Patent Publication Number: US-2019186287-A1

Title: Power-generation Turbine Including Resonator-based Diagnostics

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); “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” (identified by attorney docket number 17-1533); “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). 
     Power-generation turbines can produce energy. That energy can be used to power a variety of structures, such as homes, offices, cars, or trains, for example. One way in which a power-generation turbine can produce energy is by combusting hydrocarbon fuel to generate heat. 
     SUMMARY 
     In a first implementation, a power-generation turbine is provided. The power-generation turbine includes a combustion chamber configured to house a combustion event of a fuel mixture. The power-generation turbine also includes a resonator having a characteristic impedance and a resonant wavelength. The resonator includes a first conductor and a second conductor separated from one another by an interstitial space that is exposed to an environment of the combustion chamber. Further, the power-generation turbine includes a controller communicatively coupled to the resonator and configured to perform operations. The operations include determining a characteristic of the resonator selected from the group consisting of the characteristic impedance and the resonant wavelength. The operations also include based on the determined characteristic, determining a parameter of the combustion chamber. 
     In a second implementation, a power-generation turbine is provided. The power-generation turbine includes a combustion chamber configured to house a combustion event of a fuel mixture. The power-generation turbine also includes a primary resonator having a primary characteristic impedance and a primary resonant wavelength. The primary resonator includes a primary first conductor and a primary second conductor separated from one another by a primary interstitial space that is exposed to a primary region of an environment of the combustion chamber. Further, the power-generation turbine includes a secondary resonator having a secondary characteristic impedance and a secondary resonant wavelength. The secondary resonator includes a secondary first conductor and a secondary second conductor separated from one another by a secondary interstitial space that is exposed to a secondary region of the environment of the combustion chamber. The primary region and the secondary region of the environment of the combustion chamber are disposed at different locations within the combustion chamber. In addition, the power-generation turbine includes a controller communicatively coupled to the primary resonator and the secondary resonator and configured to perform operations. The operations include determining a primary characteristic of the primary resonator selected from the group consisting of the primary characteristic impedance and the primary resonant wavelength. The operations also include determining a secondary characteristic of the secondary resonator selected from the group consisting of the secondary characteristic impedance and the secondary resonant wavelength. Further, the operations include, based on the determined primary characteristic and the determined secondary characteristic, determining a differential selected from the group consisting of a temperature differential, a pressure differential, an air composition differential, a differential in fuel-to-air ratio, and a combustion-percentage differential. 
     In a third implementation, a power-generation turbine is provided. The power-generation turbine includes a combustion chamber configured to house a combustion event of a fuel mixture. The power-generation turbine also includes a resonator having a characteristic impedance and a resonant wavelength. The resonator includes a first conductor. The resonator also includes a second conductor. Further, the resonator includes a dielectric between the first conductor and the second conductor. A distal end of the resonator is exposed to an environment of the combustion chamber. In addition, the power-generation turbine includes a controller communicatively coupled to the resonator and configured to perform operations. The operations include determining a characteristic of the resonator selected from the group consisting of the characteristic impedance and the resonant wavelength. The operations also include, based on the determined characteristic, determining a parameter of the combustion chamber. 
     In a fourth implementation, a method is provided. The method includes determining, by a controller communicatively coupled to a resonator, a characteristic of a resonator selected from the group consisting of a characteristic impedance and a resonant wavelength. The resonator includes a first conductor and a second conductor separated from one another by an interstitial space that is exposed to an environment of a combustion chamber configured to house a combustion event of a fuel mixture within a power-generation turbine. The method also includes, based on the determined characteristic, determining, by the controller, a parameter of the combustion chamber. 
     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 core components of a power-generation turbine. 
         FIG. 9  illustrates a partial cross-sectional view of a combustor of a power-generation turbine. 
         FIG. 10A  illustrates a combustion chamber, according to example implementations. 
         FIG. 10B  illustrates a combustion chamber, according to example implementations. 
         FIG. 10C  illustrates a combustion chamber, according to example implementations. 
         FIG. 10D  illustrates a combustion chamber, according to example implementations. 
         FIG. 11A  illustrates a combustion chamber, according to example implementations. 
         FIG. 11B  illustrates a combustion chamber, according to example implementations. 
         FIG. 12  illustrates a 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 
     As described in the present disclosure, a power-generation turbine or a combustion chamber of a power-generation turbine can include a resonator used for diagnostics. In some implementations, for example, the resonator could include a coaxial resonator, such as a QWCCR structure. The resonator can have an associated resonant wavelength. The resonant wavelength can depend on qualities of the resonator, such as geometry of the resonator, dimensions of the resonator, and materials of the resonator. Similarly, the resonator can also have an associated characteristic impedance. The characteristic impedance can depend on qualities of the resonator, as well. The qualities that determine the characteristic impedance of the resonator can be similar qualities or the same qualities as the qualities that determine the resonant wavelength of the resonator, for example. 
     In addition, both the resonant wavelength and the characteristic impedance of the resonator might depend on an environment of the resonator. For example, the resonant wavelength and the characteristic impedance of the resonator might depend on the temperature of the environment, pressure of the environment, and/or a chemical composition of the environment. In an example implementation, where the resonator is a coaxial resonator, the resonator can include an inner conductor separated by a distance from an outer conductor. The space between the inner conductor and the outer conductor can be referred to as an “interstitial space.” If the environment near the resonator is permitted to enter/occupy the interstitial space, the environment can alter the resonant wavelength and/or the characteristic impedance of the resonator. For example, because the resonant wavelength and characteristic impedance depend on the relative dielectric permittivity of a dielectric located between the inner conductor and the outer conductor, and the relative dielectric permittivity of a fuel/air mixture changes with temperature, pressure, and chemical composition, the resonant wavelength and/or characteristic impedance depend on the conditions of the environment within the interstitial space. In some implementations, the relative magnetic permeability of the fuel/air mixture, which also affects the resonant wavelength and characteristic impedance, may also change with temperature, pressure, and/or chemical composition. For example, if one or more of the compounds within the fuel/air mixture is paramagnetic, the relative magnetic permeability of the fuel/air mixture may be non-unity. Even further, the environment located proximate to the distal end of the resonator can also affect the characteristic impedance and/or resonant wavelength of the resonator. This may be in addition to or instead of any effect the environment occupying the interstitial space has on the characteristic impedance and/or resonant wavelength of the resonator. 
     Further, the resonator could be communicatively coupled to a controller. The controller can determine the resonant wavelength and/or the characteristic impedance of the resonator. Such a determination can be made by the controller directly. Alternatively, such a determination can be made by the controller indirectly through a diagnostic sensor that is also communicatively coupled to the controller. For example, the controller can be communicatively coupled to an oscilloscope, spectrum analyzer, AC volt meter, or other impedance measurement device to determine the impedance of the resonator. In some implementations, the controller can be communicatively coupled to a power meter used to determine a power reflected from the resonator when the resonator is excited by an RF power source such as the signal generator  202  illustrated in  FIG. 2 . Further, the controller can repeatedly determine the resonant wavelength and/or the characteristic impedance in order to track changes in the resonant wavelength and/or the characteristic impedance. Still further, the controller can be communicatively coupled to one or more auxiliary sensors whose input is used by the controller to determine the characteristic impedance and/or the resonant wavelength. For example, the controller can be communicatively coupled to a thermometer to receive a temperature reading. Using the temperature reading as an auxiliary input (in addition to the oscilloscope, for example), the controller can determine the pressure within the environment of the resonator. 
     Based on the determined characteristic impedance and/or the determined resonant wavelength, the controller can determine a parameter of the combustion chamber. The determined characteristic impedance can include a change in the characteristic impedance, and/or the determined resonant wavelength can include a change in the resonant wavelength. Further, in some implementations, other characteristics of the resonator in addition to or instead of the characteristic impedance and the resonant wavelength can be measured to determine a parameter of the combustion chamber. In some implementations, because the characteristic impedance and the resonant wavelength depend upon the temperature of the environment within the interstitial space, a measurement of the characteristic impedance or the resonant wavelength can indicate the temperature within the interstitial space. Additionally or alternatively, the controller can determine pressure within the environment within the interstitial space and/or chemical composition of the environment within the interstitial space (such as chemical composition of a fuel/air mixture). The pressure, temperature, chemical composition, or other parameters within the combustion chamber can be determined by the controller using a look-up table, in some implementations. 
     Based on the determined parameter, the controller can make control decisions for the ignition and combustion of fuel and/or a fuel/air mixture within the combustion chamber. For example, if the controller determines that the temperature or pressure within the combustion chamber is too low or too high, the controller can change one or more operating conditions, such as a fuel type of the fuel mixture, a fuel-to-air ratio of the fuel mixture, a fuel flow rate, an operating temperature, an operating pressure, a fuel-injection location in the combustion chamber, a fuel-injection frequency in the combustion chamber, etc. Other adjustments made by the controller based on the determined parameter of the combustion chamber are also possible. 
     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 j et 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 v 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, v 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 (v a ) 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 e ). 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, ∂ y  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 
                   
                 
                 -&gt; 
                 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 
                       
                     
                     ) 
                   
                 
                 -&gt; 
                 
                   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 (h) can include ohmic losses (P a ) 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 H //  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 (E) 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 (A) 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 
                 ) 
               
             
             = 
             
               
                 
                   ∫ 
                   
                     π 
                     2 
                   
                 
                 0 
               
                
               
                 
                   
                     
                       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 
               
                 r 
                  
                 
                     
                 
                  
                 ad 
               
             
             = 
             
               
                 
                   1 
                   4 
                 
                  
                 
                   ( 
                   
                     
                       B 
                       r 
                     
                     ω 
                   
                   ) 
                 
                  
                 
                   V 
                   ab 
                   2 
                 
               
               = 
               
                 
                   
                     
                       
                         
                           ɛ 
                            
                           V 
                         
                         0 
                         2 
                       
                        
                       
                         ( 
                         
                           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 
                     + 
                     
                       U 
                       rad 
                     
                   
                   ) 
                 
               
               
                 
                   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 (A). 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 (ω) (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: ¾λ 0 , 5/4λ 0 , 7/4λ 0 , 9/4λ 0 , 11/4λ 0 , 13/4λ 0 , etc.). 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, a 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 a 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, ½λ 0 , 3/2λ 0 , 5/2λ 0 , 7/2λ 0 , 9/2λ 0 , 11/2λ 0 , 13/2λ 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. Power-Generation Turbines 
     The above coaxial resonators could be usefully employed in the context of a power-generation turbine. 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 power-generation turbine includes a compressor coupled to a turbine through a shaft, and the power-generation turbine also includes a combustion chamber or area, called a combustor. It is understood that, as presently described, the terms “power-generation turbine,” “power-generation gas turbine,” and “gas turbine” are used synonymously and/or interchangeably. 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. 
     An example gas turbine includes an upstream rotating compressor coupled to a downstream turbine, and a combustion chamber or area, called a combustor, in between the compressor and the turbine. 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 the exhaust pressure, producing a shaft work output in the process. In a power-generation turbine, the shaft work is used to drive the compressor and an electric generator that can be coupled to the shaft. 
       FIG. 8  illustrates core components of an example power-generation turbine  800 . In this arrangement, large amounts of surrounding air (free stream) are continuously brought into an inlet or intake  802 . At the rear of the intake  802 , the air then enters a compressor  804  (axial, centrifugal, or both). The compressor  804  operates as many rows of airfoils, with each row producing an increase in pressure. At the exit of the compressor  804 , the air is therefore at a much higher pressure than when it enters the intake  802 . 
     Fuel is mixed with the compressed air exiting the compressor  804 , and the fuel-compressed air mixture is burned in a combustor  806 , generating a flow of hot, high pressure gas. The hot, high pressure air exiting the combustor  806  is then passed through a first turbine  808 . The first turbine  808  extracts energy from a flow of gas by making blades of the first turbine  808  spin in the flow. The first turbine  808  can include several stages, and the energy extracted by the first turbine  808  is used to turn the compressor  804  by linking or coupling the compressor  804  and the first turbine  808  by a central shaft  810 . 
     The above-mentioned components of the power-generation turbine  800  can be referred to collectively as the gas generator. The power-generation turbine  800  further includes a power section having a second turbine  812  and an output shaft  814 . The output shaft  814  can be coupled to an electric generator. Particularly, the output shaft  814  can be connected to a rod or shaft of the electric generator that turns one or more magnets surrounded by coils of copper wire. The fast-revolving generator magnet creates a powerful magnetic field that lines up the electrons around the copper coils and causes them to move, providing an electrical current, and thereby generating electricity. 
     In examples, the gas generator and power section of the power-generation turbine  800  are mechanically-separate so they can each rotate at different speeds appropriate for the conditions. In other examples, the power-generation turbine  800  might not include two turbines  808 ,  812  but can have a single turbine driving both the compressor  804  and the output shaft  814 . Further, although  FIG. 8  illustrates the output shaft  814  exiting an end of the power-generation turbine  800  that is opposite the intake  802 , in some examples, the output shaft  814  is disposed and rotatable within the central shaft  810  and exits the power-generation turbine  800  from the intake  802 . 
     One way to boost efficiency of the power-generation turbine  800  is to install a recuperator or to use a heat-recovery steam generator (HRSG) to recover energy from the exhaust of the second turbine  812 . If a recuperator is installed, the recuperator captures waste heat in the gases exiting the turbines  808 ,  812  to preheat the compressed air discharged by the compressor  804  before the compressed air enters the combustor  806 . If a HRSG is used, the HRSG generates steam by capturing heat from the gases exiting the turbines  808 ,  812 . High-pressure steam generated by the HSRG can be used to generate additional electric power with steam turbines in a “combined cycle” configuration. 
     The combustor  806 , which can also be referred to as a burner, a combustion chamber, or a flame holder, comprises the area of the power-generation turbine  800  where combustion takes place. The combustor  806  of the power-generation turbine  800  is configured to contain and maintain stable combustion despite high air flow rates. As such, in examples, the combustor  806  is configured to mix the air and fuel, ignite the air-fuel mixture, and then mix in more air to complete the combustion process. 
     Combustors of power-generation turbines can be classified into several types. For example, a first type of combustor can be referred to as an annular combustor in which the combustor is configured as a continuous chamber that encircles the air in a plane perpendicular to the air flow. A second type of combustor can be referred to as can-annular, which is similar to the annular type but incorporates several can-shaped combustion chambers rather than a single continuous chamber. The can-shaped combustion chambers can be disposed in a radial array about a longitudinal axis of the power-generation turbine. The can-shaped combustion chambers could be disposed perpendicular to the longitudinal axis, parallel to the longitudinal axis, or at a particular angle relative to the longitudinal axis. A third type of combustor can be referred to as a can or silo combustor that can include one or more self-contained combustion chambers mounted externally to the power-generation turbine. 
       FIG. 9  illustrates a partial cross-sectional view of a combustor  900  of a power-generation turbine. In an example implementation, the combustor  900  could represent the combustor  806  of the power-generation turbine  800  described above. 
     The combustor  900  includes a case  902  that is configured as an outer shell of the combustor  900 . The case  902  can be protected from thermal loads by the air flowing in it, and can operate as a pressure vessel configured to withstand the difference between the high pressures inside the combustor  900  and the lower pressure outside. 
     The combustor  900  further includes a liner  904  that could be slot-cooled and configured to contain the combustion process. The liner  904  is configured to withstand extended high temperature cycles, and therefore can be made from superalloys. Furthermore, the liner  904  is cooled with air flow. In some example implementations, in addition to air cooling, the combustor  900  can include thermal barrier coatings to further cool the liner  904 . 
       FIG. 9  further illustrates air flow paths through the combustor  900 . Compressed discharge air exiting the compressor  804  can flow through a compressor discharge air opening  906  disposed in the combustor  900 . The air entering through the compressor discharge air opening  906  flows through a flow sleeve  908  and is the source of combustion air  910 , which is highly compressed air. The combustion air  910  can be decelerated using a diffuser and is fed through main channels of the combustor  900 . This air is mixed with fuel, and then combusted in a combustion zone  912 . 
     A portion of the compressed discharge air, referred to as dilution air  914 , is injected through dilution air holes in the liner  904  at the end of the combustion zone  912  to help cool the air before it reaches the first turbine  808 . The dilution air  914  can be used to produce the uniform temperature profile desired in the combustor  900 . 
     Further, a portion of the compressed discharge air, referred to as cooling air  916 , is injected through cooling air holes in the liner  904  to generate a layer (film) of cool air to protect the liner  904  from the high combustion temperatures. The combustor  900  can be configured such that the cooling air  916  does not directly interact with the combustion air  910  and the combustion process. 
     The combustor  900  further includes a fuel injector  918  configured to introduce fuel to the combustion zone  912  for mixing the fuel with the combustion air  910 . The fuel injector  918  can be configured as any of several types of fuel injectors, including without limitation: pressure-atomizing, air blast, vaporizing, and premix/prevaporizing injectors. 
     Pressure-atomizing fuel injectors utilize high fuel pressures (as much as 500 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 fuel injector can include a port  920  configured to receive atomizing air. The air blast injector “blasts” fuel with a stream of air received through the port  920 , atomizing the fuel into homogeneous droplets, and can cause the combustor  900  to be smokeless. The air blast fuel 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 combustion air  910  is mixed with the fuel as it is injected into the combustion zone  912 . However, with the vaporizing fuel injector, the fuel-air mixture travels through a tube within the combustion zone  912 . Heat from the combustion zone  912  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  904 . 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  912 . In such a scenario, the fuel is uniformly mixed with the air, and emissions from the power-generation turbine  800  can be reduced. However, in some cases, fuel can auto-ignite or otherwise combust before the fuel-air mixture reaches the combustion zone  912 , and the combustor  900  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  918  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 the electromagnetic waves radiated by the resonator could be used to energize the air-fuel mixture and stimulate combustion. 
     In examples, the power-generation turbine  800  could be a dual-fuel turbine. A dual-fuel turbine can run primarily with one type of gas (for example, natural gas) as fuel but can also have a back-up fuel supply system if the gaseous fuel is not available. For instance, the dual-fuel turbine can be configured to also receive liquid fuel and water through a pipe system. 
     In an example, to accommodate different types of fuel, the fuel injector  918  could be configured as a dual-fuel nozzle assembly configured to receive two types of fuel. For instance, the fuel injector  918  can have a gas-fuel port  922  configured to be fluidly coupled to a source of gaseous fuel, and can also have a liquid-fuel port  924  configured to be fluidly coupled to a source of liquid fuel. 
     Example fuels that could be provided to the power-generation turbine  800  include, without limitation: Arabian Extra Light Crude Oil (AXL), Arabian Super Light (ASL), Biodiesel Condensate or Natural Gas Liquids (NGL), Dimethyl Ether (DME), Distillate Oil #2 (DO2), Ethane (C 2 ), Heavy Crude Oil, Heavy Fuel Oil (HFO), High H 2 , Hydrogen Blends, Kerosene (Jet A or Jet A-1), Lean Methane, Light Crude Oil (LCO), Liquid Natural Gas (LNG), Liquefied Propane Gas (LPG), Medium Crude Oil, Methanol/Ethanol (Alcohol), Naphtha, Natural Gas (NG), Sour Gas (H 2 S), Steel Mill Gases, and Syngas. 
     Each of these fuels can have a particular air-to-fuel mixture ratio (or desirable mixture ratio range) at which the fuel is burnt. Under some conditions, if the air-fuel mixture has an air-to-fuel ratio that is less than the particular air-to-fuel ratio, combustion might not occur. Further, each fuel can have different combustion characteristics. The resonators disclosed in the present disclosure may enable gas turbines to operate on a wide variety of gaseous and liquid fuels while burning fuels efficiently and without changes to the gas turbines. 
     The combustor  900  also includes an igniter  926 . In examples, the igniter  926  can be configured as an electrical spark igniter, similar to an automotive spark plug. However, there are several disadvantages to such configuration. For instance, a spark plug might not be capable of igniting different types of fuel with different air-to-fuel ratios and combustion characteristics. Further, even if the spark plug is capable of igniting some mixtures, achieving high efficiencies for different types of fuel and air-to-fuel ratios can be difficult. 
     The igniter  926  can be disposed proximate to the combustion zone  912  where the fuel and air are already mixed. To avoid damage by the combustion itself, the igniter  926  can be located proximate to the combustion zone  912 , but upstream from the combustion location. In example implementations, once combustion is initially started by the igniter  926 , the combustion can be self-sustaining and the igniter  926  need no longer be used. However, in some examples, it can be desirable to have the igniter  926  configured to facilitate detection of changes in operational characteristics of the gas turbine or the combustion process that could lead to extinguishing combustion, and proactively prevent such extinguishment. 
     The combustor  900  can further include a transition assembly  928  that couples the combustor  900  to the first turbine  808  such that hot air resulting from the combustion zone  912  flows through the transition assembly  928  to the first turbine  808 . 
     The combustor  900  illustrated in  FIG. 9  represents one implementation, and other possible variations are possible. For example, rather than having a fuel injector including two ports for two different types of fuel, the combustor can include different, independent fuel injectors, each fuel injector configured to provide a respective type of fuel to the combustion zone  912 . In other examples, the combustor  900  can have a port configured to receive water or steam injection to provide control of NO x  gases in the combustion zone  912 . 
     Additionally, in examples, the combustor  900  can have several combustion stages, including, for example, a pilot stage. The power-generation turbine  800  can be configured to provide fuel to each stage in the combustor  900  through a respective tube. Other example variations are possible. 
     The combustion taking place at the combustor  900  may affect many of the operating characteristics of the power-generation turbine  800 . As examples, combustion may determine fuel efficiency, output power level, and levels of emissions of the power-generation turbine  800 . It can thus be desirable to have an ignition system that prepares the fuel for efficient and thorough combustion regardless of the type of fuel, reduces emissions, and that facilitates starting and sustaining ignition regardless of air-to-fuel ratio and the type of fuel. 
     IX. Resonator-based Diagnostics in a Power-generation Turbine 
       FIG. 10A  illustrates a combustion chamber  1010  configured to house a combustion event of a fuel mixture, according to example implementations. In some implementations, the combustion chamber  1010  can be a component of a power-generation turbine (for example, the power-generation turbine  800  illustrated in  FIG. 8 ). The combustion chamber  1010  can be similar to the combustor  900  illustrated in  FIG. 9 , for example. Unlike  FIG. 9 , however, the arrangement of  FIG. 10A  includes a resonator. In various implementations, the resonator can include a coaxial-cavity resonator, a dielectric resonator, a crystal resonator, a ceramic resonator, a surface-acoustic-wave resonator, a 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 description, it will be understood that other types of resonators are possible and contemplated. 
     In addition to the resonator,  FIG. 10A  illustrates an impedance sensor, an RF power source, a controller, and a user interface  1002 . In various implementations, the impedance sensor can include the impedance sensor  404  shown and described with reference to  FIG. 4A , the RF power source can include the signal generator  202  shown and described with reference to  FIG. 2 , and/or the controller can include the controller  402  shown and described with reference to  FIGS. 4A and 4B . 
     As shown by way of example in  FIG. 10A , the resonator can be the coaxial resonator  201  illustrated in  FIG. 2 , in some implementations. As described above, the coaxial resonator  201  can include the inner conductor  324 , the outer conductor  322 , and the dielectric  328 . In some implementations, the coaxial resonator can also include the electrode  326 . The electrode  326 , and possibly an associated concentrator, can concentrate the electric field of the coaxial resonator  201  in implementations that provide a plasma corona  1014 . Further, the coaxial resonator  201  can have a characteristic impedance and a resonant wavelength based, at least in part, on the dimension, relative locations, and materials of the inner conductor  324 , the outer conductor  322 , and the dielectric  328 , as well as on the environment in and/or around the coaxial resonator  201  (for example, the environment in or around the combustion chamber  1010 ). 
     As illustrated in  FIG. 10A , the coaxial resonator  201  can be disposed near the fuel injector  918  within the combustion zone  912 . Further, the coaxial resonator  201  can be configured to radiate electromagnetic waves  1012  (for example, microwaves) when excited by a radio-frequency power source (for example, the signal generator  202  illustrated in  FIG. 2 ) with a signal having a wavelength proximate to an odd-integer multiple of one-quarter (¼) of the resonant wavelength of the coaxial resonator  201 . The electromagnetic waves  1012  can interact with the injected fuel and modify the injected fuel. For example, the electromagnetic waves  1012  can modify the fuel by ionizing at least one hydrogen atom in a hydrocarbon chain, liberating at least one hydrogen atom from a hydrocarbon chain, exciting a hydrocarbon chain at one or more natural resonant frequencies to break one or more carbon-hydrogen bonds, altering an energy state of the fuel, exciting electrons within a valence band of a hydrocarbon chain to a higher energy level, and/or reorienting polar hydrocarbon chains. 
     Further, because a portion or the entirety of the combustion zone  912  of the combustion chamber  1010  can be exposed to the electromagnetic waves  1012 , the electromagnetic waves  1012  can also modify qualities of a fuel/air mixture. For example, electromagnetic waves  1012  can impart a torque on any substance having an electric dipole moment. Hence, the electromagnetic waves  1012  can reorient polar molecules within an air portion of the fuel/air mixture. In one implementation, for instance, the electromagnetic waves  1012  can reorient water molecules within the air portion of the fuel/air mixture. The act of reorienting polar molecules can impart a kinetic energy on the polar molecules, thereby increasing a temperature and/or an energy state of the polar molecules within the fuel/air mixture. In other implementations, other modifications by the electromagnetic waves  1012  to the fuel and/or the fuel/air mixture are also possible. 
     Additionally or alternatively, the coaxial resonator  201  can be configured to provide the plasma corona  1014  when excited by the signal generator  202  with a signal having a wavelength proximate to an odd-integer multiple of one-quarter (¼) of the resonant wavelength of the coaxial resonator  201 . The plasma corona  1014  can be used as an ignition source to ignite a fuel/air mixture within the combustion zone  912 , for example. Such an ignition source can augment and/or replace the igniter  926 , in some implementations. 
     In still other implementations, the coaxial resonator  201  might not be configured to radiate electromagnetic waves  1012  or provide the plasma corona  1014 . For example, the coaxial resonator  201  could be configured solely as a diagnostic device (sensor) used to sense environmental conditions within the combustion zone  912  of the combustion chamber  1010 . In various implementations, the coaxial resonator  201  can have various orientations relative to the fuel injector  918 . For example, the distal end of the resonator  201  can be facing toward the fuel injection site. In other implementations, the distal end of the resonator  201  can be facing away from the fuel injection site. In still other implementations, such as the implementation illustrated in  FIG. 10A , the distal end of the resonator  201  can be facing somewhere in between directly toward and directly away from the fuel injection site. In other words, the coaxial resonator could be arranged at a variety of orientations, including facing upstream, downstream, or at another position with regard to at least one of a fuel injection direction or an airflow direction within the combustion zone  912 . 
     In alternate implementations, the coaxial resonator  201  could be disposed in other regions of the combustion zone  912 . For example, the coaxial resonator  201  could be disposed near an exhaust region of the combustion zone  912  in order to monitor parameters of exhaust gases (for example, temperature, pressure, and/or chemical composition). In various implementations, the coaxial resonator  201  can be disposed entirely within the combustion zone  912 , mostly outside of the combustion zone  912  with just a distal end of the coaxial resonator  201  being exposed to the combustion zone  912 , or entirely outside of the combustion zone  912  (for example, to monitor other regions of the combustion chamber  1010 ). 
     As illustrated in  FIG. 10A , the distal end of the coaxial resonator  201  can be exposed to the combustion zone  912 . When calculating characteristic impedance, fringing electric and magnetic fields near the distal end of the coaxial resonator  201  might be neglected. However, if the fringing electric and fringing magnetic fields are not neglected, an environment near the distal end of the coaxial resonator  201  (in addition to or instead of the environment within the interstitial space) can affect the resulting characteristic impedance calculation. For example, the characteristic impedance of the coaxial resonator  201  may depend on the temperature, pressure, or chemical composition of the environment near the coaxial resonator  201 . The environment can include the environment of the combustion zone  912  (for example, including a fuel/air mixture in the combustion zone  912 ) or an ambient environment near the combustion chamber  1010  (for example, if the coaxial resonator  201  were disposed outside of the combustion chamber  1010 ). 
     Regardless of whether the fringing electric and fringing magnetic fields are neglected, the dielectric  328  between the inner conductor  324  and the outer conductor  322  can affect the results of a calculation of the characteristic impedance and the resonant wavelength of the coaxial resonator  201 . For example, a dielectric material used to fabricate the dielectric  328  that has a non-unity relative dielectric permittivity can impact a calculated characteristic impedance of the coaxial resonator  201 . In some implementations, however, the dielectric  328  can be removed, and the environment may be permitted to occupy some or all of the interstitial space between the inner conductor  324  and the outer conductor  322 . In this additional way, the environment can alter the characteristic impedance and/or the resonant wavelength of the coaxial resonator  201 . 
     Because the environment impacts a characteristic impedance of and/or a resonant wavelength of the coaxial resonator  201 , the characteristic impedance and the resonant wavelength of the coaxial resonator  201  can be measured to determine various parameters about the environment. Such parameters can be used to diagnose the functionality of the combustion chamber  1010  and to suggest modifications to operating conditions of the combustion chamber  1010 . Such suggested modifications could provide partial or full solutions to one or more issues detected based on the determined parameter of the combustion chamber  1010 . For example, if the determined parameter indicated that a fuel/air mixture within the combustion zone  912  was not completely combusting, a suggested modification to the ignition sequence that increases the amount of ignition could be determined. 
     As such, one way of analyzing present conditions within the combustion chamber  1010  (for example, within the combustion zone  912  of the combustion chamber  1010 ) is to measure the characteristic impedance of the coaxial resonator  201  using the impedance sensor  404 . Similar to the impedance sensor  404  illustrated in  FIG. 4A , the impedance sensor  404  illustrated in  FIG. 10A  measures the characteristic impedance of the coaxial resonator  201 . The characteristic impedance measured by the impedance sensor can then be fed to the controller  402 . The impedance measured by the impedance sensor  404  can be transmitted to the controller  402  as a digital signal or an analog signal, in various implementations. This can be done through a communicative coupling between the controller  402  and the impedance sensor  404 . For example, 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. Further, the controller  402  can modify settings of the impedance sensor  404  through such a communicative coupling. For example, the controller  402  can adjust how frequently (for example, in Hz) the impedance sensor  404  measures the impedance of the coaxial resonator  201  and/or the controller  402  can adjust how frequently (for example, in Hz) the impedance sensor  404  provides the measured impedance of the coaxial resonator  201  to the controller  402 . 
     In some implementations, the controller  402  can transmit an excitation frequency value, used by the signal generator  202  to excite the coaxial resonator  201 , to the impedance sensor  404  such that the impedance sensor  404  can factor in the excitation frequency into a characteristic impedance calculation. In alternate implementations, the controller  402  can receive a raw value from the impedance sensor  404 , which the controller  402  can use along with the excitation frequency value to determine the characteristic impedance of the coaxial resonator  201 . In still other implementations, the excitation frequency can be assumed to be sufficiently high such that the approximation of the characteristic impedance as 
     
       
         
           
             
               
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     can be used, thereby obviating the inclusion of the excitation frequency in any calculations. 
     The impedance sensor  404  can periodically transmit a measured impedance value to the controller  402 . In alternate implementations, the controller  402  can periodically poll the impedance sensor  404  for the measured impedance value, and the impedance sensor  404  can respond by transmitting the measured impedance value. The periodic transmission and/or periodic polling of the measured impedance value can occur according to a predetermined schedule. The predetermined schedule can be based on a scheduling parameter. In various implementations, the scheduling parameter could include a periodic diagnostic rate (for example, a diagnostic frequency at which the controller  402  determines the conditions of the combustion chamber  1010 ), a diagnostic request (for example, a request from an end-user to determine the present conditions of the combustion chamber  1010 ), and/or an operating condition for a power-generation turbine corresponding to the combustion chamber  1401  (for example, a fuel type of the fuel mixture, a fuel-to-air ratio of the fuel mixture, a fuel flow rate, an operating temperature, an operating pressure, a fuel-injection location in the combustion chamber, a fuel-injection frequency in the combustion chamber, etc.). 
     As described above with respect to  FIG. 4A , the impedance sensor  404  can be connected to the coaxial resonator  201  (for example, with 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 the 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. Other impedance sensors are also possible. 
     Using the mathematics described above, for example, the characteristic impedance of the coaxial resonator  201  can be used to determine relative dielectric permittivity and/or relative magnetic permeability of the environment near the coaxial resonator  201 . In some implementations, such a determination can take into account the dimensions and materials of the coaxial cavity  201 . Relative dielectric permittivity and/or relative magnetic permeability can depend on a variety of parameters of the environment. The relationships between the characteristic impedance and the relative dielectric permittivity and/or between the characteristic impedance and the relative magnetic permeability may be known and/or calculable. Hence, the characteristic impedance can be used to determine one or more parameters of the combustion chamber  1010 . For example, the characteristic impedance can be used to determine a compression ratio of air within the fuel mixture relative to ambient air outside of a power-generation turbine corresponding to the combustion chamber  1010 , a pressure of air within the fuel mixture, a composition of air within the fuel mixture, a fuel-to-air ratio of the fuel mixture, a percentage of unburned fuel within the fuel mixture, a temperature of the fuel mixture, and/or a rotational rate of a shaft within a power-generation turbine corresponding to the combustion chamber  1010 . 
     In some implementations, determining the characteristic impedance can include determining a resonant frequency of the coaxial resonator  201 , an open-circuit condition of the coaxial resonator  201 , a short-circuit condition of coaxial resonator  201 , a cut-off frequency of the coaxial resonator  201 , a capacitance of the coaxial resonator  201 , an inductance of the coaxial resonator  201 , a lumped-circuit model of the coaxial resonator  201 , and/or a failure condition of the coaxial resonator  201 . 
     Determining the one or more parameters of the combustion chamber  1010  can include the controller  402  performing a look-up table operation. The look-up table can be stored within a memory (for example, the memory  454  illustrated in  FIG. 4B ) of the controller  402 , in some implementations. Further, the look-up table operation can yield a value for one or more of the corresponding parameters based on the characteristic impedance. In addition to the characteristic impedance, the values for the one or more of the corresponding parameters can also be based on dimensions and materials of the coaxial cavity  201 . Still further, the values for the one or more of the corresponding parameters can be based on one or more sensor values from auxiliary sensors. For example, sensor values from a thermometer, a power meter, an anemometer, a barometer, a fuel gauge, a sensor that measures fuel composition, a gas chromatograph, a sensor measuring fuel-to-air ratio in a given fuel mixture, and/or a vibrometer, could be transmitted to the controller  402  and used by the controller  402  in the look-up table operation. The controller  402  can use the sensor values to determine one or more additional parameters of the combustion chamber  1010 , such as an ambient air temperature outside of the power-generation turbine, an ambient pressure outside of the power-generation turbine, an ambient air composition outside of the power-generation turbine, a sensed vibration, a fuel flow rate of fuel being injected into the combustion chamber, a power demand on the power-generation turbine, and/or a rotational rate of a shaft within the power-generation turbine. As just one of many examples of a look-up table operation, in one implementation, an ambient temperature measured by an ambient thermometer, an ambient pressure measured by an ambient barometer, an impedance measured by the impedance sensor  404 , and an excitation frequency used by the signal generator  202  to excite the coaxial resonator  201  could be fed into the look-up table in order to determine a fuel/air ratio of a fuel mixture within the combustion zone  912 , where the fuel mixture is occupying the interstitial space of the coaxial resonator  201 . Numerous additional example look-up table operations are contemplated by the present disclosure. 
     In some implementations, the look-up table can be developed according to a mathematical model. Such a mathematical model can be determined analytically according to equations describing physical phenomena, such as the equations described above. Alternatively, such a mathematical model can be machine-learned (for example, according to a support vector machine or an artificial neural network) based on training data. For example, training data can include multiple known characteristic impedances in conjunction with various impedance values from the impedance sensor  404  and various auxiliary sensor values from the one or more auxiliary sensors. In alternate implementations, the look-up table can be hard-coded and/or set by a user (for example, using the user interface  1002 ). Even further, the look-up table can be developed purely empirically. For example, the look-up table could include a correspondence of pressure values and temperature values to the characteristic impedance. Such a correspondence could be built from a library of prior measurements that recorded the temperature from a thermometer, the pressure from a barometer, and the characteristic impedance from an impedance sensor all simultaneously or substantially simultaneously (for example, within 1 ms, 10 ms, 100 ms, or 1 second) in order to identify a possible interrelationship between temperature, pressure, and characteristic impedance. 
     In addition to or instead of a look-up table operation, the controller  402  can perform a calculation to determine the characteristic impedance. The calculation can be based on the impedance value from the impedance sensor  404 , an excitation frequency used by the signal generator  202  to excite the coaxial resonator  201 , dimensions and materials of the coaxial cavity  201 , and/or auxiliary sensor values from one or more auxiliary sensors. Further, the calculations can be performed using analytical mathematical models and/or empirical mathematical models (for example, statistical approximations based on collected data sets). In such calculations, the auxiliary sensor values from the one or more auxiliary sensors can be used to reduce the number of unknown variables within a system of equations. For example, multiple equations can be used to describe the interrelationship between the characteristic impedance and other parameters of the combustion chamber  1010 . As just one example of many, the ideal gas law could be used to interrelate a volume of the combustion zone  912 , a pressure of the fuel/air mixture in the combustion zone  912 , and a temperature in the combustion zone  912 . By eliminating enough unknown variables using the auxiliary sensor data, a system of linear equations can be reduced to a system with a number of unknown variables equal to the number of linearly independent equations in the system, thereby resulting in a singular solution for each unknown variable. As one example, the controller  402  could use a measured characteristic impedance, the dimensions of the coaxial resonator  201 , and an assumption that the surrounding environment has a relative magnetic permeability of 1.0 to, based on the following equations from above, determine the relative dielectric permittivity (ε r ) of the environment within the interstitial space of the coaxial resonator  201 : 
     
       
         
           
             
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     The controller  402 , based on the determined relative dielectric permittivity of the environment and a correspondence between relative dielectric permittivity of the environment and temperature of the environment, could then determine the temperature of the environment within the interstitial region of the coaxial resonator  201 . The temperature of the environment may correspond to a temperature of a fuel/air mixture within the combustion zone  912  of the combustion chamber  1010  that has entered the interstitial region of the coaxial resonator  201 , for example. The correspondence between relative dielectric permittivity of the environment and temperature of the environment (or whatever parameter of the combustion chamber  1010  is being evaluated) may have been previously determined experimentally. For example, it may have been determined that there is a positive, linear relationship between relative dielectric permittivity and temperature in the environment. Thus, a regression line with a predetermined slope and x-intercept could be used to determine the temperature of the environment based on the relative dielectric permittivity of the environment. It is understood that other ways of determining a correspondence, besides experimentally, between physical quantities (such as relative dielectric permittivities) and parameters (such as temperature) could be used. For example, a finite element method (FEM) analysis or finite difference method analysis could be performed to determine these correspondences. In some implementations, look-up tables and calculations can both be used, in tandem, by the controller  402  to determine the parameter of the combustion chamber  1010 , rather than using look-up tables or calculations individually. 
     The controller  402 , in response to determining the parameter, can adjust an operating condition of the combustion chamber  1010  and/or of a power-generation turbine associated with the combustion chamber  1010 . Adjusting the operating condition can include modifying a type of fuel being injected into the combustion zone  912  in order to form a fuel mixture, a fuel-to-air ratio of the fuel mixture within the combustion zone  912  (for example, by injecting fuel into the combustion zone  912  at an increased or decreased rate), a fuel flow rate of fuel within a fuel conduit coupled to the combustion chamber  1010  (for example, coupled at a fuel injector), an operating temperature of the combustion zone  912  and/or the combustion chamber  1010 , an operating pressure of the combustion zone  912  and/or the combustion chamber  1010 , a fuel-injection location in the combustion zone  912  of the combustion chamber  1010 , and/or a fuel-injection frequency into the combustion zone  912  of the combustion chamber  1010 . In one implementation, for example, the determined parameter can indicate that a fuel mixture within the combustion chamber  1010  was not fully combusting. In response, the controller  402  could adjust the fuel-injection location within the combustion chamber  1010  to increase the combustion of the fuel mixture. In other implementations, the controller  402  could increase input power to the coaxial resonator  201  or a duration of a firing pulse used to excite the coaxial resonator  201 . Alternatively, adjusting the operating condition can include moving the coaxial resonator  201  to a different location region within the combustion chamber  1010  and/or changing an orientation of the coaxial resonator  201  relative to the combustion chamber  1010 . For example, the coaxial resonator  201  can be coupled to a six-axis stage that is controlled by the controller  402  in order to change the position and/or orientation of the coaxial resonator  201 . 
     Adjusting the operating condition(s) within the combustion chamber can improve operation of and/or within the combustion chamber  1010 . In one implementation, adjusting the operating condition(s) can ensure that a fuel-to-air ratio of a fuel mixture within the combustion zone  912  of the combustion chamber  1010  is above a predetermined threshold. For example, if the controller  402  determines a parameter corresponding to the fuel-to-air ratio, and the determined parameter is below a predetermined threshold value, the controller  402  can cause fuel to be injected from a reserve fuel tank into the combustion chamber  1010 . Injecting fuel from the reserve fuel tank can increase the fuel-to-air ratio of the fuel mixture and/or change a fuel composition (in other words, fuel type) of the fuel mixture. Alternatively, adjusting the operating condition(s) can increase the combustion percentage within the combustion zone  912  of the combustion chamber  1010 . For example, if the determined parameter corresponds to a combustion percentage of a fuel mixture within the combustion zone  912  and the determined parameter is below a predetermined threshold value, the temperature and/or pressure within the combustion zone  912  can correspondingly be increased such that the combustion percentage of the fuel mixture is increased. Additionally or alternatively, the controller  402  could, for example, decrease the intervals between which an igniter within the combustion zone  912  attempts to ignite the fuel mixture in order to increase ignition and/or combustion percentage. 
     Additionally or alternatively, the controller  402  can modify a signal being output by the signal generator  202  to excite the coaxial resonator  201 . Modifying the signal can include adjusting a wavelength/frequency of the signal generated by the signal generator  202 . Modifying the wavelength/frequency of the signal can include tuning or detuning the signal relative to a resonant frequency of the coaxial resonator  201  by adjusting the output frequency of the signal generator  202 , for example. In doing so, ignition can be made more or less efficient in terms of power consumption and resulting output power production. Further, modifying the signal can include adjusting the frequency of the signal such that the signal has a wavelength proximate to an odd-integer multiple of one-quarter of the resonant wavelength of the coaxial resonator  201  (for example, such that the resonator provides the plasma corona  1014  proximate to an electrode of the coaxial resonator  201 ). Still further, modifying the signal can include modifying an output power of the signal generator  202 . 
     In addition to adjusting the operating condition(s), the controller  402  can output the determined parameter to the user interface  1002 . In some implementations, the user interface  1002  can include a control panel (for example, a touch screen) on an exterior of a power-generation turbine associated with the combustion chamber  1010 . Additionally or alternatively, the user interface  1002  can be a display associated with a mobile computing device, tablet computing device, laptop computing device, and/or desktop computing device. Such computing devices can be communicatively coupled with the controller  402  through a network interface of the controller  402  (for example, the network interface  456  illustrated in  FIG. 4B ) or in another manner. In some implementations, the user interface  1002  can include other forms of output devices (for example, a speaker or a status light) and/or one or more input devices (for example, a joystick, a keyboard, a mouse, or a microphone). 
     Outputting the determined parameter can indicate to a user the current status of the combustion chamber  1010 . As such, outputting the determined parameter can include outputting an alert. For example, a status light of the user interface  1002  can illuminate to indicate the current fuel-to-air ratio of a fuel mixture being combusted within the combustion zone  912  of the combustion chamber  1010  when the fuel-to-air ratio is the determined parameter. In addition, outputting the determined parameter can indicate an ameliorative or corrective action to be taken in response. Returning to the fuel-to-air ratio example, outputting the determined parameter could indicate to an engineer operating the combustion chamber  1010  to modify a valve used to let air into the fuel chamber and/or a valve used to let fuel into the fuel chamber in order to modify the fuel-to-air ratio of the fuel mixture (for example, to decrease the fuel-to-air ratio by completely or partially closing one or more fuel valves and/or completely or partially opening one or more air valves). Additionally or alternatively, outputting the alert can include providing an indication to a mechanic that a specific region of the combustion chamber  1010  or that a specific component of the combustion chamber  1010  requires servicing. The alert can also indicate a recommended service action to be taken to alleviate or fix an issue within the combustion chamber  1010 . For example, outputting the alert could include an indication to a mechanic that the fuel injector  918  is not working as intended (for example, because it is bent or clogged and insufficient fuel is being injected into the combustion zone  912  of the combustion chamber  1010 ) and recommend a suggested modification to the combustion chamber  1010  (for example, a replacement of the fuel injector  918 ) and/or a power-generation turbine corresponding to the combustion chamber  1010  in order to adjust the determined parameter. 
     Some implementations may not include a user interface  1002 . For example, if a power-generation turbine associated with the combustion chamber  1010  is autonomously controlled by the controller  402 , an output to a user interface might not be needed. Further, in addition to or instead of outputting the determined parameter to the user interface  1002 , in some implementations, the controller  402  could output the determined parameter to a separate interface. For example, the controller  402  could output the determined parameter to a machine-learning interface. In some implementations, the machine-learning interface could be stored within a memory of the controller  402  itself (for example, the memory  454  illustrated in  FIG. 4B ). In other implementations, the machine-learning interface could be stored within a memory of a server (for example, a cloud server communicatively coupled to the controller  402 ). In addition to providing the machine-learning interface with the determined parameter, the controller  402  could also provide the impedance value from the impedance sensor  404  and auxiliary sensor values from auxiliary sensors to the machine-learning interface. In this way, the machine-learning interface could use the resulting determined parameter, the impedance value, and the auxiliary sensor values as training data for a machine-learning model. 
     In one implementation, for example, the impedance value and the auxiliary sensor values could be values of neurons within a first level of an artificial neural network and the determined parameter could be a value of a neuron within a second level of the artificial neural network, where the second level of the artificial neural network is a weighted sum of the neurons in the first level of the neural network. Using each set of impedance values, auxiliary sensor values, and determined parameters received from the controller  402  as training data, the weights between the first level and the second level of the artificial neural network could be refined. In other implementations, other machine-learning models, including supervised learning models, unsupervised learning models, and semi-supervised learning models, can be used. As examples, rather than an artificial neural network, machine-learning models such as decision tree learning, association rule learning, inductive logic programming, support vector machines, relevance vector machines, clustering, Bayesian networks, reinforcement learning, representation learning, similarity and metric learning, and/or genetic algorithms can be used. 
     Illustrated in  FIG. 10B  is a combustion chamber  1020 , according to example implementations. In some implementations, the combustion chamber  1020  can be a component of a power-generation turbine (for example, the power-generation turbine  800  illustrated in  FIG. 8 ). The combustion chamber  1020  can be analogous to the combustion chamber  1010  illustrated in  FIG. 10A . However, unlike in  FIG. 10A , the arrangement of  FIG. 10B  also includes a modulator  1022 . The modulator  1022  can be used to modulate the output of the signal generator  202 . For example, the modulator  1022  can be used as a trigger signal for the signal generator  202 , such that the modulator  1022  periodically triggers the signal generator  202  to output a signal to the coaxial resonator  201 . Thus, in addition to having a signal frequency (for example, a radio frequency between 300 MHz and 300 GHz) associated with the signal created by the signal generator  202  to excite the coaxial resonator  201 , the combustion chamber  1020  can include a modulation frequency at which the modulator  1022  modulates the signal generator  202 . In various implementations the modulation frequency can take various values, such as 0 Hz (continuous wave), between 0.1 Hz and 1.0 Hz, between 1.0 Hz and 10.0 Hz, between 10.0 Hz and 100.0 Hz, between 100.0 Hz and 1.0 kHz, between 1.0 kHz and 10.0 kHz, between 100.0 kHz and 1.0 MHz, or between 1.0 MHz and 10.0 MHz, or between 10.0 MHz and 100.0 MHz. Other modulation frequencies are also possible. The modulation frequency can also include an associated duty cycle. For example, the associated duty cycle can be any integer multiple of 5%. Other duty cycle values are also possible. Further, in some implementations, the modulation frequency and/or the associated duty cycle can be adjustable (for example, the frequency and/or the associated duty cycle could be adjusted by the controller  402  using a control signal transmitted to the modulator  1022  based on the determined parameter). Such adjustments can correspondingly modify how often the electromagnetic waves are radiated by the coaxial resonator  201 . 
     Alternate implementations may not include a modulator  1022 . In such implementations, the controller  402 , itself, could directly modulate the signal generator  202 . The controller  402  controlling the modulator  1022  can include changing settings on the modulator  1022  (for example, using a control signal). Additionally, the controller  402  can change such settings in response to dynamic conditions within the combustion chamber  1020  or in order to change conditions within the combustion chamber  1020 . For example, the controller  402  can change the settings of the modulator  1022  based on the determined parameter of the combustion chamber  1020  and/or until the determined parameter of the combustion chamber  1020  reaches a predetermined threshold value. Further, the controller  402  can control the modulator  1022  by executing instructions stored within a non-transitory, computer-readable medium (for example the memory  454  illustrated in  FIG. 4B ), in some implementations. 
     In addition to or instead of controlling the modulator  1022 , the controller  402  can also control the signal generator  202  (for example, using a control signal). Controlling the signal generator  202  can include modifying an output frequency, an output wavelength, an output current, an output voltage, an output power, an output amplitude, and/or an output waveform shape (for example, a sinusoidal waveform, a square waveform, a triangular waveform, a pulsed waveform, or a sawtooth waveform) of the signal generator  202 . For example, the controller  402  could receive a desired combustion percentage of a fuel mixture within the combustion zone  912  based on a user-input or based on a feedback loop, and modify the modulation frequency and/or duty cycle based on the present combustion percentage of the fuel mixture within the combustion zone  912  (for example, as determined by the controller  402  based on the characteristic impedance of the coaxial resonator  201 ). 
     Similarly, the controller  402  can modify the modulator  1022  and/or the signal generator  202  in order to improve combustion within the combustion zone  912  of the combustion chamber  1020 . For example, if sufficient and/or total combustion is not occurring (as sensed by a combustion sensor, in some implementations), if ignition is not occurring, and/or based on the determined parameter, the modulation frequency and/or duty cycle can be increased by the controller such that more electromagnetic waves  1012  are radiated by the coaxial resonator  201  to modify the fuel and/or the fuel mixture. Additionally or alternatively, if sufficient and/or total combustion is not occurring, if ignition is not occurring, and/or based on the determined parameter, the frequency, amplitude, and/or power output by the signal generator  202  to excite the coaxial resonator  201  can be increased to increase the amount and/or strength of the electromagnetic waves  1012  modifying the fuel and/or the fuel mixture. Additionally or alternatively, if sufficient and/or total combustion is not occurring, if ignition is not occurring, and/or based on the determined parameter, the controller  402  can modify excitation of the coaxial resonator  201  in order to provide and/or modify the plasma corona  1014 . 
     In some implementations, in order to modify combustion and/or ignition conditions within the combustion zone  912 , the coaxial resonator  201  can provide the plasma corona  1014 . In order to provide the plasma corona  1014 , some implementations can include a direct-current power source. An example of such an implementation is illustrated in  FIG. 10C . Illustrated in  FIG. 10C  is a combustion chamber  1030 , according to example implementations. In some implementations, the combustion chamber  1030  can be a component of a power-generation turbine (for example, the power-generation turbine  800  illustrated in  FIG. 8 ). The combustion chamber  1030  can be analogous to the combustion chamber  1010  illustrated in  FIG. 10A . However, unlike in  FIG. 10A , the arrangement of  FIG. 10C  includes a direct-current power source (for example, the DC power source  302  illustrated in  FIGS. 3A and 3B ) electrically coupled to the coaxial resonator  201 . The direct-current power source can be configured to provide a bias signal between a first conductor (for example, the inner conductor  324 ) of the coaxial resonator  201  and a second conductor (for example, the outer conductor  322 ) of the coaxial resonator  201 . The bias signal can increase an electric field at an electrode of the first conductor of the coaxial resonator  201 , thereby reducing the power output needing to be provided by the signal generator  202  in order to produce the plasma corona  1014 . 
     As described with reference to  FIG. 4A , the controller  402  can control one or more settings of the DC power source  302  in the combustion chamber  1030  (for example, switching on or off or adjusting the level of the bias signal). For example, the controller  402  can control the voltage of the bias signal in order to modify the excited plasma corona. Analogous to the description above with respect to the controller  402  controlling the signal generator  202  and the modulator  1022 , the controller  402  can control the DC power source  302  in response to dynamic conditions within the combustion chamber  1030  or in order to change conditions within the combustion chamber  1030 . For example, the controller  402  can change the settings of the DC power source  302  based on the determined parameter of the combustion chamber  1030  and/or until the determined parameter of the combustion chamber  1030  reaches a predetermined threshold value. For example, if the determined parameter is an indication that ignition is not occurring within the combustion zone  912 , the controller  402  can send a control signal to the DC power source  302  that causes the DC power source  302  to increase a voltage of the bias signal output by the DC power source  302  to the coaxial resonator  201 . Also analogous with the description above, the controller  402  can control the DC power source  302  by executing instructions stored within a non-transitory, computer-readable medium (for example the memory  454  illustrated in  FIG. 4B ), in some implementations. 
     Illustrated in  FIG. 10D  is a combustion chamber  1040 , according to example implementations. In some implementations, the combustion chamber  1040  can be a component of a power-generation turbine (for example, the power-generation turbine  800  illustrated in  FIG. 8 ). The combustion chamber  1040  can be analogous to the combustion chamber  1010  illustrated in  FIG. 10A . However, unlike  FIG. 10A , the arrangement of  FIG. 10D  includes a power meter  1046  rather than the impedance sensor  404 . In alternate implementations, the arrangement of  FIG. 10D  can also include the impedance sensor  404 , a modulator (for example, the modulator  1022  illustrated in  FIG. 10B ), and/or a direct-current power source (for example, the DC power source  302  illustrated in  FIG. 10C ). As illustrated in  FIG. 10D , the power meter  1046  can be disposed inline and between the signal generator  202  and the coaxial resonator  201 . Further, a power value measured by the power meter  1046  can be used by the controller  402  to determine reflected power and, ultimately, to determine a characteristic of the combustion chamber  1040 . 
     In one implementation, for example, the power meter  1046  can measure the portion of the power transmitted from the signal generator  202  toward the coaxial resonator  201  that is reflected from the coaxial resonator  201  back toward the power meter  1046 . Such a reflected power measurement can be indicated by a percentage (for example, a percentage of incident power reflected) or as a raw value (for example, number of Watts reflected). This reflected power measurement can then be transmitted to the controller  402 . Analogous to the impedance sensor  404  illustrated in  FIG. 10A , the reflected power measurement can be transmitted to the controller  402  using a communicative coupling between the controller  402  and the power meter  1046 . Further, the controller  402  can modify settings of the power meter  1046  through such a communicative coupling. For example, the controller  402  can adjust how frequently (for example, in Hz) the power meter  1046  measures the reflected power and/or the controller  402  can adjust how frequently (for example, in Hz) the power meter  1046  provides the measured reflected power to the controller  402 . 
     Based on the reflected power, the controller  402  can adjust the excitation frequency used by the signal generator  202  to excite the coaxial resonator  201 . After adjusting the excitation frequency (and thus the excitation wavelength), the controller  402  can reobtain the reflected power measurement from the power meter  1046  (for example, by polling the power meter  1046  for the reflected power). The process of adjusting the excitation frequency of the signal generator  202  and reobtaining the reflected power measurement can be repeated until the reflected power measurement reaches a local minimum value or is within a predetermined threshold amount of a local minimum value. The excitation frequency at the local minimum value of reflected power can correspond to a resonant frequency of the coaxial resonator  201 . Using this method, therefore, the controller  402  can determine the resonant frequency of the coaxial resonator  201 . In some implementations, the controller  402  can additionally or alternatively perform a look-up table operation based on the received power reflected and the wavelength of the signal when the power reflected is minimized to determine the resonant wavelength. Other methods of determining the resonant wavelength of the coaxial resonator  201  are also possible. 
     Similar to the characteristic impedance outlined above, the controller  402  can use the resonant wavelength of the coaxial resonator  201  to determine a parameter of the combustion chamber  1040 . The determined parameter of the combustion chamber  1040  can include a compression ratio of air within the fuel mixture relative to ambient air outside of the power-generation turbine, a pressure of air within the fuel mixture, a composition of air within the fuel mixture, a fuel-to-air ratio of the fuel mixture, a percentage of unburned fuel within the fuel mixture, a temperature of the fuel mixture, and/or a rotational rate of a shaft within the power-generation turbine. Also analogous to the characteristic impedance, determining the parameter of the combustion chamber  1040  based on the resonant wavelength can include the use of auxiliary sensor data from auxiliary sensors. 
     Based on the determined characteristic of the combustion chamber  1040 , the controller  402  can output the data to the user interface  1002 , use the determined characteristic as a portion of training data within a machine-learning interface, and/or adjust an operating condition of a power-generation turbine associated with the combustion chamber  1040 . Adjusting the operating condition can include modifying a type of fuel being injected into the combustion zone  912  in order to form a fuel mixture, a fuel-to-air ratio of the fuel mixture within the combustion zone  912  (for example, by injecting fuel into the combustion zone  912  at an increased or decreased rate), a fuel flow rate of fuel within a fuel conduit coupled to the combustion chamber  1040  (for example, coupled at a fuel injector), an operating temperature of the combustion zone  912  and/or the combustion chamber  1040 , an operating pressure of the combustion zone  912  and/or the combustion chamber  1040 , a fuel-injection location in the combustion zone  912  of the combustion chamber  1040 , and/or a fuel-injection frequency into the combustion zone  912  of the combustion chamber  1040 . In addition, adjusting the operating condition can include moving the coaxial resonator  201  to a different location region within the combustion chamber  1040  and/or changing an orientation of the coaxial resonator  201  relative to the combustion chamber  1040 . 
     Illustrated in  FIG. 11A  is a combustion chamber  1110 , according to example implementations. In some implementations, the combustion chamber  1110  can be a component of a power-generation turbine (for example, the power-generation turbine  800  illustrated in  FIG. 8 ). The combustion chamber  1110  can be analogous to the combustion chamber  1010  illustrated in  FIG. 10A . However, unlike in  FIG. 10A , the arrangement of  FIG. 11A  includes two (or more) coaxial resonators  201 . As illustrated, each of the coaxial resonators  201  can be excited by a respective signal generator  202 . In alternate implementations, a single signal generator  202  could be used to excite both of the coaxial resonators  201 . Further, in such implementations, the controller  402  could independently control one or more switches to allow the single signal generator  202  to individually excite each of the coaxial resonators  201 . Also as illustrated, the arrangement of  FIG. 11A  includes a respective impedance sensor  404  used to measure the impedance of each of the coaxial resonators  201 . In alternate implementations, inline power meters (for example, similar to the power meter  1046  illustrated in  FIG. 10D ) could be used, in addition to or instead of one or more of the impedance sensors  404 , in order to measure reflected power to determine resonant wavelength. 
     As described with respect to  FIG. 10A , an impedance value from an impedance sensor  404  can be used, possibly in conjunction with an excitation frequency output from the signal generator  202 , in order to determine the characteristic impedance of a coaxial resonator  201 . This characteristic impedance (or resonant wavelength in alternate implementations that use power meters) can then be used to determine a characteristic about the environment of the coaxial resonator  201 . Hence, using the multiple coaxial resonators  201 , multiple signal generators  202 , and multiple impedance sensors  404  illustrated in  FIG. 11A , the controller  402  can determine one or more characteristics about each of two or more different regions (for example, two or more different regions within the combustion zone  912 ). For example, if the measured impedance for one coaxial resonator  201  (a “primary characteristic impedance”) is different than the measured impedance for another coaxial resonator  201  (a “secondary characteristic impedance”), this can indicate to the controller  402  that at least one characteristic is different in the environment near one coaxial resonator  201  than in the environment near the other coaxial resonator  201 . Based on this difference between determined characteristics, the controller  402  can determine a differential or gradient within the combustion chamber  1110  (for example, a differential within the combustion zone  912  of the combustion chamber  1110 ). For example, the controller  402  can determine a temperature differential, a pressure differential, an air composition differential, a differential in fuel-to-air ratio, or a combustion-percentage differential. 
     In some implementations, the controller  402  can use one or more determined differentials to adjust an operating condition of a power-generation turbine corresponding to the combustion chamber  1110 . For example, adjusting the operating condition can include modifying a type of fuel being injected into the combustion zone  912  in order to form a fuel mixture, a fuel-to-air ratio of the fuel mixture within the combustion zone  912  (for example, by injecting fuel into the combustion zone  912  at an increased or decreased rate), a fuel flow rate of fuel within a fuel conduit coupled to the combustion chamber  1110  (for example, coupled at a fuel injector), an operating temperature of a given region of the combustion zone  912 , an operating pressure of a given region of the combustion zone  912 , a fuel-injection location in the combustion zone  912 , a fuel-injection frequency into the combustion zone  912 , an ignition sequence, the excitation frequency of one or more of the coaxial resonators  201 , and/or the excitation power of one or more of the coaxial resonators  201 . 
     Illustrated in  FIG. 11B  is a combustion chamber  1120 , according to example implementations. In some implementations, the combustion chamber  1120  can be a component of a power-generation turbine (for example, the power-generation turbine  800  illustrated in  FIG. 8 ). The combustion chamber  1120  can be analogous to the combustion chamber  1110  illustrated in  FIG. 11A . However, unlike in  FIG. 11A , the additional coaxial resonator  201  in the arrangement of  FIG. 11B  has its distal end exposed to a recirculation region  1122 . The recirculation region  1122  can be configured to recirculate heated air or steam in order to improve an efficiency of the power-generation turbine. For example, as illustrated in  FIG. 11B , the recirculation region  1122  can include a recirculation conduit that runs from an exhaust region of the combustion chamber  1120  to a heat exchanger  1124 . The heat exchanger  1124  can be another component of the recirculation region  1122  that is configured to heat air and/or steam using exhaust gas from the combustion chamber  1120 . The air and/or steam heated by the exhaust air can then be transported through an additional recirculation conduit and injected into the combustion chamber  1120  at the gas-fuel port  922  to assist in combustion, for example. 
     As illustrated, each of the coaxial resonators  201  can be excited by a respective signal generator  202 . In alternate implementations, a single signal generator  202  could be used to excite both of the coaxial resonators  201 . Further, in such implementations, the controller  402  could independently control one or more switches to allow the single signal generator  202  to individually excite each of the coaxial resonators  201 . Also as illustrated, the arrangement of  FIG. 11A  includes a respective impedance sensor  404  used to measure the impedance of each of the coaxial resonators  201 . In alternate implementations, inline power meters (for example, similar to the power meter  1046  illustrated in  FIG. 10D ) could be used, in addition to or instead of one or more of the impedance sensors  404 , in order to measure reflected power to determine resonant wavelength. 
     As described with respect to  FIG. 11A , an impedance value from an impedance sensor  404  can be used, possibly in conjunction with an excitation frequency output from the signal generator  202 , in order to determine the characteristic impedance of a coaxial resonator  201 . This characteristic impedance (or resonant wavelength in alternate implementations that use power meters) can then be used to determine a characteristic about the environment of the coaxial resonator  201 . Hence, using the multiple coaxial resonators  201 , multiple signal generators  202 , and multiple impedance sensors  404  illustrated in  FIG. 11A , the controller  402  can determine one or more characteristics about each of two or more different regions (for example, a region within the combustion zone  912  as well as a region within the recirculation region). Hence, using the determined characteristic about the recirculation region, the controller  402  can determine a parameter of the recirculation region (in addition to or instead of a parameter about the combustion zone  912 , for example). The parameter of the recirculation region can include a temperature of the recirculation region, a pressure of the recirculation region, or a chemical composition of air in the recirculation region. Other parameters of the recirculation region can also be determined. 
     In some implementations, the controller  402  can use one or more determined parameters of the recirculation region to adjust an operating condition of a power-generation turbine corresponding to the combustion chamber  1120 . For example, adjusting the operating condition can include modifying a fuel type of the fuel mixture, a fuel-to-air ratio of the fuel mixture, a fuel flow rate, an operating temperature, an operating pressure, a fuel-injection location in the combustion chamber, a fuel-injection frequency in the combustion chamber, a recirculation frequency, a volume of recirculated air, and/or a volume of recirculated steam. 
     X. Example Methods 
       FIG. 12  illustrates a method  1200 , according to example implementations. The method  1200  can be performed by a power-generation turbine. For example, the method  1200  can be performed by a power-generation turbine including the combustion chamber  1010  illustrated in  FIG. 10A  or other power-generation turbines presently disclosed. Various features described above can be applied in the context of the method  1200 . Such features can be applied in addition to or instead of the features of the method  1200  described below. 
     At block  1202 , the method  1200  can include determining, by a controller communicatively coupled to a resonator, a characteristic of a resonator selected from the group consisting of a characteristic impedance and a resonant wavelength. The resonator can include a first conductor and a second conductor separated from one another by an interstitial space that is exposed to an environment of a combustion chamber configured to house a combustion event of a fuel mixture within a power-generation turbine. 
     At block  1204 , the method  1200  can include, based on the determined characteristic, determining, by the controller, a parameter of the combustion chamber. 
     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.