed in this disclosure. Electrical circuitry connected to the signal generator  1802  and/or the DC power source  1804  can connect to the resonator  1932 . In some example implementations, the resonator  1932  can include a fuel conduit. In accordance with those implementations, the fuel conduit can be fluidly coupled to a fuel passage within the strut  1908 . The resonator  1932  can be configured to provide electromagnetic waves and/or a plasma corona in response to being excited by a radio frequency signal from the signal generator  1802 . 
       FIG. 19D  is a cross-sectional view of the fueling section  1930 .  FIG. 19D  includes an arrow  1924  to indicate a direction that a gas could flow through the afterburner channel  1308  and the cooling passage  1416  within the fueling section  1930 . A resonator, or at least a portion of a resonator that extends from the casing, through the duct, and into the afterburner channel  1308 , can be disposed between a strut of the fueling section  1900 ,  1930  and the open end  1406  or  1408  of the afterburner duct  1400 . 
       FIG. 20A  is a cross-sectional view of a resonator section  2000  for an example implementation in which a shape of at least a portion of the afterburner duct  1400  is annular. The casing  1402  can, but need not necessarily, have an annular shape. The resonator section  2000  is an example implementation of the resonator section  1426  shown in  FIG. 14 . 
     The resonator section  2000  includes a resonator  2002 . A portion  2004  of the resonator  2002  is disposed within the afterburner channel  1308 , and another portion of the resonator  2002  is disposed outside of the afterburner channel  1308 . In accordance with an example implementation, the portion of the resonator  2002  outside of the afterburner channel  1308  can include a portion  2006  outside of the casing  1402 , a portion  2008  between the afterburner duct  1400  and the casing  1402 , a portion (not shown) that is within a port in the afterburner duct  1400 , and a portion (not shown) that is within a port in the casing  1402 . The portion  2004  can include an electrode for providing electromagnetic waves and/or a plasma corona within the afterburner channel  1308  when the resonator  2002  is excited by a signal from the signal generator  1802 . 
     The resonator  2002  can be configured as any resonator discussed in this disclosure. Electrical circuitry connected to the signal generator  1802  and/or the DC power source  1804  can connect to the resonator portion  2006 . In this way, the electrical circuitry connected to the resonator  2002  does not have to be routed through the casing  1402 , through the afterburner duct  1400 , or within the afterburner channel  1308 . In some example implementations, the resonator  2002  can include a fuel conduit. In accordance with those implementations, a fuel supply line can connect to the portion  2006  so that the fuel supply line to the resonator  2002  does not have to be routed through the casing  1402 . 
       FIG. 20B  is a cross-sectional view of the resonator section  2000 .  FIG. 20B  includes an arrow  1924  to indicate a direction that a gas could flow through the afterburner channel  1308  and the cooling passage  1416  within the resonator section  2000 . 
       FIG. 20C  is a cross-sectional view of a resonator section  2010  for an example implementation in which a shape of at least a portion of the afterburner duct  1400  is annular. The casing  1402  can, but need not necessarily, have an annular shape. The resonator section  2010  is one of many possible variations of the resonator section  2000  shown in  FIG. 20 . This variation shows the resonator section  2010  with resonators at a top and bottom of the afterburner channel  1308 . 
     The resonator section  2010  includes multiple resonators.  FIG. 20C  shows the resonator  2002  and a resonator  2012 . As with the resonator  2002  discussed above, a portion  2014  of the resonator  2012  is disposed within the afterburner channel  1308 , and another portion of the resonator  2012  is disposed outside of the afterburner channel  1308 . Similarly, in accordance with an example implementation, the portion of the resonator  2012  outside of the afterburner channel  1308  can include a portion  2016  outside of the casing  1402 , a portion  2018  between the afterburner duct  1400  and the casing  1402 , a portion (not shown) that is within a port in the afterburner duct  1400 , and a portion (not shown) that is within a port in the casing  1402 . 
     As with the resonator  2002 , the resonator  2012  can be configured as any resonator discussed in this disclosure. Electrical circuitry connected to the signal generator  1802  and/or the DC power source  1804  can connect to the resonator portion  2016 . In this way, the electrical circuitry connected to the resonator  2012  does not have to be routed through the casing  1402 , through the afterburner duct  1400 , nor within the afterburner channel  1308 . In some example implementations, the resonator  2012  can include a fuel conduit. In accordance with those implementations, a fuel supply line can connect to the portion  2016  so that the fuel supply line to the resonator  2012  does not have to be routed through the casing  1402 . 
     The multiple resonators within the resonator section  2010  can be spaced apart equally. For example, adjacent resonators can be spaced apart by a common number of degrees. As shown in  FIG. 20C , the resonators  2002  and  2012  are spaced apart by one-hundred eighty degrees. If the multiple resonators within the resonator section  2010  include more than two resonators, those multiple resonators can, but need not necessarily, be spaced apart equally. The multiple resonators within the resonator section  2010  can be part of and/or form a ring of resonators. 
       FIG. 20D  is a cross-sectional view of the resonator section  2010 .  FIG. 20D  includes an arrow  1924  to indicate a direction that a gas could flow through the afterburner channel  1308  and the cooling passage  1416  within the resonator section  2010 . The portions  2004 ,  2014  can include an electrode for providing electromagnetic waves and/or a plasma corona within the afterburner channel  1308  when the resonators  2002 ,  2012 , respectively, are excited by a signal from the signal generator  1802 . As discussed above, the signal that excites multiple resonators can include multiple signals from one signal generator or multiple signals from multiple signal generators. 
     The resonators  2002 ,  2012  can be disposed such that an axis of each of those resonators is perpendicular to a central axis of the afterburner channel  1308 . Attaching the resonators  2002 ,  2012  to the casing  1402  and/or the duct as shown in  FIGS. 20A and 20B  may provide for easy installation of the resonators  2002 ,  2012  into the casing  1402  and/or the afterburner duct  1400 . 
       FIG. 21A  is a cross-sectional view of a resonator section  2100  for an example implementation in which a shape of at least a portion of the afterburner duct  1400  is annular. At least a portion of the casing  1402  can, but need not necessarily, have an annular shape. The resonator section  2100  is an example implementation of the resonator section  2000  shown in  FIG. 20 . 
     The resonator section  2100  includes a resonator  2102  within the afterburner channel  1308 . The resonator  2102  can be disposed in proximity to one or more ports in the afterburner duct  1400  that are aligned with a respective port in the casing  1402 . Electrical circuitry and/or a fuel supply line can be routed through those ports into the afterburner channel  1308  for connecting to the resonator  2102 . Furthermore, the resonator section  2100  can include a strut  2108  disposed within a port in the afterburner duct  1400  and a port in the casing  1402 . The electrical circuitry and/or the fuel supply line can be routed through one or more passages in the strut  2108 . 
     The resonator  2102  can be configured as any resonator discussed in this disclosure. Electrical circuitry connected to the signal generator  1802  and/or the DC power source  1804  can connect to the resonator  2102 . In some example implementations, the resonator  2102  can include a fuel conduit. The resonator  2102  can be clamped or otherwise attached to the afterburner duct  1400 . 
     The resonator  2102  includes ends  2104  and  2106 . In an example implementation, the end  2104  can be a proximal end of any example resonator and the end  2106  can be a distal end of that example resonator. In accordance with this implementation, the portion of the resonator extending from the proximal end  2104  to the distal end  2106  can be used to shield the distal end  2106  from the gas flowing within the afterburner channel  1308 . In another example implementation, the end  2104  can be a distal end of any example resonator and the end  2106  can be a proximal end of that example resonator. In accordance with this implementation, the electromagnetic waves provided by the resonator  2102  can affect the gas flowing within the afterburner channel  1308 . A distal end of the resonator  2012  can include an electrode for providing electromagnetic waves and/or a plasma corona within the afterburner channel  1308  when the resonator  2102  is excited by a signal from the signal generator  1802 . 
       FIG. 21B  is a cross-sectional view of the resonator section  2100 .  FIG. 21B  includes an arrow  1924  to indicate a direction that a gas could flow through the afterburner channel  1308  and the cooling passage  1416  within the resonator section  2100 . 
       FIG. 21C  is a cross-sectional view of a resonator section  2110  for an example implementation in which a shape of at least a portion of the afterburner duct  1400  is annular. The casing  1402  can, but need not necessarily, have an annular shape. The resonator section  2110  is one of many possible variations of the resonator section  2000  shown in  FIG. 20 . This variation shows the resonator section  2110  with resonators at a top and bottom of the afterburner channel  1308 . 
     The resonator section  2110  includes multiple resonators.  FIG. 21C  shows the resonator  2102  and a resonator  2112 . The resonator  2112  can be disposed in proximity to one or more ports in the afterburner duct  1400  that are aligned with a respective port in the casing  1402 . Electrical circuitry and/or a fuel supply line can be routed through those ports into the afterburner channel  1308  for connecting to the resonator  2112 . 
     As with the resonator  2102 , the resonator  2112  can be configured as any resonator discussed in this disclosure. Electrical circuitry connected to the signal generator  1802  and/or the DC power source  1804  can connect to the resonator  2112 . In some example implementations, the resonator  2112  can include a fuel conduit. The resonator section  2110  can include multiple struts, such as the strut  2108  and a strut  2118  disposed within a port in the afterburner duct  1400  and a port in the casing  1402 . The electrical circuitry and/or the fuel supply line can be routed through one or more passages in the strut  2108 ,  2118 . The resonator  2112  can be clamped to the afterburner duct  1400 . The resonator  2112  includes ends  2114  and  2116 , which can be configured as the ends  2104 ,  2106 . 
     The multiple resonators within the resonator section  2110  can be spaced apart equally. For example, adjacent resonators can be spaced apart by a common number of degrees. As shown in  FIG. 21C , the resonators  2102  and  2112  are spaced apart by one-hundred eighty degrees. If the multiple resonators within the resonator section  2110  include more than two resonators, those multiple resonators can, but need not necessarily, be spaced apart equally. The multiple resonators within the resonator section  2110  can be part of and/or form a ring of resonators. 
       FIG. 21D  is a cross-sectional view of the resonator section  2110 .  FIG. 21D  includes an arrow  1924  to indicate a direction that a gas could flow through the afterburner channel  1308  and the cooling passage  1416  within the resonator section  2110 . 
     In an example implementation, a resonator within the resonator section  2100  can be disposed within the afterburner channel  1308  such that an axis of that resonator is parallel to a central axis of the afterburner channel  1308 . In another example implementation, a resonator within the resonator section  2100  can be disposed within the afterburner channel  1308  such that an axis of that resonator is oblique to the central axis of the afterburner channel  1308  and parallel to the afterburner duct  1400  proximate to that resonator. In yet another example implementation, a resonator within the resonator section  2100  can be disposed within the afterburner channel  1308  such that an axis of that resonator is oblique to the central axis of the afterburner channel  1308  and oblique to the afterburner duct  1400  proximate to that resonator. 
       FIG. 22A  is a cross-sectional view of a resonator section  2200  for an example implementation in which a shape of at least a portion of the afterburner duct  1400  is annular. The casing  1402  can, but need not necessarily, have an annular shape. The resonator section  2200  is an example implementation of the resonator section  2000  shown in  FIG. 20 . 
     The resonator section  2200  includes a resonator  2202 . A portion  2204  of the resonator  2202  is disposed within the afterburner channel  1308 , and another portion of the resonator  2202  is disposed outside of the afterburner channel  1308 . In accordance with an example implementation, the portion of the resonator  2202  outside of the afterburner channel  1308  can include a portion  2206  outside of the casing  1402 , a portion  2208  between the afterburner duct  1400  and the casing  1402 , a portion (not shown) that is within a port in the afterburner duct  1400 , and a portion (not shown) that is within a port in the casing  1402 . The portion  2204  can include an electrode for providing electromagnetic waves and/or a plasma corona within the afterburner channel  1308  when the resonator  2202  is excited by a signal from the signal generator  1802 . 
     The resonator  2202  is disposed obliquely to the afterburner duct  1400  and/or the casing  1402  such that the portion  2204  is further downstream in the afterburner  1300  as compared to the portion  2206 . Attaching the resonator  2202  obliquely in that manner allows for some of the portion  2204  to block and/or redirect the gas flowing in proximity to the portion  2204  so as to help provide a better shaped plasma corona and/or to help improve fuel injection from a fuel conduit, if included within the resonator  2202 . 
     The resonator  2202  can be configured as any resonator discussed in this disclosure. Electrical circuitry connected to the signal generator  1802  and/or the DC power source  1804  can connect to the resonator portion  2206 . In this way, the electrical circuitry connected to the resonator  2202  does not have to be routed through the casing  1402 , through the afterburner duct  1400 , nor within the afterburner channel  1308 . In some example implementations, the resonator  2202  can include a fuel conduit. In accordance with those implementations, a fuel supply line can connect to the portion  2206  so that the fuel supply line to the resonator  2202  does not have to be routed through the casing  1402 . 
       FIG. 22B  is a cross-sectional view of the resonator section  2200 .  FIG. 22B  includes an arrow  1924  to indicate a direction that a gas could flow through the afterburner channel  1308  and the cooling passage  1416  within the resonator section  2200 . 
       FIG. 22C  is a cross-sectional view of a resonator section  2210  for an example implementation in which a shape of at least a portion of the afterburner duct  1400  is annular. The casing  1402  can, but need not necessarily, have an annular shape. The resonator section  2210  is one of many possible variations of the resonator section  2000  shown in  FIG. 20 . This variation shows the resonator section  2210  with resonators at a top and bottom of the afterburner channel  1308 . 
     The resonator section  2210  includes multiple resonators.  FIG. 22C  shows the resonator  2202  and a resonator  2212 . The portions of the resonator  2202  are discussed above. A portion  2214  of the resonator  2212  is disposed within the afterburner channel  1308 , and another portion of the resonator  2212  is disposed outside of the afterburner channel  1308 . In accordance with an example implementation, the portion of the resonator  2212  outside of the afterburner channel  1308  can include a portion  2216  outside of the casing  1402 , a portion  2218  between the afterburner duct  1400  and the casing  1402 , a portion (not shown) that is within a port in the afterburner duct  1400 , and a portion (not shown) that is within a port in the casing  1402 . 
     As with the resonator  2202 , the resonator  2212  is disposed obliquely to the afterburner duct  1400  and/or the casing  1402  such that the portion  2214  is further downstream in the afterburner  1300  as compared to the portion  2216 . Attaching the resonator  2212  obliquely in that manner allows for some of the portion  2214  to block and/or redirect the gas flowing in proximity to the portion  2214  so as to provide a better shaped plasma corona and/or for improved fuel injection from a fuel conduit, if included within the resonator  2212 . 
     The resonator  2212  can be configured as any resonator discussed in this disclosure. Electrical circuitry connected to the signal generator  1802  and/or the DC power source  1804  can connect to the resonator portion  2216 . In this way, the electrical circuitry connected to the resonator  2212  does not have to be routed through the casing  1402 , through the afterburner duct  1400 , nor within the afterburner channel  1308 . In some example implementations, the resonator  2212  can include a fuel conduit. In accordance with those implementations, a fuel supply line can connect to the portion  2216  so that the fuel supply line to the resonator  2212  does not have to be routed through the casing  1402 . 
     The multiple resonators within the resonator section  2210  can be spaced apart equally. For example, adjacent resonators can be spaced apart by a common number of degrees. As shown in  FIG. 22C , the resonators  2202  and  2212  are spaced apart by one-hundred eighty degrees. If the multiple resonators within the resonator section  2210  include more than two resonators, those multiple resonators can, but need not necessarily, be spaced apart equally. The multiple resonators within the resonator section  2210  can be part of and/or form a ring of resonators. 
       FIG. 22D  is a cross-sectional view of the resonator section  2210 .  FIG. 22D  includes an arrow  1924  to indicate a direction that a gas could flow through the afterburner channel  1308  and the cooling passage  1416  within the resonator section  2210 . The portions  2204 ,  2214  can include an electrode for providing electromagnetic waves and/or a plasma corona within the afterburner channel  1308  when the resonators  2202 ,  2212 , respectively, are excited by a signal from the signal generator  1802 . 
       FIG. 23A  is a cross-sectional view of a resonator section  2300  for an example implementation in which a shape of at least a portion of the afterburner duct  1400  is annular. The casing  1402  can, but need not necessarily, have an annular shape. The resonator section  2300  is an example implementation of the resonator section  2000  shown in  FIG. 20 . This variation is an example implementation in which a resonator section includes multiple resonators and multiple rings of at least one resonator.  FIG. 23B  is a cross-sectional view of the resonator section  2300 .  FIG. 23B  shows a resonator  2302  and a resonator  2310  at a top of the afterburner channel  1308 . 
     As shown in  FIG. 23B , a portion  2304  of the resonator  2302  is disposed within the afterburner channel  1308 , and another portion of the resonator  2302  is disposed outside of the afterburner channel  1308 . In accordance with an example implementation, the portion of the resonator  2302  outside of the afterburner channel  1308  can include a portion  2306  outside of the casing  1402 , a portion  2308  between the afterburner duct  1400  and the casing  1402 , a portion (not shown) that is within a port of the afterburner duct  1400 , and a portion (not shown) that is within a port of the casing  1402 . 
     Similarly, as shown in  FIG. 23B , a portion  2312  of the resonator  2310  is disposed within the afterburner channel  1308 , and another portion of the resonator  2310  is disposed outside of the afterburner channel  1308 . In accordance with an example implementation, the portion of the resonator  2310  outside of the afterburner channel  1308  can include a portion  2314  outside of the casing  1402 , a portion  2316  between the afterburner duct  1400  and the casing  1402 , a portion (not shown) that is within the afterburner duct  1400 , and a portion (not shown) that is within the casing  1402 . 
     The portions  2304 ,  2312  of the resonators  2302 ,  2310  can include a respective electrode for providing electromagnetic waves and/or a plasma corona within the afterburner channel  1308  when the resonators  2302 ,  2310 , respectively, are excited by a signal from the signal generator  1802 . 
     The resonators  2302 ,  2310  are disposed obliquely to the afterburner duct  1400  and/or the casing  1402  such that the portions  2304 ,  2312  are further downstream in the afterburner  1300  as compared to the portions  2306 ,  2314 , respectively. Attaching the resonators  2302 ,  2310  obliquely in that manner allows for some of the portion  2304  to block and/or redirect the gas flowing in proximity to the portion  2304  and some of the portion  2312  to block and/or redirect the gas flowing in proximity to the portion  2312 , so as to provide a better shaped plasma corona and/or for improved fuel injection from a fuel conduit, if included within the resonators  2302 ,  2310 . In an example implementation, the resonators  2302 ,  2310  can be at different angles than each other. 
     The resonators  2302 ,  2310  can be configured as any resonator discussed in this disclosure. Electrical circuitry connected to the signal generator  1802  and/or the DC power source  1804  can connect to the resonator portions  2306 ,  2314 . In this way, the electrical circuitry connected to the resonator  2302 ,  2310  does not have to be routed through the casing  1402 , through the afterburner duct  1400 , nor within the afterburner channel  1308 . In some example implementations, the resonator  2302  and/or the resonator  2310  can include a fuel conduit. In accordance with those implementations, a fuel supply line can connect to the portion  2306  and/or the portion  2314  so that the fuel supply line(s) to the resonator  2302  and/or the resonator  2310  do not have to be routed through the casing  1402 . 
       FIG. 23B  includes an arrow  1924  to indicate a direction that a gas could flow through the afterburner channel  1308  and the cooling passage  1416  within the resonator section  2300 . In an example implementation, the resonator  2310 , being upstream of the resonator  2302 , can include a fuel conduit to transport fuel to be exposed to electromagnetic waves provided when the resonator  2310  is excited with a radio-frequency signal from the signal generator  1802 . The fuel can be treated by the electromagnetic waves while the fuel is in the fuel conduit and/or after the fuel is output by a fuel outlet. In accordance with the foregoing implementation, the resonator  2302 , being downstream of the resonator  2310 , can be excited with a radio-frequency signal from the signal generator  1802  in order to provide a plasma corona for causing combustion of fuel output by the resonator  2310 . The resonator  2310  can, but need not necessarily, generate a plasma corona for causing combustion of fuel. 
       FIG. 23C  is a cross-sectional view of a resonator section  2320  for an example implementation in which a shape of at least a portion of the afterburner duct  1400  is annular. The casing  1402  can, but need not necessarily, have an annular shape. The resonator section  2320  is one of many possible variations of the resonator section  2000  shown in  FIG. 20 . This variation shows the resonator section  2010  with multiple resonators at a top of the afterburner channel  1308  and multiple resonators at a bottom of the afterburner channel  1308 .  FIG. 23D  is a cross-sectional view of the resonator section  2320 . 
     The resonator section  2320  includes multiple resonators.  FIG. 23D  shows resonators  2302 ,  2310 ,  2322 ,  2330 . The portions of the resonators  2302 ,  2310  are discussed above. A portion  2324  of the resonator  2322  is disposed within the afterburner channel  1308 , and another portion of the resonator  2322  is disposed outside of the afterburner channel  1308 . In accordance with an example implementation, the portion of the resonator  2322  outside of the afterburner channel  1308  can include a portion  2326  outside of the casing  1402 , a portion  2328  between the afterburner duct  1400  and the casing  1402 , a portion (not shown) that is within a port in the afterburner duct  1400 , and a portion (not shown) that is within a port in the casing  1402 . 
     Similarly, a portion  2332  of the resonator  2330  is disposed within the afterburner channel  1308 , and another portion of the resonator  2330  is disposed outside of the afterburner channel  1308 . In accordance with an example implementation, the portion of the resonator  2330  outside of the afterburner channel  1308  can include a portion  2334  outside of the casing  1402 , a portion  2336  between the afterburner duct  1400  and the casing  1402 , a portion (not shown) that is within a port in the afterburner duct  1400 , and a portion (not shown) that is within a port in the casing  1402 . 
     The portions  2324 ,  2332  of the resonators  2322 ,  2330  can include a respective electrode for providing electromagnetic waves and/or a plasma corona within the afterburner channel  1308  when the resonators  2322 ,  2330 , respectively, are excited by a signal from the signal generator  1802 . 
     The resonators  2322 ,  2330  are disposed obliquely to the afterburner duct  1400  and/or the casing  1402  such that the portions  2324 ,  2332  are further downstream in the afterburner  1300  as compared to the portions  2326 ,  2334 , respectively. Attaching the resonators  2322 ,  2330  obliquely in that manner allows for some of the portion  2324  to block and/or redirect the gas flowing in proximity to the portion  2324  and some of the portion  2332  to block and/or redirect the gas flowing in proximity to the portion  2332 , so as to provide a better shaped plasma corona and/or for improved fuel injection from a fuel conduit, if included within the resonators  2302 ,  2310 . 
     The resonator  2322 ,  2330  can be configured as any resonator discussed in this disclosure. Electrical circuitry connected to the signal generator  1802  and/or the DC power source  1804  can connect to the resonator portions  2326 ,  2336 . In this way, the electrical circuitry connected to the resonators  2322 ,  2330  does not have to be routed through the casing  1402 , through the afterburner duct  1400 , nor within the afterburner channel  1308 . In some example implementations, the resonator  2322  and/or the resonator  2330  can include a fuel conduit. In accordance with those implementations, a fuel supply line can connect to the portion  2326  and/or the portion  2336  so that the fuel supply line(s) to the resonator  2322  and/or the resonator  2330  do not have to be routed through the casing  1402 . 
     In an example implementation, at least some of the multiple resonators disposed partly within the resonator section  2320  can be arranged as a ring of resonators or multiple rings of resonators. As an example, the resonator section  2320  can include a first ring of resonators within a first cross section of the resonator section  2320  including the resonators  2310 ,  2330 , and a second ring of resonators within a second cross section of the resonator section  2320  including the resonators  2302 ,  2322 . As another example, some of the multiple resonators disposed partly within the resonator section  2320  can be within a ring of resonators in which the resonators of the ring are equally spaced from one another around the inner surface  1432  of the afterburner duct  1400 . The equal spacing between resonators can be defined as a number of degrees, such as one hundred eighty degree spacing between the resonators  2302  and  2322 . In another example implementation, the multiple resonators disposed partly within the resonator section  2320  can be disposed in proximity to one another in a particular part of resonator section  2320 , such as at a top of the inner surface  1432 . If the multiple resonators within the resonator section  2320  include more than two resonators, those multiple resonators can, but need not necessarily, be spaced apart equally. 
       FIG. 23D  includes an arrow  1924  to indicate a direction that a gas could flow through the afterburner channel  1308  and the cooling passage  1416  within the resonator section  2320 . In an example implementation, the resonator  2330 , being upstream of the resonator  2322 , can include a fuel conduit for outputting fuel to be exposed to electromagnetic waves provided when the resonator  2330  is excited with a radio-frequency signal from the signal generator  1802 . The fuel can be treated by the electromagnetic waves while the fuel is in the fuel conduit and/or after the fuel is output by a fuel outlet. In accordance with the foregoing implementation, the resonator  2322 , being downstream of the resonator  2330 , can be excited with a radio-frequency signal from the signal generator  1802  in order to provide a plasma corona for causing combustion of fuel output by the resonator  2330 . The resonator  2322  can, but need not necessarily, generate a plasma corona for causing combustion of fuel. 
     The fueling sections  1900 ,  1930  shown in  FIGS. 19A-D  and the resonator sections  2000 ,  2010 ,  2100 ,  2110 ,  2200 ,  2210 ,  2300 ,  2320  shown in  FIGS. 20A-23D  are shown with the afterburner duct  1400  and the casing  1402  having an annular cross-section. The afterburner duct  1400  and the casing  1402  for the afterburner  1300  can have different shaped cross-sections, such as an elliptical cross-section, a rectangular cross-section or a different shaped cross-section. 
     The resonator in the resonator sections  2000 ,  2100 ,  2200 ,  2300  is shown as being at a top portion of the afterburner channel  1308 . The resonators in the resonator sections  2010 ,  2110 ,  2210 ,  2320  are shown as being at a top or bottom portion of the afterburner channel  1308 . In other example implementations, the resonator can be located at a portion of the afterburner channel  1308  other than the top or bottom portion of the afterburner channel  1308 . Multiple resonators in a resonator section of the afterburner  1300  can be arranged a ring of resonators. The afterburner  1300  can include multiple rings of resonators, such as a first ring of resonators in the fueling section  1422  and a second ring of resonators in the resonator section  1426 . The first ring of resonators can include a first set of resonators and the second ring of resonators can include a second set of resonators. At least one signal generator  1802  can provide a signal to each resonator of the first set of resonators, and to each resonator of the second set of resonators. Moreover, at least one DC power source  1804  can provide a signal to each resonator of the first set of resonators, and/or each resonator of the second set of resonators. 
     The afterburner  1300  can include a ring of resonators within a section of the afterburner  1300 , such as a fueling section  1422 ,  1900 ,  1930 , a resonator section  1426 ,  2000 ,  2010 ,  2100 ,  2110 ,  2200 ,  2210 ,  2300 ,  2320 , or some other cross-section of the afterburner  1300 . A ring of resonators includes multiple resonators. In an example implementation, a resonator of a ring of resonators can be (i) disposed partly within the afterburner channel  1308  and disposed partly outside of the afterburner channel  1308 , or disposed completely within the afterburner channel  1308 . In an example implementation, the resonators of a ring of resonators can be equally spaced from one another. In an example implementation, the resonators of a ring of resonators can be staggered within the afterburner channel  1308  such that some of the resonators within the afterburner channel  1308  are downstream of other resonators of the ring of resonators within the afterburner channel  1308 . In an example implementation, a resonator in a ring of resonators can be disposed in the afterburner  1300  such that a center axis of the resonator is perpendicular, parallel, or oblique to a portion of the afterburner duct  1400  in proximity to the resonator.  FIG. 24A  to  FIG. 27D , discussed below, illustrate additional examples of a ring of resonators. 
       FIG. 24A  is a cross-sectional view of a resonator section  2400  for an example implementation in which a shape of at least a portion of the afterburner duct  1400  is elliptical. At least a portion of the casing  1402  can, but need not necessarily, have an elliptical shape. The resonator section  2400  is another one of the many variation of the resonator section  2000  shown in  FIG. 20 .  FIG. 24A  shows the cooling passage  1416 , the afterburner channel  1308 , and a longitudinal axis  2420  of the afterburner channel  1308 . 
       FIG. 24B  is a cross-sectional view of the resonator section  2400 .  FIG. 24B  shows the longitudinal axis  2420  as an arrow. A gas could flow through the afterburner channel  1308  and the cooling passage  1416  within the resonator section  2400  in a direction shown by that arrow. 
     The resonator section  2400  includes a bracket  2402 , multiple struts, and a ring of resonators including multiple resonators. At least a portion of the bracket  2402  is disposed in the afterburner channel  1308 . The bracket  2402  includes an upstream end  2422  and a downstream end  2424 . A bracket within a resonator section, such as the bracket  2402 , can provide support for at least one resonator. In an example implementation, the at least one resonator supported by a bracket in a resonator section can be disposed at least partially within the bracket and/or can attach to a surface of the bracket. A bracket within a resonator section can be made from a metal tube or a metal bar, for example. 
     The bracket  2402  can, but need not necessarily, have an elliptical shape. Any bracket described as having an elliptical shape can be annular and/or circular. Furthermore, any portion of the afterburner duct  1400  described as having an elliptical shape can be annular and/or circular. Furthermore still, any portion of the casing  1402  described as having an elliptical shape can be annular and/or circular. Furthermore still, a bracket in a resonator section, such as the bracket  2402 , can be at least partially hollow, as shown in  FIG. 24B . 
     As shown in  FIG. 24A , a ring of resonators within a resonator section can include four resonators, such as resonators  2412 ,  2414 ,  2416 ,  2418 . In an alternative implementation, a ring of resonators within a resonator section can include fewer or more than four resonators. Furthermore, each resonator within a resonator section can be configured as any resonator discussed in this description. 
     As shown in  FIG. 24B , the resonators  2412 ,  2414 ,  2416 , are disposed within the bracket  2402 . Likewise, the resonator  2418  can be disposed within the bracket  2402 . In alternative implementations in which a portion of a resonator is disposed within a bracket, a portion of the resonator can extend upstream beyond an upstream end of the bracket and/or a portion of the resonator can extend downstream of a downstream end of the bracket. For instance, a proximal end of the resonator  2416  can extend upstream in the afterburner channel  1308  beyond the upstream end  2422  and/or a distal end of the resonator  2416  can extend downstream in the afterburner channel  1308  beyond the downstream end  2424 . A resonator may extend beyond a bracket in a resonator section to improve ease in connecting a fuel conduit and/or electrical circuitry to the resonator. Furthermore, a resonator may extend beyond a bracket in a resonator section to increase the likelihood that the bracket does not interfere with a plasma corona generated by the resonator. 
     As further shown in  FIG. 24A , the multiple struts of a resonator section can include four struts, such as struts  2404 ,  2406 ,  2408 ,  2410 . In an alternative implementation, a resonator section can include fewer or more than four struts. A strut in a resonator section can support (i) a bracket in the resonator section, such as the bracket  2402 , and/or a resonator in the resonator section, such as the resonator  2412 ,  2414 ,  2416 ,  2418 . A strut in a resonator section, such as the strut  2404 ,  2406 ,  2408 ,  2410 , can have a portion of the strut disposed within a port in the afterburner duct  1400 . Similarly, a strut in a resonator section, such as the strut  2404 ,  2406 ,  2408 ,  2410 , can have a portion of the strut disposed within a port in the casing  1402 . 
     In an example implementation, at least one strut within a resonator section, such as the strut  2404 ,  2406 ,  2408 ,  2410  in the resonator section  2400 , can include at least one passage. As an example, a passage within a strut can extend from the casing  1402  to (i) a bracket, such as the bracket  2402 , and/or (ii) a resonator within the resonator section including that strut. As another example, a passage within a strut can extend just partially through the strut. Such a passage can be configured for carrying fuel. A passage for carrying fuel can, but need not necessarily, extend from one end of that strut to some point before the opposite end of the strut so that the strut does not expel fuel through the opposite end of the strut. That strut may include one or more fuel outlets between the two ends of the strut. 
     Furthermore, electrical circuitry connectable to a resonator within a resonator section, such as the resonator section  2400 , can be routed through a passage in a strut, such as the strut  2404 ,  2406 ,  2408 ,  2410 . Furthermore still, electrical circuitry connectable to a resonator within a resonator section can be routed through a first passage in a strut and fuel can flow through a second passage in that strut. In an implementation in which a strut includes a fuel passage, the strut can include one or more fuel outlets for outputting fuel from the strut to the afterburner channel  1308 . In another implementation in which a strut includes a fuel passage, the strut can pass the fuel to a fuel conduit within a resonator. 
       FIG. 24A  and/or  FIG. 24B  illustrate the resonators  2412 ,  2414 ,  2416 ,  2418  disposed such that a longitudinal axis of each of the resonators  2412 ,  2414 ,  2416 ,  2418  is parallel to the longitudinal axis  2420 . In an alternative implementation, a longitudinal axis of at least one resonator  2412 ,  2414 ,  2416 ,  2418  is oblique to the longitudinal axis  2420 . 
       FIG. 24C  is a cross-sectional view of a resonator section  2430  for an example implementation in which a shape of at least a portion of the afterburner duct  1400  is elliptical. At least a portion of the casing  1402  can, but need not necessarily, have an elliptical shape. The resonator section  2430  is one of many possible variations of the resonator section  2000  shown in  FIG. 20 . This variation includes a bracket  2432  having an outer exterior surface  2452 , an inner exterior surface  2454 , an upstream end  2456 , a downstream end  2458 , and multiple resonators attached to the inner exterior surface  2454  and/or attached in proximity to the inner exterior surface  2454 .  FIG. 24C  shows the cooling passage  1416 , the afterburner channel  1308 , and a longitudinal axis  2450  of the afterburner channel  1308 . 
       FIG. 24D  is a cross-sectional view of the resonator section  2430 .  FIG. 24D  shows the longitudinal axis  2450  as an arrow. A gas could flow through the afterburner channel  1308  and the cooling passage  1416  within the resonator section  2430  in a direction shown by that arrow. 
     The resonator section  2430  includes the bracket  2432 , multiple struts, and a ring of resonators including multiple resonators. As shown in  FIG. 24C , the ring of resonators of the resonator section  2430  includes resonators  2442 ,  2444 ,  2446 ,  2448 . The multiple struts of the resonator section  2430  include struts  2434 ,  2436 ,  2438 ,  2440 . The bracket  2432  can, but need not necessarily, have an elliptical shape.  FIG. 24D  shows that a resonator section can include a bracket (for example, the bracket  2432 ) having at least a portion that is solid. 
     As shown in  FIG. 24D , the resonators  2442 ,  2444 ,  2446  are attached to the inner exterior surface  2454  and/or in proximity to the inner exterior surface  2554 . Likewise, the resonator  2448  can be attached to the inner exterior surface  2454  and/or in proximity to the inner exterior surface  2554 . In alternative implementations in which a portion of a resonator is attached to an inner or outer exterior surface of a bracket and/or in proximity to the inner or outer exterior surface of the bracket, a portion of the resonator can extend upstream beyond an upstream end of the bracket and/or a portion of the resonator can extend downstream of a downstream end of the bracket. For instance, a proximal end of the resonator  2444  can extend upstream in the afterburner channel  1308  beyond the upstream end  2456  and/or a distal end of the resonator  2444  can extend downstream in the afterburner channel  1308  beyond the downstream end  2458 . 
       FIG. 24C  and/or  FIG. 24D  illustrate the resonators  2442 ,  2444 ,  2446 ,  2448  disposed such that a longitudinal axis of each of the resonators  2442 ,  2444 ,  2446 ,  2448  is parallel to the longitudinal axis  2450 . In an alternative implementation, a longitudinal axis of at least one resonator  2442 ,  2444 ,  2446 ,  2448  is oblique to the longitudinal axis  2450 . 
       FIG. 25A  is a cross-sectional view of a resonator section  2500  for an example implementation in which a shape of at least a portion of the afterburner duct  1400  is elliptical. At least a portion of the casing  1402  can, but need not necessarily, have an elliptical shape. The resonator section  2500  is one of many possible variations of the resonator section  2000  shown in  FIG. 20 . This variation includes the bracket  2432  and multiple resonators attached to the outer exterior surface  2452  and/or attached in proximity to the outer exterior surface  2452 .  FIG. 25A  shows the cooling passage  1416 , the afterburner channel  1308 , and the longitudinal axis  2450 .  FIG. 25B  is a cross-sectional view of the resonator section  2500 . 
     The resonator section  2500  includes the bracket  2432 , multiple struts, and a ring of resonators including multiple resonators. As shown in  FIG. 25A , the ring of resonators within the resonator section  2500  includes resonators  2502 ,  2504 ,  2506 ,  2508 . The multiple struts of the resonator section  2500  include struts  2404 ,  2406 ,  2408 ,  2410 . 
     As shown in  FIG. 25B , the resonators  2502 ,  2504 ,  2506  are attached to the outer exterior surface  2452  and/or in proximity to the outer exterior surface  2452 . Likewise, the resonator  2508  can be attached to the outer exterior surface  2452  and/or in proximity to the outer exterior surface  2452 .  FIG. 25B  shows the resonators  2502 ,  2504 ,  2506  disposed between the upstream end  2456  and the downstream end  2458 . Similarly, the resonator  2508  can be disposed between the upstream end  2456  and the downstream end  2458 . 
       FIG. 25A  and/or  FIG. 25B  illustrate the resonators  2502 ,  2504 ,  2506 ,  2508  disposed such that a longitudinal axis of each of the resonators  2502 ,  2504 ,  2506 ,  2508  is parallel to the longitudinal axis  2450 . In an alternative implementation, a longitudinal axis of at least one resonator  2502 ,  2504 ,  2506 ,  2508  is oblique to the longitudinal axis  2450 . 
       FIG. 25C  is a cross-sectional view of a resonator section  2530  for an example implementation in which a shape of at least a portion of the afterburner duct  1400  is elliptical. At least a portion of the casing  1402  can, but need not necessarily, have an elliptical shape. The resonator section  2530  is one of many possible variations of the resonator section  2000  shown in  FIG. 20 . This variation includes multiple resonators attached to the afterburner duct  1400 .  FIG. 25C  shows the cooling passage  1416 , the afterburner channel  1308 , and a longitudinal axis  2532  of the afterburner channel  1308 . 
       FIG. 25D  is a cross-sectional view of the resonator section  2530 .  FIG. 25D  shows the longitudinal axis  2532  as an arrow. A gas could flow through the afterburner channel  1308  and the cooling passage  1416  within the resonator section  2430  in a direction shown by that arrow. 
     The resonator section  2530  further includes a ring of resonators including multiple resonators arranged. As shown in  FIG. 25C , the ring of resonators of the resonator section  2530  includes resonators  2534 ,  2536 ,  2538 ,  2540 . The resonators  2534 ,  2536 ,  2538 ,  2540  are attached to the afterburner duct  1400 . In an implementation, a resonator attached to the afterburner duct  1400  can have a portion of the resonator disposed within the afterburner duct  1400 . Furthermore, a resonator attached to the afterburner duct  1400  can have a portion of the resonator disposed within the afterburner duct  1400  and another portion of the resonator disposed within the casing  1402 . Furthermore still, a resonator attached to the afterburner duct  1400  can have a portion of the resonator disposed in the afterburner channel  1308 , another portion of the resonator disposed in the afterburner duct  1400 , and another portion disposed in the casing  1402 . Furthermore still, a resonator attached to the afterburner duct  1400  can have a portion of the resonator disposed in the afterburner channel  1308 , a portion of the resonator disposed in the afterburner duct  1400 , a portion of the resonator disposed in the casing  1402 , and a portion of the resonator disposed outside of the casing  1402 . A portion of a resonator disposed within the afterburner duct  1400  can be disposed within a port in the afterburner duct  1400 . Likewise, a portion of a resonator disposed within the casing  1402  can be disposed within a port in the casing  1402 . In another implementation, a resonator attached to the afterburner duct  1400  can be disposed entirely within the afterburner channel  1308 . As an example, one or more clamps and/or fasteners can be used to attach a resonator to the afterburner duct  1400 . 
     In an implementation, electrical circuitry and/or a fuel supply line connectable to a resonator within a resonator section can be routed along the casing  1402  and connected to the resonator outside of the casing. In another implementation, electrical circuitry and/or a fuel supply line connectable to a resonator within a resonator section can be routed through a port in the casing  1402  and/or a port in the afterburner duct  1400  for routing to the resonator. 
       FIG. 25D  illustrates the resonators  2534 ,  2536 ,  2538  are disposed such that a longitudinal axis of the resonators  2534 ,  2536 ,  2538  is oblique to the longitudinal axis  2532 . A longitudinal axis of the resonator  2540  can also be oblique to the longitudinal axis  2532 . In an alternative implementation, at least one resonator  2534 ,  2536 ,  2538 ,  2540  can be disposed such that a longitudinal axis of the resonator  2534 ,  2536 ,  2538 ,  2540  is parallel or perpendicular to the longitudinal axis  2532 . 
     Furthermore, a resonator section arranged like the resonator section  2400 ,  2430 ,  2500  shown in  FIG. 24A ,  FIG. 24C ,  FIG. 25A , respectively, can include at least one resonator attached to the afterburner duct  1400  as discussed with respect to  FIG. 25C  and/or  FIG. 25D . In such implementations, the at least one resonator attached to the afterburner duct  1400  can, but need not necessarily, be disposed so as to not contact a strut within the resonator section. Furthermore still, for an implementation in which a shape of at least a portion of the afterburner duct  1400  is elliptical, a resonator section can include multiple resonators in contact with (i) the elliptical shaped portion of the afterburner duct  1400 , and (ii) two adjacent resonators, such that the multiple resonators are arranged in an elliptical shape. Likewise, a resonator section that includes an elliptical shaped bracket, such as the bracket  2402 ,  2432 , can include multiple resonators in contact with (i) the elliptical shaped bracket, and (ii) two adjacent resonators, such that the multiple resonators are arranged in an elliptical shape. 
       FIG. 26A  is a cross-sectional view of a resonator section  2600  for an example implementation in which a shape of at least a portion of the afterburner duct  1400  is ovoid. At least a portion of the casing  1402  can, but need not necessarily, have an ovoid shape. The resonator section  2600  is one of many possible variations of the resonator section  2000  shown in  FIG. 20 . This variation includes a bracket  2602  having an outer exterior surface  2622 , an inner exterior surface  2624 , an upstream end  2626  (shown in  FIG. 26B ), a downstream end  2628  (shown in  FIG. 26B ), and multiple resonators. 
     In an implementation shown in  FIG. 26A , the multiple resonators of the resonator section  2600  are attached to the inner exterior surface  2624  and/or attached in proximity to the inner exterior surface  2624 . In another implementation, the multiple resonators of the resonator section  2600  can be attached to the outer exterior surface  2622  and/or attached in proximity to the outer exterior surface  2622 . In yet another implementation, the multiple resonators of the resonator section  2600  can be disposed within the bracket  2602 .  FIG. 26A  shows the cooling passage  1416 , the afterburner channel  1308 , and a longitudinal axis  2620  of the afterburner channel  1308 . 
       FIG. 26B  is a cross-sectional view of the resonator section  2600 .  FIG. 26B  shows the longitudinal axis  2620  as an arrow. A gas could flow through the afterburner channel  1308  and the cooling passage  1416  within the resonator section  2600  in a direction shown by that arrow. 
     The resonator section  2600  includes the bracket  2602 , multiple struts, and a ring of resonators including multiple resonators. As shown in  FIG. 26A , the ring of resonators within the resonator section  2600  includes resonators  2612 ,  2614 ,  2616 ,  2618 . The multiple struts of the resonator section  2600  include struts  2604 ,  2606 ,  2608 ,  2610 . The bracket  2602  can, but need not necessarily, have an ovoid shape. The bracket  2602  is disposed in the afterburner channel  1308 . 
     As shown in  FIG. 26B , the resonators  2612 ,  2614 ,  2616  are disposed between the upstream end  2626  and the downstream end  2628 . Similarly, the resonator  2618  can be disposed between the upstream end  2626  and the downstream end  2628 . 
       FIG. 26A  and/or  FIG. 26B  illustrate the resonators  2612 ,  2614 ,  2616 ,  2618  disposed such that a longitudinal axis of each of the resonators  2612 ,  2614 ,  2616 ,  2618  is parallel to the longitudinal axis  2620 . In an alternative implementation, a longitudinal axis of at least one resonator  2612 ,  2614 ,  2616 ,  2618  is oblique to the longitudinal axis  2620 . 
       FIG. 26C  is a cross-sectional view of a resonator section  2630  for an example implementation in which a shape of at least a portion of the afterburner duct  1400  is ovoid. At least a portion of the casing  1402  can, but need not necessarily, have an ovoid shape. The resonator section  2630  is one of many possible variations of the resonator section  2000  shown in  FIG. 20 . This variation includes multiple resonators attached to the afterburner duct  1400 .  FIG. 26C  shows the cooling passage  1416 , the afterburner channel  1308 , and a longitudinal axis  2640  of the afterburner channel  1308 . 
       FIG. 26D  is a cross-sectional view of the resonator section  2630 .  FIG. 26D  shows the longitudinal axis  2640  as an arrow. A gas could flow through the afterburner channel  1308  and the cooling passage  1416  within the resonator section  2630  in a direction shown by that arrow. 
     The resonator section  2630  further includes a ring of resonators including multiple resonators. As shown in  FIG. 26C , the ring of resonators of the resonator section  2630  includes resonators  2632 ,  2634 ,  2636 ,  2638 . The resonators  2632 ,  2634 ,  2636 ,  2638  are attached to the afterburner duct  1400 . 
       FIG. 26D  illustrates the resonators  2632 ,  2634 ,  2636  are disposed such that a longitudinal axis of the resonators  2632 ,  2634 ,  2636  is oblique to the longitudinal axis  2640 . A longitudinal axis of the resonator  2638  can also be oblique to the longitudinal axis  2640 . In an alternative implementation, at least one resonator  2632 ,  2634 ,  2636 ,  2638  can be disposed such that a longitudinal axis of the resonator  2632 ,  2634 ,  2636 ,  2638  is parallel or perpendicular to the longitudinal axis  2640 . 
     Furthermore, a resonator section arranged like the resonator section  2600  shown in  FIG. 26A  can include at least one resonator attached to the afterburner duct  1400  as discussed with respect to  FIG. 26C  and/or  FIG. 26D . In such implementations, the at least one resonator attached to the afterburner duct  1400  can, but need not necessarily, be disposed so as to not contact a strut within the resonator section. Furthermore still, for an implementation in which a shape of at least a portion of the afterburner duct  1400  is ovoid, a resonator section can include multiple resonators in contact with (i) the ovoid shaped portion of the afterburner duct  1400 , and (ii) two adjacent resonators, such that the multiple resonators are arranged in an ovoid shape. Likewise, a resonator section that includes n ovoid shaped bracket, such as the bracket  2602 , can include multiple resonators in contact with (i) the ovoid shaped bracket, and (ii) two adjacent resonators, such that the multiple resonators are arranged in an ovoid shape. 
     In the fueling sections shown in  FIG. 19A-D , the afterburner duct  1400  and the casing  1402  are shown as having the same shape, but in alternative implementations, the afterburner duct  1400  and the casing  1402  in a fueling section can have different shapes. For example the afterburner duct  1400  can have the shapes shown in  FIGS. 19A-D , and the casing  1402  can have a different shape. Likewise, in the resonator sections shown in  FIG. 20A  to  FIG. 27D , the afterburner duct  1400  and the casing  1402  are shown as having the same shape, but in alternative implementations, the afterburner duct  1400  and the casing  1402  in a resonator section can have different shapes. For example the afterburner duct  1400  can have the shapes shown in  FIG. 20A  to  FIG. 27D , and the casing  1402  can have a different shape than shown in that same figure. 
       FIG. 27A  is a cross-sectional view of a resonator section  2700  for an example implementation in which a shape of at least a portion of the afterburner duct  1400  is rectangular. The casing  1402  can, but need not necessarily, have a rectangular shape. The resonator section  2700  is one of many possible variations of the resonator section  2000  shown in  FIG. 20 . This variation includes a bracket  2702  having an outer exterior surface  2722 , an inner exterior surface  2724 , an upstream end  2726  (shown in  FIG. 27B ), a downstream end  2728  (shown in  FIG. 27B ), and multiple resonators. 
     In an implementation shown in  FIG. 27A , the multiple of the resonator section  2700  are attached to the inner exterior surface  2724  and/or attached in proximity to the inner exterior surface  2724 . In another implementation, the multiple resonators of the resonator section  2700  can be attached to the outer exterior surface  2722  and/or attached in proximity to the outer exterior surface  2722 . In yet another implementation, the multiple resonators of the resonator section  2700  can be disposed within the bracket  2702 .  FIG. 27A  shows the cooling passage  1416 , the afterburner channel  1308 , and a longitudinal axis  2720  of the afterburner channel  1308 . 
       FIG. 27B  shows the longitudinal axis  2720  as an arrow. A gas could flow through the afterburner channel  1308  and the cooling passage  1416  within the resonator section  2700  in a direction shown by that arrow. 
     The resonator section  2700  includes the bracket  2702 , multiple struts, and a ring of resonators including multiple resonators. As shown in  FIG. 27A , the ring of resonators within the resonator section  2700  includes resonators  2712 ,  2714 ,  2716 ,  2718 . The multiple struts of the resonator section  2700  include struts  2704 ,  2706 ,  2708 ,  2710 . The bracket  2702  can, but need not necessarily, have a rectangular shape. The bracket  2702  is disposed in the afterburner channel  1308 .  FIG. 27B  shows portions of the resonators  2712 ,  2714  disposed between the upstream end  2726  and the downstream end  2728 , and portions of the resonators  2712 ,  2714  extending downstream in the channel beyond the downstream end  2728 . 
       FIG. 27A  and/or  FIG. 27B  illustrate the resonators  2712 ,  2714 ,  2716 ,  2718  disposed such that a longitudinal axis of each of the resonators  2712 ,  2714 ,  2716 ,  2718  is parallel to the longitudinal axis  2720 . In an alternative implementation, a longitudinal axis of at least one resonator  2712 ,  2714 ,  2716 ,  2718  is oblique to the longitudinal axis  2720 . 
       FIG. 27C  is a cross-sectional view of a resonator section  2730  for an example implementation in which a shape of at least a portion of the afterburner duct  1400  is rectangular. The casing  1402  can, but need not necessarily, have a rectangular shape. The resonator section  2730  is one of many possible variations of the resonator section  2000  shown in  FIG. 20 . This variation includes multiple resonators attached to the afterburner duct  1400 .  FIG. 27C  shows the cooling passage  1416 , the afterburner channel  1308 , and a longitudinal axis  2640  of the afterburner channel  1308 . 
       FIG. 27D  is a cross-sectional view of the resonator section  2730 .  FIG. 27D  shows the longitudinal axis  2740  as an arrow. A gas could flow through the afterburner channel  1308  and the cooling passage  1416  within the resonator section  2730  in a direction shown by that arrow. 
     The resonator section  2730  further includes a ring of resonators including multiple resonators. As shown in  FIG. 27C , the ring of resonators of the resonator section  2730  includes resonators  2732 ,  2734 ,  2736 ,  2738 . The resonators  2732 ,  2734 ,  2736 ,  2738  are attached to the afterburner duct  1400 . 
       FIG. 27C  and/or  FIG. 27D  illustrate the resonators  2732 ,  2734 ,  2736 ,  2738  disposed such that a longitudinal axis of each of the resonators  2732 ,  2734 ,  2736 ,  2738  is parallel or perpendicular to the longitudinal axis  2740 . In an alternative implementation, a longitudinal axis of at least one resonator  2732 ,  2734 ,  2736 ,  2738  is oblique to the longitudinal axis  2740 . 
     Furthermore, a resonator section arranged like the resonator section  2700  shown in  FIG. 27A  can include at least one resonator attached to the afterburner duct  1400  as discussed with respect to  FIG. 27C  and/or  FIG. 27D . In such implementations, the at least one resonator attached to the afterburner duct  1400  can, but need not necessarily, be disposed so as to not contact a strut within the resonator section. Furthermore still, for an implementation in which a shape of at least a portion of the afterburner duct  1400  is rectangular, a resonator section can include multiple resonators in contact with (i) the rectangular shaped portion of the afterburner duct  1400 , and (ii) two adjacent resonators, such that the multiple resonators are arranged in a rectangular shape. Likewise, a resonator section that includes a rectangular shaped bracket, such as the bracket  2702 , can include multiple resonators in contact with (i) the rectangular shaped bracket, and (ii) two adjacent resonators, such that the multiple resonators are arranged in a rectangular shape. 
     As discussed above, the afterburner  1300 , the fueling section  1422 , and/or the resonator section  1426  can include at least one strut. In example implementation, a portion of such a strut can be, for example, a solid bar. Moreover, as discussed previously, a strut can include one or more passages. A passage within a strut can provide a passage for routing fuel and/or electrical circuitry. In implementations with a strut having multiple passages, electrical circuitry could be disposed within at least one of the multiple passages. Two electrical circuits could be shielded from each other by routing one of the electrical circuits within one of the multiple passages and routing another one of the electrical circuits within another one of the multiple passages. In some implementations with a strut having multiple passages, fuel could be routed within one of the multiple passages and at least one electrical circuit could be routed in another one of the multiple passages. A strut passage configured for carrying fuel can be open and one end of the strut, plugged as an opposite end of the strut, and could have one or more fuel outlets fluidly coupled to the passage configured for carrying fuel. 
       FIG. 28  illustrates at least a portion of an example strut  2800 . The strut  2800  can be disposed in the afterburner channel  1308  to support a bracket and/or a resonator within a resonator section, such as the resonator section  2400 . The strut  2800  includes a strut passage  2802  and strut ends  2804 ,  2806 . The strut passage  2802  can extend from the strut end  2804  to the strut end  2806 , and can extend through the strut ends  2804 ,  2806 . In an example implementation, a portion of the strut  2800  proximate to the strut end  2804  can be disposed within ports in the afterburner duct  1400  and the casing  1402 , and a portion of the strut  2800  proximate to the strut end  2806  can be disposed and/or attached to a bracket and/or a resonator within a resonator section, such as the resonator section  2400 . In an example implementation, a portion of electrical circuitry connectable to (i) a resonator within a resonator section, and (ii) the signal generator  1802  and/or the DC power source  1804 , can be disposed within the strut passage  2802 . In an example implementation, the strut  2800  can be made of a metal, such as steel or aluminum. 
       FIG. 29  illustrates at least a portion of an example strut  2900 . The strut  2900  is one of many possible variations of the strut  2800  shown in  FIG. 28 . This variation includes multiple strut passages. As shown in  FIG. 29 , the strut  2900  includes tubes  2910 ,  2912 , strut passages  2906 ,  2908 , and strut ends  2902 ,  2904 . The strut passages  2906 ,  2908  can extend within the tubes  2910 ,  2912  from the strut end  2902  to the strut end  2904 . The strut passages  2906 ,  2908  can extend through the strut ends  2902 ,  2904 . In an example implementation, a portion of the strut  2900  proximate to the strut end  2902  can be disposed within ports in the afterburner duct  1400  and the casing  1402 , and a portion of the strut  2900  proximate to the strut end  2904  can be disposed and/or attached to a bracket and/or a resonator within a resonator section, such as the resonator section  2400 . In an example implementation, a portion of electrical circuitry connectable to (i) a resonator within a resonator section, and (ii) the signal generator  1802  and/or the DC power source  1804 , can be disposed within the strut passage  2906 , and a fuel supply line, such as the fuel supply line  1814 , can connect to and/or include the tube  2912 . The strut passage  2908  can carry fuel to a fuel conduit within a resonator in the afterburner channel  1308  and/or to a fuel supply line connected to the tube  2912 . In an example implementation, the strut  2900  and/or the tubes  2910 ,  2912  can be made of a metal, such as steel or aluminum. 
       FIG. 30  illustrates at least a portion of an example strut  3000 . The strut  3000  is one of many possible variations of the strut  2800  shown in  FIG. 28 . This variation includes multiple strut passages and multiple fuel outlets. As shown in  FIG. 30 , the strut  3000  includes a strut divider  3016 , strut passages  3006 ,  3008 , strut ends  3002 ,  3004 , and fuel outlets  3012 ,  3014 . The strut divider  3016  can separate multiple strut passages in the strut  3000 . As shown in  FIG. 30 , the strut divider  3016  separates the strut passages  3006 ,  3008 . 
     In an example implementation, a portion of the strut  3000  proximate to the strut end  3002  can be disposed within ports in the afterburner duct  1400  and the casing  1402 , and a portion of the strut  3000  proximate to the strut end  3004  can be disposed and/or attached to a bracket and/or a resonator within a resonator section, such as the resonator section  2400 . 
     The strut passage  3006  can extend from the strut end  3002  to the strut end  3004 , and can extend through the strut ends  3002 ,  3004 . In an example implementation, a portion of electrical circuitry connectable to (i) a resonator within the afterburner  1300 , and (ii) the signal generator  1802  and/or the DC power source  1804 , can be disposed within the strut passage  3006 . 
     The strut passage  3008  can extend just partially through the strut  3000 . For instance, the strut end  3004  can include a strut wall  3010  so that the strut passage  3008  extends just partially through the strut  3000 . 
     In an example implementation, a fuel supply line, such as the fuel supply line  1814 , can connect to and/or include the strut  3000  for providing fuel into the strut passage  3008 . The fuel provided to the strut passage  3008  can be output through the fuel outlets  3012 ,  3014 . The fuel output by the fuel outlets  3012 ,  3014  can mix with a gas in the afterburner channel  1308 . The strut  3000  can include fewer or more than two fuel outlets. In an example implementation, the strut  3000 , the strut wall  3010 , and/or the strut divider  3016  can be made of a metal, such as steel or aluminum. 
     A strut, such as the strut  2800 ,  2900 ,  3000  or a strut used in a resonator section or a fueling section discussed in this disclosure can include threads, such as internal threads or external threads, for fastening the strut to a threaded portion on a bracket and/or a threaded portion on the afterburner duct  1400  and/or the casing  1402 . Additionally or alternatively, a strut can be fastened to a bracket, the afterburner duct  1400 , and/or the casing  1402  using a clamp or some other fastening device(s). 
     XI. Additional Example Resonators 
     As discussed above, a resonator used in an afterburner can include a fuel conduit that is fluidly connected to a fuel supply line. A fuel pump can pump fuel through the fuel supply line and, in turn, through the fuel conduit, and further in turn, out a fuel outlet disposed within the fuel conduit. Example implementations of such a resonator and several variations are discussed below. 
       FIG. 31  illustrates a resonator  3100  including a fuel conduit  3118 .  FIG. 31  includes labels “distal end” and “proximal end” to distinguish different ends of the resonator  3100 . The resonator  3100  is one of the many possible variations of a resonator that can be used in the jet engine  802 , the afterburner  1300 , and/or the torch igniter  1414 . This variation shows a resonator with a base  3114  at the proximal end of the resonator  3100 .  FIG. 31  also shows a fuel tank  3130 , a fuel pump  3126 , a fuel supply line  3132  that fluidly couples the fuel tank  3130  and the fuel pump  3126 , and a fuel supply line  3128  that fluidly couples the fuel pump  3126  and the fuel conduit  3118 . In an example implementation, the fuel pump  3126  can be disposed within the fuel tank  3130 . 
     As shown in  FIG. 31 , the resonator  3100  includes an outer conductor  3102  having both an exterior surface  3104  and an interior surface  3106 . The resonator  3100  also includes an inner conductor  3108  having both an exterior surface  3110  and an interior surface  3112 . The interior surface  3106  and the exterior surface  3110  define a cavity  3144  that extends from a proximal end of the outer conductor  3102  to a distal end of the outer conductor  3102 . The resonator  3100  can include a dielectric within the cavity  3144 . Similar to the dielectric  108  shown in  FIG. 1C , the dielectric can include air and/or one or more dielectric materials. The interior surface  3112  defines a cavity  3142  that can extend from a proximal end of the inner conductor  3108  to a distal end of the inner conductor  3108 . In an example implementation, the interior surface  3112  defines at least a portion of the fuel conduit  3118 . In that implementation, fuel flowing through the fuel conduit  3118  flows through the cavity  3142  and can contact the interior surface  3112 . In another example implementation, the fuel conduit  3118  includes a structure distinct from the inner conductor  3108 . In that implementation, at least a portion of the fuel conduit  3118  is disposed within the cavity  3142  and can contact the interior surface  3112 . 
     The base  3114  can include a hole  3136  in which a portion of the inner conductor  3108  can be disposed. A wall  3138  of the base  3114  and that portion of the inner conductor  3108  can form a joint  3134 . In an implementation, the joint  3134  can include one or more fasteners, an adhesive material, and/or a friction force. The friction force can result from pressing the inner conductor  3108  into the hole  3136  or by turning a threaded portion of the inner conductor  3108  into a threaded portion of the wall  3138 . In an implementation, at least a portion of the hole  3136  is a through-hole so that a portion of the fuel conduit  3118  and/or a portion of fuel supply line  3128  can pass through or be disposed within the base  3114 . 
     The base  3114  and the outer conductor  3102  can form a joint  3116 . In an implementation, the joint  3116  can include one or more fasteners, an adhesive material, and/or a friction force. The friction force can result from pressing one of the base  3114  and the outer conductor  3102  into the other. In yet another implementation, one of the base  3114  and the conductor  3102  can include an entry hole and a slot and the other can include a flange that can be disposed in the entry hole and slid within the slot to securely join the base  3114  and the conductor  3102 . In an example implementation, the joint  3116  can extend from the exterior surface  3104  to the interior surface  3106 . 
     In an example implementation, the base  3114  can be made of an insulated material such that the base  3114  does not electrically short the outer conductor  3102  to the inner conductor  3108 . In another example implementation, the base  3114  can be made of a conductive material that electrically shorts the outer conductor  3102  to the inner conductor  3108 . In that implementation, the base  3114  can operate as a base conductor, similar to the implementations in which the base conductor  110  electrically shorts together the outer conductor  102  and the inner conductor  104  (all shown in  FIG. 5 ). 
     In yet another example implementation, the base  3114  can be made of a conductive material and the joint  3116  and/or the joint  3134  can be insulated joints such that the base  3114  does not electrically short the outer conductor  3102  to the inner conductor  3108 . In such implementation, the insulated joints can include one or more insulated fasteners, such as electrical standoff insulators, a dielectric material, or some other insulated material. 
     As mentioned above, at least a portion of the fuel conduit  3118  can include a structure distinct from the inner conductor  3108 . In such an implementation, the fuel conduit  3118  can include a tube that is at least partly disposed with the inner conductor  3108 . The portion of the tube within the inner conductor  3108  can be maintained in place by friction and/or an adhesive, for example. In an implementation, the tube of the fuel conduit  3118  can extend from the proximal end of the resonator  3100  to the distal end of the resonator  3100 . In that or a different implementation, the tube of the fuel conduit  3118  can extend beyond the proximal end of the resonator  3100  and/or the distal end of the resonator  3100 . 
     The tube of the fuel conduit  3118  can have an opening proximate to the proximal end of the resonator  3100  so that fuel from the fuel supply line  3128  can enter the tube. The tube of the fuel conduit  3118  can include one or more fuel outlets. As an example, an end of the tube proximate the distal end of the resonator  3100  can have an opening configured as a fuel outlet. As another example, the tube of the fuel conduit  3118  can include one or more fuel outlets, such as a fuel outlet  3120  between a distal end and a proximal end of the tube. 
     The fuel conduit  3118  can be made of a material such that fuel contained within the fuel conduit can be treated by electromagnetic waves provided by the resonator  3100  when the resonator  3100  is excited by a signal from a radio frequency power source. For the implementations in which at least a portion of the fuel conduit  3118  includes a tube, the tube can include a glass tube, a sapphire tube, a quartz tube, an aliphatic polyamide tube, or a non-porous ceramic tube, for example. 
     In some implementations, the fuel conduit  3118  can act, at least in part, as a Faraday cage (for example, by encapsulating the fuel within a conductor that makes up the fuel conduit  3118 ) to prevent electromagnetic radiation in the resonator  3100  from interacting with the fuel while the fuel is transiting the fuel conduit  3118 . In other implementations, the fuel conduit  3118  can allow electromagnetic radiation to interact with (for example, reform) the fuel within the fuel conduit  3118 . Accordingly, a resonator with a fuel conduit can be configured to provide at least some of the electromagnetic waves provided by the resonator within the fuel conduit. 
     The resonator  3100  can include a connector  3122  to connect the fuel conduit  3118  to the fuel supply line  3128 . Likewise, the fuel supply line  3128  can include a connector  3124  that is connectable to the connector  3122 .  FIG. 31  shows the connector  3122  outside of the base  3114 . In another implementation, at least a portion of the connector  3122  can be disposed within the base  3114 . 
     In some implementations, the fuel conduit  3118  can include the connector  3122 , and the fuel supply line  3128  can include the connector  3124 . As an example of those implementations, the fuel conduit  3118  and the fuel supply line  3128  can each comprise a steel tube, and the connector  3122  can include a flared portion of the steel tube of the fuel conduit  3118  and a threaded fastener, and the connector  3124  can include a flared portion of the other steel tube and a threaded fastener. The flared portion of a steel tube can include a double flare, a bubble flare, or an inverted flare, for example. The threaded fittings of two steel tubes can mate together to provide a leak-proof connection. 
     In some implementations, the connector  3122  can be separate from fuel conduit  3118 . In those implementations, the connector  3122  can include a clamp (such as a hose clamp), for example. In some implementations, the connector  3122  can include a friction connection made by pressing one of the fuel conduit  3118  or the fuel supply line  3128  into the other, or by screwing a threaded portion of one of the fuel conduit  3118  or the fuel supply line  3128  into the other. One or both of the connectors  3122 ,  3124  can include a gasket, such as a rubber o-ring, to prevent fuel leakage at the connectors  3122 ,  3124 . 
     Similar to other resonators discussed above, the resonator  3100  can connect to a radio frequency power source that is configured to provide a signal to excite the resonator  3100 . The resonator  3100  can further connect to a direct-current power source that is configured to provide a bias signal between the outer conductor  3102  and the inner conductor  3108 . Furthermore, in some implementations, a distal end of the inner conductor  3108  can include an electrode  3140  having a concentrator. The concentrator of the electrode can be located at a distal end of the electrode  3140 . The resonator  3100  can provide a plasma corona proximate to the concentrator of the electrode  3140  when the resonator  3100  is excited by a signal from the radio frequency power source. The plasma corona can be provided within the afterburner channel  1308  for at least implementations in which the concentrator of the electrode  3140  is disposed within the afterburner channel  1308 . Likewise, the plasma corona can be provided within a torch igniter channel for at least implementations in which the concentrator of the electrode  3140  is disposed within a torch igniter channel. 
     In example implementations, the resonator  3100 , or at least the distal end of the resonator  3100 , can be disposed within the afterburner channel  1308 . In those implementations, the fuel output by the fuel outlet(s) can mix with a gas within the afterburner channel  1308 . Furthermore, one or more of the fuel outlet(s) can output the fuel proximate to a source of ignition energy (for example, proximate to a plasma corona generated near a concentrator of the electrode  3140 ), which can allow for efficient ignition and combustion. 
     Furthermore, in some implementations, the resonator  3100  can include multiple fuel conduits  3118  (for example, multiple fuel conduits running from the proximal end of the resonator  3100  to the distal end of the resonator  3100 ). Additionally or alternatively, one or more fuel conduits can be disposed within the outer conductor  3102 . 
       FIG. 32  illustrates a resonator  3200 . The resonator  3200  is one of the many possible variations of a resonator that includes a fuel conduit and can be used in the jet engine  802 , the afterburner  1300 , and/or the torch igniter  1414 . This variation does not include the base  3114  shown in  FIG. 31 .  FIG. 32  includes labels “distal end” and “proximal end” to distinguish different ends of the resonator  3200 . 
     Similar to the resonator  3100  shown in  FIG. 31 , the resonator  3200  includes (i) the outer conductor  3102  having the exterior surface  3104 , the interior surface  3106 , and the cavity  3144 , (ii) the inner conductor  3108  having the exterior surface  3110 , the interior surface  3112 , the electrode  3140 , and the cavity  3142 , and (iii) the fuel conduit  3118  including the fuel outlet  3120 , all of which are discussed above. Like the fuel conduit  3118  for the resonator  3100 , the fuel conduit  3118  for the resonator  3200  can include a different configuration of fuel outlet(s).  FIG. 32  also shows the fuel tank  3130 , the fuel pump  3126 , the fuel supply line  3132 , and the fuel supply line  3128 , all of which are discussed above. 
     The interior surface  3112  can define the cavity  3142 . The cavity  3142  and/or the interior surface  3112  can define at least a portion of the fuel conduit  3118 . Alternatively, the inner surface  3112  can define a cavity in which at least a portion of the fuel conduit  3118  with a structure distinct from the inner conductor  3108  is disposed. Examples of that distinct structure of the fuel conduit  3118  and examples of the materials used to make the fuel conduit  3118  are discussed above. 
     The interior surface  3106  can define a cavity that extends from a proximal end of the outer conductor  3102  to a distal end of the outer conductor  3102 . The resonator  3200  includes a dielectric  3202 . The dielectric  3202  can include a dielectric material disposed between the interior surface  3106  of the outer conductor  3102  and the exterior surface  3110 . Similar to the dielectric  108  shown in  FIG. 1C , the dielectric  3202  can include air and/or one or more dielectric materials. 
     The resonator  3200  can include a connector  3204  to fluidly connect the fuel conduit  3118  to the fuel supply line  3128 . Likewise, the fuel supply line  3128  can include a connector  3206  that is connectable to the connector  3204 .  FIG. 32  shows the connector  3204  outside of the cavity defined by the interior surface  3106 . In another implementation, at least a portion of the connector  3222  can be disposed within the cavity defined by the interior surface  3106 . 
     In some implementations, at least a portion of the connector  3204  can be a portion of the fuel conduit  3118 , and at least a portion of the connector  3206  can be a portion of the fuel supply line  3128 . As an example of those implementations, the fuel conduit  3118  and the fuel supply line  3128  can each comprise a steel tube, and the portion of the connector  3204  can be a flared portion of the steel tube of the fuel conduit  3118 , and the portion of the connector  3206  can be a flared portion of the other steel tube. 
     In some implementations, the connector  3204  can be separate from fuel conduit  3118 . In those implementations, the connector  3204  can include a clamp (such as a hose clamp), for example. In some implementations, the connector  3204  can include a friction connection made by pressing one of the fuel conduit  3118  or the fuel supply line  3128  into the other, or by screwing a threaded portion of one of the fuel conduit  3118  or the fuel supply line  3128  into the other. One or both of the connectors  3204 ,  3206  can include a gasket, such as a rubber o-ring, to prevent fuel leakage at the connectors  3204 ,  3206 . 
     In some implementations, the resonator  3200  can include multiple fuel conduits  3118  (for example, multiple fuel conduits running from the proximal end of the resonator  3200  to the distal end of the resonator  3200 ). Additionally or alternatively, one or more fuel conduits can be positioned within the dielectric  3202  and/or within the outer conductor  3102 . 
       FIG. 33A  is an elevation view of a conductor  3300  that can be used as an inner conductor of a resonator including a fuel conduit. The conductor  3300  is a variation of the inner conductor  3108  shown in  FIG. 31  and  FIG. 32 . In this variation, multiple fuel outlets are shown.  FIG. 33B  is a cross-sectional view of the conductor  3300  shown in  FIG. 33A , and includes labels “distal end” and “proximal end” to distinguish different ends of the conductor  3300 . The proximal end of the conductor  3300  is shown in  FIG. 33A . 
     The conductor  3300  includes an inner surface  3302 , an outer surface  3310 , and a fuel conduit  3308 . The interior surface  3302  defines the fuel conduit  3308 . A fuel outlet  3304  extends from the interior surface  3302  to the exterior surface  3310 . Likewise, a fuel outlet  3306  extends from the interior surface  3302  to the exterior surface  3310 . As shown in  FIG. 33B , the fuel outlets  3304 ,  3306  can pass through the conductor  3300  obliquely. In an alternative implementation, one or more fuel outlets can pass through the conductor  3300  squarely. 
     The fuel pump  3126 , shown in  FIG. 31  and  FIG. 32 , can pump fuel into the fuel conduit  3308  at the proximal end of the conductor  3300 . That fuel can flow through the fuel conduit  3308  and out the fuel outlets  3304 ,  3306 . In an example implementation, the fuel outlets  3304 ,  3306  can output the fuel into the cavity  3144  shown in  FIG. 31 . In another example implementation, the fuel outlets  3304 ,  3306  can output the fuel into the dielectric  3202  shown in  FIG. 32 . For that implementation, if the dielectric  3202  includes a dielectric material, the dielectric material can include one or more fuel conduits for further transportation of the fuel. 
       FIG. 33C  is an elevation view of a conductor  3320  that can be used as an inner conductor of a resonator including a fuel conduit. The conductor  3320  is another variation of the inner conductor  3108  shown in  FIG. 31  and  FIG. 32 . This variation shows (i) a fuel conduit structure  3312  distinct from the conductor  3320 , and (ii) a fuel conduit  3318 . This variation also shows multiple fuel outlets.  FIG. 33D  is a cross-sectional view of the conductor  3320  shown in  FIG. 33C , and includes labels “distal end” and “proximal end” to distinguish different ends of the conductor  3320 . The proximal end of the conductor  3320  is shown in  FIG. 33C . 
     The conductor  3320  includes an outer surface  3322 , and the fuel conduit structure  3312  includes an inner surface  3324  that defines the fuel conduit  3318 . A portion of the inner surface of the conductor  3320  and a portion of an outer surface  3326  of the fuel conduit structure  3312  can form a joint  3328 . In an implementation, the joint  3328  can include an adhesive material and/or a friction force. The friction force can result from pressing the fuel conduit structure  3312  into a cavity defined by the inner surface of the conductor  3320 . 
     A fuel outlet  3314  extends from the interior surface  3324  to the exterior surface  3326  and/or to the exterior surface  3322 . Likewise, a fuel outlet  3316  extends from the interior surface  3324  to the exterior surface  3326  and/or to the exterior surface  3322 . As shown in  FIG. 33D , the fuel outlets  3314 ,  3316  can pass through the conduit  3320  obliquely. In an alternative implementation, one or more fuel outlets can pass through the fuel conduit  3320  squarely. 
     The fuel pump  3126  shown in  FIG. 31  and  FIG. 32  can pump fuel into the fuel conduit  3318  at the proximal end of the conductor  3320 . That fuel can flow through the fuel conduit  3318  and out the fuel outlets  3314 ,  3316 . In an example implementation, the fuel outlets  3314 ,  3316  can output the fuel into the cavity  3144  shown in  FIG. 31 . In another example implementation, the fuel outlets  3314 ,  3316  can output the fuel into the dielectric  3202  shown in  FIG. 32 . For that implementation, if the dielectric  3202  includes a dielectric material, the dielectric material can include one or more fuel conduits for further transportation of the fuel. 
       FIG. 34A  illustrates an elevation view of a resonator  3410 . The resonator  3410  is one of the many possible variations of a resonator (like the resonator  3200  shown in  FIG. 32 ) including a dielectric and the conductor  3300  shown in  FIG. 33A  and  FIG. 33B . This variation shows the conductor  3300  as an inner conductor disposed within the outer conductor  3102  and the dielectric  3202  disposed between the conductor  3300  and the outer conductor  3102 .  FIG. 34B  is a cross-sectional view of the conductor  3410  shown in  FIG. 34A , and includes labels “distal end” and “proximal end” to distinguish different ends of the conductor  3410 . The distal end of the conductor  3410  is shown in  FIG. 34A . 
     The fuel outlet  3304  is fluidly coupled to a fuel conduit  3400  within the dielectric  3202 . The fuel conduit  3400  includes a fuel outlet  3402 . Likewise, the fuel outlet  3306  is fluidly coupled to a fuel conduit  3404  within the dielectric  3202 , and the fuel conduit  3404  includes a fuel outlet  3406 . The fuel conduits  3400 ,  3404  can transport fuel from the fuel outlets  3304 ,  3306  to the fuel outlets  3402 ,  3406 , respectively. The fuel outlets  3402 ,  3406  can output the fuel into a combustion area, such as the afterburner channel  1308 , and/or in proximity to an ignition source, such as a plasma corona the resonator  3410  can generate when excited by a signal from a radio frequency power source. 
       FIG. 35  illustrates a cross-sectional view of a coaxial resonator  3500 . The resonator  3500  is one of the many possible variations of a resonator that include a fuel conduit and that can be used in the jet engine  802 , the afterburner  1300 , and/or the torch igniter  1414 . The resonator  3500  includes the components of the coaxial resonator  700  shown in  FIG. 7  and a fuel conduit  3502  in the interior center conductor portion  750  and the transition zone  758 . The description of the other components shown in  FIG. 7  pertains to the components having the same reference number shown in  FIG. 35 . 
     The fuel conduit  3502  can extend from the proximal end  748  to the second cylindrical cavity  736 . In an example implementation, the fuel conduit  3502  can include multiple branches, such as fuel conduit branches  3504 ,  3506 . The fuel conduit  3502  can include a fuel outlet within the transition zone  758  for outputting fuel into the second cylindrical cavity  736 . As illustrated in  FIG. 33 , the fuel conduit branch  3504  includes a fuel outlet  3508 , and the fuel conduit branch  3506  includes a fuel outlet  3510 . 
     The resonator  3500  can include a connector (not shown) to connect the fuel conduit  3502  to the fuel supply line  3128 . In an implementation, the connector of the resonator  3500  can be configured like the connector  3122  shown in  FIG. 31  or the connector  3204  shown in  FIG. 32 . 
     Fuel received at fuel conduit  3502  at the proximal end of the  748  can flow towards the fuel conduit branches  3504 ,  3506 . Some of the fuel within the fuel conduit  3502  can be provided to each of the fuel conduit branches  3504 ,  3506  for delivery through the fuel outlets  3508 ,  3510  respectively. The fuel output through the fuel outlets  3508 ,  3510  can be exposed to electromagnetic waves provided by the resonator  3500  in response to being excited by a signal from a radio-frequency power source. 
       FIG. 36A  is an elevation view of a conductor  3600  that can be used as an inner conductor of a resonator including a fuel conduit. The conductor  3600  is a variation of the inner conductor  3108  shown in  FIG. 31  and  FIG. 32 . In this variation, a fuel outlet  3610  is at a distal end of the conductor  3600 .  FIG. 36B  is a cross-sectional view of the conductor  3600  shown in  FIG. 36A , and includes labels “distal end” and “proximal end” to distinguish different ends of the conductor  3600 . The proximal end of the conductor  3600  is shown in  FIG. 36A . 
     The conductor  3600  includes an inner surface  3602 , an exterior surface  3604 , and a fuel conduit  3606 . The interior surface  3602  defines the fuel conduit  3606 . The conductor  3600  also includes a proximal end opening  3608 . A fuel supply line, such as the fuel supply line  3128  shown in  FIG. 31 , can fluidly couple to the fuel conduit  3606  proximate the proximal end opening  3608 . 
     The fuel pump  3126 , shown in  FIG. 31  and  FIG. 32 , can pump fuel into the fuel conduit  3606  at the proximal end of the conductor  3600 . That fuel can flow through the fuel conduit  3606 , and then out the fuel outlet  3610  into the afterburner channel  1308  of the afterburner  1300 . 
       FIG. 36C  is an elevation view of a conductor  3620  that can be used as an inner conductor of a resonator including a fuel conduit. The conductor  3620  is another variation of the inner conductor  3108  shown in  FIG. 31  and  FIG. 32 . This variation shows (i) a fuel conduit structure  3622  distinct from the conductor  3620 , and (ii) a fuel conduit  3624  having a fuel outlet  3626  at a distal end of the fuel conduit structure  3622 . The conductor  3620  includes a proximal end opening  3632  and a distal end opening  3628 . The fuel conduit structure  3622  includes a proximal end opening  3630 .  FIG. 36D  is a cross-sectional view of the conductor  3620  shown in  FIG. 36C , and includes labels “distal end” and “proximal end” to distinguish different ends of the conductor  3620 . The proximal end of the conductor  3620  is shown in  FIG. 36C . 
     The conductor  3620  includes an exterior surface  3634 , and the fuel conduit structure  3622  includes an interior surface  3636  that defines the fuel conduit  3624 . At least a portion of an interior surface of the conductor  3620  and at least a portion of an exterior surface of the fuel conduit structure  3622  can form a joint  3638 . In an implementation, the joint  3638  can include an adhesive material and/or a friction force. The friction force can result from pressing the fuel conduit structure  3622  into a cavity defined by the inner surface of the conductor  3620 . 
     A fuel supply line, such as the fuel supply line  3128  shown in  FIG. 31 , can fluidly couple to the conductor  3620  and/or the fuel conduit structure  3622  proximate the proximal end opening  3632  and/or the proximal end opening  3630 . The fuel pump  3126  shown in  FIG. 31  and  FIG. 32  can pump fuel into the fuel conduit  3624  at the proximal end of the conductor  3620 . That fuel can flow through the fuel conduit  3624  and out the fuel outlet  3626 . In an example implementation, the distal end of the conduit structure  3622  can be flush within a distal end opening  3628 . In that implementation, the fuel outlet  3626  can output fuel into the afterburner channel  1308  of the afterburner  1300 . In another implementation, the distal end of the conduit structure  3622  can end prior to the distal end of the conductor  3620 . In that implementation, the fuel outlet  3626  can output fuel into the conductor  3620  for delivery of the fuel through a portion of the conductor  3620 , out the distal end opening  3628 , and into the afterburner channel  1308  of the afterburner  1300 . 
       FIG. 37  illustrates a resonator  3700  and includes labels “distal end” and “proximal end” to distinguish different ends of the resonator  3700 . The resonator  3700  is one of the many possible variations of a resonator that can be used in the jet engine  802 , the afterburner  1300  and/or the torch igniter  1414 . This variation shows a resonator with an outer conductor  3702 , a base  3716  at the proximal end of the resonator  3700 , and fuel conduits  3734 ,  3736  in the outer conductor  3702 .  FIG. 37  also shows the fuel tank  3730 , the fuel pump  3726 , and the fuel supply lines  3728 ,  3732 , all of which are discussed above. 
     As shown in  FIG. 37 , the outer conductor  3702  has an outer surface  3704 , an inner surface  3706 , distal end openings  3738 ,  3740 , and proximal end openings  3742 ,  3744 . The inner surface  3706  can define a cavity  3712  that extends from a proximal end of the outer conductor  3702  to a distal end of the outer conductor  3702 . The resonator  3700  also includes an inner conductor  3708  having an electrode  3710  proximate to the distal end of the resonator  3700 . The inner conductor  3708  can be disposed in the cavity  3712 . The resonator  3700  can also include a dielectric within the cavity  3712  and between the outer conductor  3702  and the inner conductor  3708 . Similar to the dielectric  108  shown in  FIG. 1C , the dielectric can include air and/or one or more dielectric materials. 
     The base  3716  can include (i) a hole  3718  in which a portion of the inner conductor  3708  can be disposed, (ii) a fuel conduit  3728  that is fluidly connectable to the fuel supply line  3128 , (iii) fuel conduit branches  3730 ,  3732 , and (iv) holes  3746 ,  3748 . A wall  3720  of the base  3716  and that portion of the inner conductor  3708  can form a joint  3722 . In an implementation, the joint  3722  can include one or more fasteners, an adhesive material, and/or a friction force. The friction force can result from pressing the inner conductor  3708  into the hole  3718  or by turning a threaded portion of the inner conductor  3708  into a threaded portion of the wall  3720 . In an implementation, at least a portion of the hole  3718  is a through-hole so that a portion of the fuel conduit  3728  and/or a portion of fuel supply line  3128  can pass through or be disposed within the base  3716 . 
     The base  3716  and the outer conductor  3702  can form a joint  3724 . In an implementation, the joint  3724  can include one or more fasteners, an adhesive material, and/or a friction force. The friction force can result from pressing one of the base  3716  and the outer conductor  3702  into the other. In yet another implementation, one of the base  3716  and the outer conductor  3702  can include an entry hole and a slot and the other can include a flange that can be disposed in the entry hole and slid within the slot to securely join the base  3716  and the outer conductor  3702 . In an example implementation, the joint  3724  can extend from the outer surface  3704  to the inner surface  3706 . 
     The joint  3724  can include a seal, such as an o-ring, in one or both of the fuel conduit branch  3730  and the fuel conduit  3734 . Likewise, the joint  3724  can include a seal in one or both of the fuel conduit branch  3732  and the fuel conduit  3736 . Those seals can provide a leak-proof coupling between the fuel conduit branches  3730 ,  3732  and the fuel conduits  3734 ,  3736 . 
     In an example implementation, the base  3716  can be made of an insulated material such that the base  3716  does not electrically short the outer conductor  3702  to the inner conductor  3708 . In another example implementation, the base  3716  can be made of a conductive material that electrically shorts the outer conductor  3702  to the inner conductor  3708 . In that implementation, the base  3716  can operate as a base conductor, similar to the implementations in which the base conductor  110  electrically shorts together the outer conductor  102  and the inner conductor  104  (all shown in  FIG. 5 ). 
     In yet another example implementation, the base  3716  can be made of a conductive material and the joints  3722  and/or the joint  3724  can be insulated joints such that the base  3716  does not electrically short the outer conductor  3702  to the inner conductor  3708 . In such implementation, the insulated joints can include one or more insulated fasteners, such as electrical standoff insulators, a dielectric material, or some other insulated material. 
     In some implementations, the fuel conduits  3734 ,  3736  can be cavities within the outer conductor  3702 , between the interior surface  3706  and the interior surface  3704 , such that interior surfaces of the outer conductor  3702 , between the interior surface  3706  and the exterior surface  3704 , define the fuel conduits. In other implementations, the fuel conduits  3734 ,  3736  can further include a fuel conduit structure within the cavities within the outer conductor  3702  between the interior surface  3706  and the exterior surface  3704 . That structure can be made of a material as described with respect to the fuel conduit  3118 . 
     In some implementations, the fuel conduits  3734 ,  3736  can act, at least in part, as a Faraday cage (for example, by encapsulating the fuel within a conductor that makes up the fuel conduits  3734 ,  3736 ) to prevent electromagnetic radiation in the resonator  3700  from interacting with the fuel while the fuel is transiting the fuel conduits  3734 ,  3736 . In other implementations, the fuel conduits  3734 ,  3736  can allow electromagnetic radiation to interact with (for example, reform) the fuel within the fuel conduits  3734 ,  3736 . 
     The resonator  3700  can include a connector  3726  to connect the fuel conduit  3728  to the fuel supply line  3728 . Likewise, the fuel supply line  3728  can include the connector  3124  discussed above.  FIG. 37  shows the connector  3726  outside of the base  3716 . In another implementation, at least a portion of the connector  3726  can be disposed within the base  3716 . 
     In some implementations, the fuel conduit  3728  can include the connector  3726 , and the fuel supply line  3128  can include the connector  3124 . The connector  3726  can be similar to the connector  3122  shown in  FIG. 15 . 
     Similar to other resonators discussed above, the resonator  3700  can connect to a radio frequency power source that is configured to provide a signal to excite the resonator  3700 . The resonator  3700  can further connect to a direct-current power source that is configured to provide a bias signal between the outer conductor  3702  and the inner conductor  3708 . The resonator  3700  can provide a plasma corona proximate to the concentrator of the electrode  3710  when the resonator  3700  is excited by a signal from the radio frequency power source. The plasma corona can be provided within the afterburner channel  1308  for implementations in which the concentrator of the electrode  3710  is disposed within the afterburner channel  1308 . 
     The fuel conduits  3734 ,  3736  include fuel outlets  3750 ,  3752 , respectively. In example implementations, the resonator  3700 , or at least the distal end of the resonator  3700 , can be disposed within the afterburner channel  1308 . In those implementations, the fuel output by the fuel outlets  3750 ,  3752  can mix with a gas within the afterburner channel  1308 . Furthermore, a distal end of one or more of the fuel conduits  3734 ,  3736  and/or a distal end of one or more of the fuel outlets  3750 ,  3752  can be angled toward the electrode  3710 . 
       FIG. 38  is a cutaway side view of a portion of the resonator section  2100  shown in  FIG. 21A . This view shows the resonator  2102  and the strut  2108 , and portions of the afterburner duct  1400 , the casing  1402 , the afterburner channel  1308 , and the cooling passage  1416 .  FIG. 38  also shows the signal generator  1802 , the DC power source  1804 , the fuel tank  1806 , the fuel pump  1808 , and the fuel supply lines  1812 ,  1814 . 
     As shown in  FIG. 38 , the resonator  2102  includes a first conductor  3800 , a second conductor  3802 , and a dielectric  3804  disposed between the first conductor  3800  and the second conductor  3802 . A base conductor  3806  is electrically coupled to the first conductor  3800  and the second conductor  3802 . A fuel conduit  3808 , having fuel outlets  3810 ,  3812 , is disposed within the first conductor  3800 . The configuration of the resonator  2102  shown in  FIG. 38  is provided by way of example and is not meant to be limiting. The resonator  2102  may be configured in accordance with any of the resonators discussed in this description. 
     As further shown in  FIG. 38 , the afterburner duct  1400  includes a port  3814  and the casing  1402  includes a port  3816 . A portion of the strut  2108  is disposed in the port  3814  and another portion of the strut  2108  is disposed in the port  3816 . Furthermore,  FIG. 38  shows the signal generator  1802  is connected to electrical circuitry  3818 , and the DC power source  1804  is connected to electrical circuitry  3820 . Furthermore still,  FIG. 38  shows the fuel supply line  1814  is connected to a fuel supply line  3822 , and the fuel supply line  3822  is connected to the fuel conduit  3808 . 
     The fuel supply line  3822  can include connectors  3824 ,  3826 . The resonator  2102  can include a connector  3828  to connect the fuel conduit  3808  to the fuel supply line  3822 . Likewise, the fuel supply line  1814  can include a connector  3830  that is connectable to the connector  3824 .  FIG. 38  shows the connector  3828  outside of the base conductor  3806 . In another implementation, at least a portion of the connector  3828  can be disposed within the base conductor  3806  or another portion of the resonator  2102 . 
     As discussed above, a strut can include multiple passages. The strut  2108  includes at least one passage for the fuel supply line  3822  and the electrical circuitry  3818 ,  3820  to pass through the casing  1402  and the afterburner duct  1400 . 
     As noted above, in an implementation providing an example system, the system includes an afterburner including an afterburner duct that defines an afterburner channel. The afterburner is configured to receive input gas from a turbine of a jet engine into the afterburner channel and to output an exhaust gas resulting from combustion of fuel within the afterburner channel. The system also includes a plurality of resonators configured to be electromagnetically coupled to at least one radio-frequency power source. Each resonator has a resonant wavelength. Each resonator includes a first conductor, a second conductor, and a dielectric between the first conductor of that resonator and the second conductor of that resonator. Each resonator is configured such that, when that resonator is excited by the at least one radio-frequency power source with a signal having a wavelength proximate to an odd-integer multiple of one-quarter (¼) of the resonant wavelength of that resonator, that resonator provides within the afterburner at least one of electromagnetic waves or a plasma corona proximate to that resonator. A first resonator of the plurality of resonators further includes a fuel conduit having a first fuel outlet that is configured to output fuel for mixing with the input gas from the turbine of the jet engine. 
     In some implementations of the example system, the plurality of resonators is arranged as at least one ring of resonators including a first ring of resonators. Furthermore, the first ring of resonators can include multiple resonators attached to (i) the afterburner duct, (ii) a bracket, or (iii) the afterburner duct and the bracket. Furthermore still, the afterburner duct can include a plurality of ports, each port having at least a portion of a respective resonator of the first ring of resonators disposed within. At least one port of the plurality of ports can be configured so that a resonator at least partially disposed within that port has a longitudinal axis that is perpendicular to a longitudinal axis of the afterburner channel. Moreover, at least one port of the plurality of ports can be configured so that a resonator at least partially disposed within that port has a longitudinal axis that is oblique to a longitudinal axis of the afterburner channel. 
     In some implementations of the example system, each resonator of the first ring of resonators is disposed entirely within the afterburner channel. A longitudinal axis of at least one resonator of the first ring of resonators can be parallel to a longitudinal axis of the afterburner channel. Moreover, a longitudinal axis of at least one resonator of the first ring of resonators can be oblique to a longitudinal axis of the afterburner channel. 
     In some implementations of the example system, the plurality of resonators is arranged as multiple rings of resonators, the multiple rings of resonators including at least a first ring of resonators and a second ring of resonators. 
     In some implementations of the example system, at least one radio-frequency power source includes at least a first radio-frequency power source and a second radio-frequency power source. The plurality of resonators includes at least (i) a first resonator set having at least one resonator configured to be electromagnetically coupled to at least the first radio-frequency power source, and (ii) a second resonator set having at least one resonator configured to be electromagnetically coupled to at least the second radio-frequency power source. Moreover, each first radio-frequency power source can be configured to provide the signal to at least one resonator of the first resonator set. Likewise, each second radio-frequency power source can be configured to provide the signal to at least one resonator of the second resonator set. 
     In some implementations of the example system, the system further includes at least one direct-current power source configured to provide a respective bias signal between the first conductor and the second conductor of at least one resonator from the first resonator set, at least one resonator from the second resonator set, or a least one resonator from both the first resonator set and the second resonator set. Furthermore, the example system of those implementations can further include a controller configured to cause at least (i) the first radio-frequency power source to provide the signal to at least one resonator of the first resonator set, or (ii) the second radio-frequency power source to provide the signal to at least one resonator of the second resonator set. Moreover, at least a portion of each resonator of the first resonator set can be disposed within a fuel supply line fluidly coupled to the fuel outlet, and at least a portion of each resonator of the second resonator set can be disposed within the afterburner channel. 
     In some implementations of the example system, each resonator of the plurality of resonators is selected from the group consisting of: a coaxial-cavity resonator, a dielectric resonator, a crystal resonator, a ceramic resonator, a surface-acoustic-wave resonator, an yttrium-iron-garnet resonator, a rectangular-waveguide cavity resonator, a parallel-plate resonator, and a gap-coupled microstrip resonator. 
     In some implementations of the example system, the plurality of resonators includes at least a first resonator and at least a second resonator. Furthermore, the resonant wavelength of at least the first resonator can be a first resonant wavelength and the resonant wavelength of at least the second resonator can be a second resonant wavelength different than the first resonant wavelength. 
     In some implementations of the example system, each resonator that provides the plasma corona proximate to that resonator includes an electrode coupled to the first conductor of that resonator. 
     In some implementations of the example system, at least a first portion of the fuel conduit is disposed within the first conductor. The first conductor can include an interior surface that defines at least the first portion of the fuel conduit. Moreover, at least the first portion of the fuel conduit is disposed within a cavity of the first conductor. As an example, at least the first portion of the fuel conduit includes a glass tube, a sapphire tube, a quartz tube, an aliphatic polyamide tube, or a non-porous ceramic tube. As another example, at least the first portion of the fuel conduit is maintained within the cavity of the first conductor by friction and/or an adhesive. Furthermore still, a second portion of the fuel conduit can be disposed within the dielectric. Furthermore still, at least a portion of the first conductor is disposed within a cavity defined by the second conductor. Furthermore still, in some implementations of the example system, the second conductor can be disposed within a cavity defined by the first conductor. 
     In some implementations of the example system, at least one resonator includes an electrode coupled to the first conductor of that resonator and disposed within the afterburner. Moreover, a concentrator of the electrode is disposed within the afterburner channel so that the plasma corona is provided within the afterburner channel. 
     In some implementations of the example system, the system can include a shield configured to shield the resonator from at least at least a portion of a force resulting from the input gas flowing in the afterburner channel. 
     In some implementations of the example system, the fuel includes JP-4, JP-9, JP-10, Jet A, Jet A-1, Jet B, a kerosene-gasoline mixture, diesel, and/or Fischer-Tropsch Synthesized Paraffinic Kerosene. 
     XII. Example Methods 
       FIG. 39  is a flow chart depicting operations of a representative method for combusting fuel in an afterburner. Two or more operations and/or portions of two more operations may, but need not necessarily, be performed at the same time. 
     At block  3900 , the method includes receiving input gas from a turbine of a jet engine into an afterburner channel defined by an afterburner duct of an afterburner. 
     At block  3902 , the method includes outputting fuel into the afterburner channel for mixing with the input gas from the turbine of the jet engine. 
     At block  3904 , the method includes exciting a plurality of resonators electromagnetically coupled to at least one radio-frequency power source. Each resonator has a resonant wavelength. Furthermore, each resonator includes a first conductor, a second conductor, and a dielectric between the first conductor of that resonator and the second conductor of that resonator. 
     At block  3906 , the method includes, in response to exciting each resonator of the plurality of resonators, providing within the afterburner at least one of electromagnetic waves or a plasma corona proximate to that resonator. 
     At block  3908 , the method includes outputting, from the afterburner channel, an exhaust gas resulting from combustion of the fuel within the afterburner channel. 
     In some implementations, the plurality of resonators is arranged as at least one ring of resonators including a first ring of resonators. As an example, the first ring of resonators includes multiple resonators attached to (i) the afterburner duct, (ii) a bracket, or (iii) the afterburner duct and the bracket. 
     In example implementations, at least a first portion of the fuel conduit is disposed within the first conductor. As an example, the first conductor includes an interior surface that defines at least the first portion of the fuel conduit. As another example, tat least the first portion of the fuel conduit is disposed within a cavity of the first conductor. 
     In some implementations, the at least one radio-frequency power source includes at least a first radio-frequency power source and a second radio-frequency power source. The plurality of resonators include at least (i) a first resonator set having at least one resonator configured to be electromagnetically coupled to at least the a first radio-frequency power source, and (ii) a second resonator set having at least one resonator configured to be electromagnetically coupled to at least the second radio-frequency power source. Moreover, each first radio-frequency power source is configured to provide the signal to at least one resonator of the first resonator set. Likewise, each second radio-frequency power is configured to provide the signal to at least one resonator of the second resonator set. 
     Furthermore, the method for the preceding implementations can also include providing, by at least one direct-current power source, a respective bias signal between the first conductor and the second conductor of at least one resonator from the first resonator set, at least one resonator from the second resonator set, or a least one resonator from both the first resonator set and the second resonator set. Furthermore still, at least a portion of each resonator of the first resonator set can be disposed within a fuel supply line fluidly coupled to the fuel outlet, and a least a portion of each resonator of the second resonator set is disposed within the afterburner channel. 
     In some implementations, each resonator of the plurality of resonators is selected from the group consisting of: a coaxial-cavity resonator, a dielectric resonator, a crystal resonator, a ceramic resonator, a surface-acoustic-wave resonator, an yttrium-iron-garnet resonator, a rectangular-waveguide cavity resonator, a parallel-plate resonator, and a gap-coupled microstrip resonator. 
     In some implementations, exciting the plurality of resonators comprises exciting the plurality of resonators simultaneously so that each resonator of the plurality of resonators provides at least one of the electromagnetic waves or the plasma corona simultaneously. As an example, the plurality of resonators can be excited simultaneously so that each resonator of the plurality of resonators provides the electromagnetic waves simultaneously. As an example, the plurality of resonators can be excited simultaneously so that each resonator of the plurality of resonators provides the electromagnetic waves and the plasma corona simultaneously. As yet another example, the plurality of resonators can be excited simultaneously so that some of the resonators provide the electromagnetic waves and the plasma corona, while the other resonators are providing the electromagnetic waves, but not the plasma corona. 
     The particular arrangements shown in the figures should not be viewed as limiting. It should be understood that other implementations can include more or less of each element shown in a given figure. Further, some of the illustrated elements can be combined or omitted. Yet further, an illustrative implementation can include elements that are not illustrated in the figures. 
     A step or block that represents a processing of information can correspond to circuitry that can be configured to perform the specific logical functions of a method or technique as presently disclosed. Alternatively or additionally, a step or block that represents a processing of information can correspond to a module, a segment, or a portion of program code (including related data). The program code can include one or more instructions executable by a processor for implementing specific logical functions or actions in the method or technique. The program code and/or related data can be stored on any type of computer-readable medium such as a storage device including a disk, hard drive, or other storage medium. 
     The computer-readable medium can also include non-transitory computer-readable media such as computer-readable media that store data for short periods of time like register memory, processor cache, and random access memory (RAM). The computer-readable media can also include non-transitory computer-readable media that store program code and/or data for longer periods of time. Thus, the computer-readable media can include secondary or persistent long term storage, like read only memory (ROM), optical or magnetic disks, compact-disc read only memory (CD-ROM), for example. The computer-readable media can also be any other volatile or non-volatile storage systems. A computer-readable medium can be considered a computer-readable storage medium, for example, or a tangible storage device. 
     While various examples and implementations have been disclosed, other examples and implementations will be apparent to those skilled in the art. The various disclosed examples and implementations are for purposes of illustration and are not intended to be limiting, with the true scope being indicated by the claims.