Patent Publication Number: US-9892882-B1

Title: Inverted magnetron with amplifying structure and associated systems and methods

Description:
GOVERNMENT INTEREST 
     The invention described herein may be manufactured and used by or for the Government of the United States for all governmental purposes without the payment of any royalty. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to magnetrons. More specifically, this invention pertains to a compact and efficient magnetron design for delivery of high power microwave (HPM) radiation, and associated systems and methods. 
     BACKGROUND OF THE INVENTION 
     Traditional relativistic magnetrons used for HPM generation suffer from several limitations that reduce their effectiveness and/or efficiency. Among these limitations are 1) very high voltage operation, 2) small cathode surface area, 3) high axial confining magnetic field, 4) large device size, 5) inefficient mode conversion, and 6) downstream current loss. 
     High voltage operation and small cathode surface area share a relationship that has historically proven to be problematic. For a relativistic magnetron, HPM generation may only occur if high electromagnetic power (of the order of Gigawatts) is delivered to the device. For relativistic magnetrons, a pulsed power system is typically utilized to deliver this power. However, for field emitting cathodes, the electric current emitted is limited by the cathode surface area. For a standard relativistic magnetron, this cathode must be smaller than the outer hull of the device where the anode/slow wave structure is located. Consequently, for high electromagnetic power P to be delivered to the magnetron, high voltages V must be used to compensate for the limitations on current I (P=IV). 
     In a standard relativistic magnetron, confinement of the electron beam typically requires a magnetic field ranging from 0.12-0.32 T. Traditionally, Helmholtz coils have been used to provide this field, thus the power burden of an HPM system includes the energy necessary to generate the current in the coils. The inefficiency of input energy versus output has been a debilitating factor in traditional magnetrons. 
     Magnetron size has also been a limiting factor for HPM system deployment and use. Relativistic magnetrons used in traditional HPM systems typically exceed a 10 cm radius, thus presenting a logistical challenge to their deployment on compact mobile platforms. The size problem of traditional relativistic magnetrons is compounded when the magnetron&#39;s radio frequency (RF) extraction method is considered. Standard relativistic magnetrons extract radially through one or more of the resonant cavities of the device. This often results in a network of slots and waveguides that further increase the size and weight of the device. Additionally, when multi-slot RF extraction schemes are used, a combiner and mode converter are used to combine the RF signal. This additional componentry increases the size and weight of traditional HPM systems. 
     Another problem with traditional HPM systems is downstream current loss. Leakage of current beyond the magnetron interaction region degrades performance and may suppress oscillation. 
     A need exists for a magnetron design that reduces the necessary magnitude of the magnetic field and causes a reduction on the power requirements of the entire HPM system. Furthermore, advances in magnetron design are desirable that result in a compact implementation that delivers HPM radiation with minimal current loss (efficiency). 
     This background information is provided to reveal information believed by the applicant to be of possible relevance to the present invention. No admission is necessarily intended, nor should be construed, that any of the preceding information constitutes prior art against the present invention. 
     BRIEF SUMMARY OF THE INVENTION 
     With the above in mind, embodiments of the present invention are related to a compact high power, low voltage, relativistic Inverted Magnetron Oscillator (IMO) for generating electromagnetic waves. The IMO may comprise a first end defined as an upstream end, and a second end positioned axially opposite the first end of the magnetron, and defined as a downstream end. The IMO may comprise a breech portion at the first end and comprising an upstream opening, a cylindrical passage, an upstream taper, and a reflector chamber in communication with the cylindrical passage. At least a portion of the magnetron may be configured to be operable within a magnetic field. The breech portion may be configured to receive pulsed input energy. 
     The IMO may further comprise a slow wave structure including an anode block characterized by an anode block first end, an anode block body, an anode block second end, and a plurality of vane panels. Each of the vane panels may be characterized by vane panel tips and each may alternate between positive and negative charges. Each of a plurality of resonant cavities defined by the vane panels may comprise a respective resonant channel positioned radially proximate to and axially coextensive with a center axis of the anode block. 
     The IMO may further comprise a field emission cathode surrounding the anode block, defining an interaction region therebetween. An RF extraction mechanism may comprise a first excitation ring connected to the anode block at alternating vane panels by a first plurality of connecting rods, and, optionally, a second excitation ring connected to the anode block by a second plurality of connecting rods at vane panels not connected to the first plurality of connecting rods. 
     The IMO may further comprise a waveguide capacitively coupled to the slow wave structure, and positioned proximate the downstream end of the magnetron. The waveguide may be configured to shape electromagnetic waves received from the RF extraction mechanism. 
     In the present invention, there are three structural elements that allow bypass of a combiner. The first is the slow wave structure which allows the device to operate in the π mode. The second is the excitation ring which, because it is mounted on alternating vanes of the slow wave structure, oscillates from positive to negative (provided the device operates in the π mode.) The third element is the downstream cylindrical waveguide. 
     The oscillating ring excites the TM 01  electromagnetic cylindrical mode (as a matter of definition, TM mn  refers to a transverse magnetic mode for a circular waveguide where m is the number of full-wave patterns along the circumference of the waveguide and n is the number of half-wave patterns along the diameter of the waveguide). The downstream cylindrical carries the TM 01  mode away from the source. If an operator is interested in radiating a TM 01  mode then there is no need for a mode converter. There is no need for combiners in the present invention because all electromagnetic energy is propagated through the waveguide. For the electrons to give up their energy to the electromagnetic wave (mode) and thus create high power electromagnetic energy, the wave and the electron must be allowed to interact in a synchronous way. This typically requires the electron and the wave to travel at about the same speed. However, the electrons have mass and thus cannot travel at the speed of light. The solution in the present invention is to slow the wave down so that the electron and wave may interact for energy exchange to take place. The slow wave structure has the effect of slowing down the ambient electromagnetic wave in the interaction and thus allowing the energy exchange to take place 
     The excitation rings of the present invention advantageously operate to extract electromagnetic energy. The terms “ring” and “RF extraction mechanism” may be used interchangeably because the ring is the key component for RF extraction. Because the ring is mounted on alternating vanes of the slow wave structure it (the ring) will have uniform polarity. This is because the slow wave structure allows the magnetron to operate in the π mode. (Π mode describes a condition where alternating vanes have identical polarity). This polarity will alternate with the alternating polarity of the vanes on which it (the ring) is mounted. The oscillations then excite the TM 01  mode of the cylindrical waveguide. The ring advantageously allows electromagnetic energy to leave the device (i.e. for radiation to occur). 
     A second ring may be mounted to the remaining vanes on which the first ring is not mounted. Thus, the second ring will have opposite polarity to the first ring. Because the second ring is approximately half a wavelength downstream of the first, the TM 01  mode that the second ring induces will interfere constructively with the mode generated by the first ring and thus boost the amplitude of the wave. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an assembled, perspective top view of a magnetron according to an embodiment of the present invention. 
         FIG. 2  is an assembled, side-sectional view of the magnetron illustrated in  FIG. 1  including a first embodiment of an anode block and taken through line  2 - 2  of  FIG. 1 . 
         FIG. 3  is an assembled, perspective top view of the first embodiment of the anode block illustrated in  FIG. 2 . 
         FIG. 4  is an assembled, upstream-sectional view of the magnetron illustrated in  FIG. 1  taken through line  4 - 4  of  FIG. 1 . 
         FIG. 5  is an assembled, upstream-sectional view of the magnetron illustrated in  FIG. 1  taken through line  5 - 5  of  FIG. 1 . 
         FIG. 6A  is an assembled, exterior upstream view of the magnetron illustrated in  FIG. 1 . 
         FIG. 6B  is an assembled, exterior downstream view of the magnetron illustrated in  FIG. 1 . 
         FIG. 7  is a graph illustrating π mode resonance for the magnetron illustrated in  FIG. 2 . 
         FIG. 8  is a graph illustrating evolution of magnetron modes as simulated for the magnetron illustrated in  FIG. 2 . 
         FIG. 9  is a schematic diagram illustrating spoking of particles as simulated for the magnetron illustrated in  FIG. 2  and taken through line  4 - 4  of  FIG. 1 . 
         FIG. 10  is a graph illustrating oscillation in π mode of the magnetron illustrated in  FIG. 2  for sampled magnetic fields. 
         FIG. 11  is a graph illustrating output power of the magnetron illustrated in  FIG. 2 . 
         FIG. 12  is a graph illustrating output power efficiency of the magnetron illustrated in  FIG. 2 . 
         FIG. 13  is an assembled, perspective top view of a second embodiment of an anode block as used with a magnetron according to an embodiment of the present invention. 
         FIG. 14  is an assembled, side-sectional view of the magnetron illustrated in  FIG. 1  including the second embodiment of the anode block of  FIG. 13  and taken through line  2 - 2  of  FIGS. 1 and 13 . 
         FIG. 15  is an assembled, exterior upstream view of the magnetron illustrated in  FIG. 14 . 
         FIG. 16  is a graph illustrating evolution of magnetron modes as simulated for the magnetron illustrated in  FIG. 14 . 
         FIG. 17  is a graph illustrating output power of the magnetron illustrated in  FIG. 14 . 
         FIG. 18  is a graph illustrating output power efficiency of the magnetron illustrated in  FIG. 14 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention will now be described more fully hereinafter with reference to the accompanying drawings, in which preferred embodiments of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Those of ordinary skill in the art realize that the following descriptions of the embodiments of the present invention are illustrative and are not intended to be limiting in any way. Other embodiments of the present invention will readily suggest themselves to such skilled persons having the benefit of this disclosure. Like numbers refer to like elements throughout. Though approximate or actual physical dimensions may be disclosed or referenced herein, such dimensions are not intended to be limiting but to enable those of ordinary skill in the art to practice exemplary embodiments of the invention. 
     In this detailed description of the present invention, a person skilled in the art should note that directional terms, such as “above,” “below,” “upper,” “lower,” and other like terms are used for the convenience of the reader in reference to the drawings. Also, a person skilled in the art should notice this description may contain other terminology to convey position, orientation, and direction without departing from the principles of the present invention. 
     Referring to  FIGS. 1-18 , an Inverted Magnetron Oscillator (IMO) according to an embodiment of the present invention is now described in detail. Throughout this disclosure, the present invention may be referred to as a IMO system, an IMO device, a magnetron system, an inverted magnetron, a magnetron, a device, a system, a product, and a method. Those skilled in the art will appreciate that this terminology is only illustrative and does not affect the scope of the invention. 
     An embodiment of the invention, as shown and described by the various figures and accompanying text, provides a compact high power, low voltage, relativistic Inverted Magnetron Oscillator (IMO). For purpose of this disclosure, inverted shall mean that a cathode surrounds an anode block, as opposed to conventional magnetrons that commonly utilize a centrally located cathode with a surrounding anode. 
     The present invention overcomes the described problems in the art in that it is a compact, high power, relativistic Inverted Magnetron Oscillator (IMO). The IMO is capable of supporting π mode oscillations over a 50 kV wide window absent any significant mode competition at output RF power levels that, in many cases, exceed 500 MW for voltages lower than 360 kV. This operation is advantageously achieved with very low axial magnetic field (0.05-0.09 T), with no downstream current loss, and with RF field amplitudes that do not exceed the vacuum breakdown threshold. 
     Several features of the IMO are innovative and produce a clear advantage over current standard relativistic magnetron designs. First, the IMO is compact. In the exemplary embodiment, the IMO has a radius of approximately 10 cm and an axial length of approximately 60 cm and is a relatively small magnetron when considering the operating voltages, magnetic fields, output power and frequency described herein. Second, the IMO has a large cathode surface area. Due to the inverted nature of the design, the large cathode surface area advantageously allows for a greater current draw than standard relativistic magnetrons. The larger current means higher output power for lower voltages, making the compact IMO ideal for high power applications and enabling a significant decrease in size and weight of an HPM system that uses the IMO. Third, the IMO advantageously operates at magnetic fields that can be at or about a third less than those required for standard relativistic magnetrons, thus featuring greatly reduced power and size demands on the electromagnet or other sources that provides the magnetic field. Fourth, because the IMO radiates axially in the TM 01  mode directly into a cylindrical waveguide, multiple waveguides and combiners are not needed. Standard relativistic magnetrons radiate radially in multiple waveguides, thus increasing HPM system size and weight. Due to the single-cylinder axial waveguide design described herein, the IMO is not burdened with any of these disadvantages. Finally, the IMO does not produce any downstream current loss, a consequence faced by standard relativistic magnetrons. 
     The above list of features and advantages make the IMO ideal as the HPM source for a new smaller and lighter HPM system. 
       FIG. 1  illustrates the IMO  100  exterior. The IMO  100  may include a first end  101 , referenced herein as an upstream end, and a second end,  102  referenced herein as a downstream end. The IMO  100  may include an exterior layer  103  that may extend from the first end  101  to the second end  102  of the IMO  100 . For example, and without limitation, the exterior layer  103  may be characterized by a supporting cylinder that may function as a housing to an internal structure and componentry of the IMO  100 . 
     Referring additionally to  FIG. 2 , the internal structure may be positioned axially inward of the exterior layer  103  and may include an upstream opening  104 , a reflector chamber  105 , an upstream taper  106 , a field emission cathode  107 , an interaction region  108 , a downstream taper  109 , a waveguide  110 , which in the exemplary embodiment is cylindrical, and a downstream opening  111 . For example, and without limitation, the upstream opening  104  may be a threshold to a cylindrical passage located substantially proximate the first end  101  of the IMO  100 . 
     Still referring to  FIG. 2 , and referring additionally to  FIGS. 3 and 4 , the internal componentry housed by the exterior layer  103  may include a slow wave structure defined as an anode block  150 . For example, and without limitation, the anode block  150  may include an anode block first end  151 , an anode block body  152 , and an anode block second end  153 . The anode block body  152  may be positioned coaxial with and surrounded by the field emission cathode  107 . The anode block first end  151  and a plurality of vane panel tapers  155  may be positioned substantially proximate to a breech portion  154  of the IMO  100 . For example, and without limitation, the breech portion  154  may include the upstream opening  104  positioned adjacent to a cylindrical passage  125  that may extend toward and may connect with the upstream taper  106 . The reflector chamber  105  may connect distally with the cylindrical passage  125 . Extending distally from the anode block second end  153  may be a first plurality of connecting rods  161  connected to an annular shaped torus, defined as a first excitation ring  162 . The anode block body  152  may include a plurality of vane panels  156 , adjacent pairs of which may define resonant cavities  157  therebetween. For example, and without limitation, each of the vane panel tapers  155  may be defined by a respective curved portion of the vane panels  156  that may extend from the anode block body  152  down to the anode block first end  151 . 
     The slow wave structure/anode block  150  may enable the electrons to give up their energy to the electromagnetic wave (mode) and thus may create high power electromagnetic energy. This happens when the wave and the electron are allowed to interact in a synchronous way. This typically requires the electron and the wave to travel at about the same speed. However, the electrons have mass and thus cannot travel at the speed of light. The solution in the present invention is to slow the wave down so that the electron and wave may interact for energy exchange to take place. The slow wave structure/anode block  150  may have the effect of advantageously slowing down the ambient electromagnetic wave in the interaction and thus may allow energy exchange to take place. 
     In one embodiment of the present invention, as illustrated in  FIG. 4 , the anode block  150  may be characterized by sixteen resonant cavities  157  each defined between a respective pair of radially-projecting vane panels  156 . In one embodiment, there may be sixteen vane panels  156 . The vane panels  156  may be angled to specifically define the dimensions of the resonant cavities  157  between them. Each of the vane panels  156  may comprise a wedge portion  402  that may be adjoined to a respective resonant channel  159 . For example, and without limitation, one segment of each vane panel  156  may include vane tips  158  and an opposing segment of each vane panel  156  may be defined by a respective adjacent pair of the resonant channels  159 . The resonant channels  159  may be characterized as substantially circular cavities as observed from the IMO  100  first and second ends  101 ,  102 , and may be substantially cylindrical cavities  159  as observed from a side-sectional view of the IMO  100 . Therefore, the same voids within the anode block  150  may be described as resonant holes  401  when viewing the anode block first or second end  151 , 153 , but may be described as resonant channels  159  when viewing the anode block  150  from the side. Each of the resonant channels  159  may present a respective open portion positioned radially-outward from a center axis of the anode block  150  which may form the segment of each resonant cavity  157  located radially proximate the anode block body  152 . The resonant channels  159  may be substantially coaxial and collinear with the center axis of the anode block  150 . 
     More specifically, each of the vane panels  156  may include a wide base  175  located proximate the resonant channels  159  and may include an opposing pair of sides that may angle toward each other to define narrowed vane tips  158 . The vane panels  156  may be disposed substantially evenly along an interior perimeter  170  defined by the anode block body  152 , and may project outward from the anode block body  152  with the wider base  175  located proximate the inner perimeter  170  and the narrowed vane tips  158  located distally thereto. As a result, the resonant cavities  157  produced by the vane panels  156  may be wider between the vane tips  158  and narrower toward the anode block body  152  inner perimeter  170 . 
     Continuing to refer to  FIG. 4 , the field emission cathode  107  may be positioned relative to the anode block  150  so as to define an interaction region  108  of the IMO  100 . For example, and without limitation, the field emission cathode  107  may be positioned adjacent to and carried by an interior surface of the exterior layer  103 . The cathode  107  may be the origin of charged electron particles that generate HPM radiation. A uniform axial magnetic field may prevent the charged electron particles from immediately accelerating across the interaction region  108 . Instead, the electron particles may undergo rotations about the field emission cathode  107 . If the electron particles&#39; azimuthal velocity component is approximately equal to the phase velocity of a particular electromagnetic mode in the interaction region  108 , the possibility exists for energy exchange between the particle and the mode. This resonance is known as the Buneman-Hartree resonance condition, Benford, J., &amp; Swegle, J. A. (1992).  High Power Microwaves , Boston, Ma.: Artech House. As the electron particles rotate about the field emission cathode  107  they gradually give up their potential energy to a mode or modes of the RF field as they migrate toward the anode block  150 . This interaction may create RF oscillations in the IMO  100 . 
     In one embodiment, the field emission cathode  107  may measure an outer radius of between 9.9 cm and 10.2 cm and may establish an outer perimeter of the interaction region  108 . In this embodiment, an outer radius of the field emission cathode  107  may be measured at 10.0 cm. An inner boundary of the interaction region  108  may be established by the anode block  150 , which may measure at a radius of 7.1 cm from its center axis to its vane tips  158 . The difference between the boundary established by the field emission cathode  107  measuring a radius of 10.0 cm and the boundary established by the anode block  150  measuring a radius of 7.1 cm may create an inter-boundary void surrounding the anode block  150 . This inter-boundary void may define the interaction region  108 . The axial length of both the field emission cathode  107  and the anode block body  152  (and, therefore, of the interaction region  108 ) may be identical and equal to 26.2526 cm. 
     For example, and without limitation, each of the vane panels  156  may present a respective angle that may measure 10.18 degrees with respect to a bisecting plane through an origin of that angle. Collectively, the vane panels  156  may define sixteen resonant cavities  157  therebetween. Each of the vane tips  158  may have a width of 0.25 cm. Circular voids, defined as resonant holes  401 , may exist at the bottom of each resonant cavity  157  when viewing the anode block from the first or second end  151 ,  153  and may define the dimensions of the resonant channels  159  that may extend substantially the length of the anode block body  152 . The resonant channels  159  are viewable from a side view of the anode block  150 . A respective radius of each resonant hole  401  (and therefore resonant channel  159 ) may measure 0.509 cm and a respective center of each resonant hole  401  and resonant channel  159  may be distanced 3.406 cm from the center axis of the anode block  150 . The resonant holes  401  and resonant channels  159  may exist to advantageously increase inductance and mode stability of the IMO  100 , as well as to advantageously lower the IMO  100  resonant frequency. Additionally, each of the resonant cavities  157  may subtend a respective angle of 39.5 degrees with respect to the respective resonant holes  401  and resonant channels  159 . 
     Referring now to  FIG. 5 , an RF extraction mechanism used in accordance with an embodiment of the present invention will now be discussed. For example, and without limitation,  FIG. 5  illustrates the RF extraction mechanism in the x-y plane where z=18.5 cm measured from the second end  102  of the IMO  100 . This measurement may represent the axial coordinate where extraction of RF energy may be accomplished via the first excitation ring  162 , otherwise known as a torus, that may be characterized by a major radius 6.6 cm and minor radius 0.45 cm. The first excitation ring  162  may be mounted on a first plurality of connecting rods  161 , each characterized by a radius of 0.2 cm and a length of 1.8 cm. In one embodiment of the present invention, the first plurality of connecting rods  161  may be eight (8) in number. Referring additionally to  FIG. 3 , the first plurality of connecting rods  161  may be connected to alternating vane tips  158  of the anode block  150  at a radius of 6.6 cm as measured from a center of the first excitation ring  162 . The first plurality of connecting rods  161  may extend distally from the vane tips  158  toward the downstream end  102  of the IMO  100 . The first excitation ring  162  may be centered at axial coordinate z=18.5 cm, and at a distance of 2.245 cm from a downstream end of the anode block  150 . The first excitation ring  162  may employ capacitive coupling with the cylindrical waveguide  110  to launch a TM 01  propagating mode therein. 
     The first excitation ring  162  may operate to extract electromagnetic energy. The terms “excitation ring” and “RF extraction mechanism” may be used interchangeably because the first excitation ring  162  advantageously operates as a component for RF extraction. Because the excitation ring  162  is mounted on alternating vane panels  156  of the anode block  150 , the first excitation ring  162  may have uniform polarity. This is because the anode block  150  may allow the IMO  100  to operate in the π mode. Π mode describes a condition where alternating vane panels  156  have identical polarity. This polarity will alternate with the alternating polarity of the vane panels  156  on which the first excitation ring  162  is mounted. The oscillations then excite the TM01 mode of the cylindrical waveguide. 
     The cylindrical waveguide  110  may be characterized by a radius of 7.4 cm and may allow for propagation of the TM 01  mode out of the IMO  100  second end  102  and downstream opening  111 . 
     Referring again to  FIG. 2 , and additionally to  FIG. 6B , the breech portion  154  of the IMO  100  may be located at the IMO first end  101  and may present the upstream opening  104  defined between the exterior layer  103  and the anode block first end  151 . The anode block first end  151 , conductively coupled to the anode block  150 , may be electrically insulated from the exterior layer  103 , which is conductively connected to the field emission cathode  107  so that the potential difference applied at the upstream end  101  may be transmitted to and may serve as the diode voltage of the magnetron  100 . 
     For example, and without limitation, the upstream opening  104  may measure an outer radius of 5 cm before tapering upward to the field emission cathode  107  characterized by a radius of 10.0 cm. The upstream taper  106  may be defined by a taper between the upstream opening  104  measuring a radius of 5 cm and the upstream end of the field emission cathode  107  measuring a radius of 10.0 cm. In some embodiments, the upstream taper  106  may be characterized as a flaring annular passage. The upstream taper  106  may represent a curved void within the exterior layer  103  that may surround the vane panel taper  155  of the anode block first end  151 . 
     The anode block first end  151  may have a radius measuring 2.84 cm before tapering upward to form the vane panels  156  of the anode block  150  that extend to radii of 7.1 cm to the vane tips  158 . To form the upstream taper  106 , its outer radius may be characterized by the relation
 
 R   o =0.05 e   (6.9348(z−z     0     ))  
 
where R o  is the outer radius, z o  is the coordinate for the starting point for the upstream taper  106 , and z o =−2 cm where z is the axial coordinate. The inner radius may be characterized by the relation
 
 R   i =0.0284 e   (9.16(z−z     o     ))  
 
where R i  represents the inner radius of the upstream taper  106 .
 
     Still referring to  FIG. 2 , located proximate to the IMO first end  101  and downstream of the breach portion  154  may be a reflector chamber  105 . For example, and without limitation, the reflector chamber  105  may be a cylindrically shaped void within the exterior layer  103  measuring 3 cm in width, extending from z=−0.28 cm to z=−0.25 cm, and characterized by an inner radius of 5 cm and outer radius of 8.85 cm. The cylindrically shaped void of the reflector chamber  105  may be positioned perpendicular to the center axis of the anode block  150  and adjacent the upstream opening  104 , thereby combining the reflector chamber  105  and the cylindrical passage  125  defined between the upstream opening  104  and the upstream taper  106 . During operation of the IMO  100 , the reflector chamber  105  may advantageously prevent upstream RF energy loss by reflecting this energy back into the interaction region  108  of the IMO  100 . 
     Located proximate to the anode block second end  153  and to a downstream end of the field emission cathode  107  may be a downstream taper  109 . For example, and without limitation, the downstream taper  109  may define a taper in the exterior layer  103  formed by the difference in diameter between the field emission cathode  107  measuring a radius of 10.0 cm and the inner radius of the cylindrical waveguide  110  measuring 7.4 cm. In some embodiments, the downstream taper  109  may be defined as a frustoconical void. 
       FIGS. 7-12  graphically represent simulation data characterizing operation of the embodiment of the IMO  100  illustrated in  FIGS. 1, 2, 3, 4, 5, 6A, and 6B . Those data are created using the Improved Concurrent Electromagnetic Particle-In-Cell code (ICEPIC), which utilizes the particle-in-cell (PIC) algorithm Hockney, R. &amp; Eastwood J. (1988).  Computer Simulation Using Particles . CRC Press. The PIC algorithm is used to solve Maxwell&#39;s equations and the relativistic Lorentz force law in the time domain on a fixed staggered grid. ICEPIC is designed to run on parallel architecture and thus meet the challenge of full 3D simulations of the MWC magnetron. The ICEPIC is a proven code that has been used in a number of high power relativistic magnetron studies Lemke, R. W., Genoni, T. C., &amp; Spencer, T. A. (1999). Three-dimensional particle-in-cell simulation study of a relativistic magnetron.  Physics of Plasmas,  6(2), 603-613; and Fleming, T., &amp; Mardahi, P. (2009). Performance Improvements in the Relativistic Magnetron: The Effect of DC Field Perturbations.  IEEE Transactions on Plasma Science,  37(11), 2128-2138. Also, referenced for prototyping design and identifying loss mechanisms. Spencer, T., Genoni, T., &amp; Lemke, R. (2000). Effects that limit efficiency in relativistic magnetrons.  IEEE Transactions on Plasma Science,  28(3), 887-897. ICEPIC has also been used to study conventional magnetron designs Luginsland, J. W., Lau, Y. Y., Neculaes, V. B., Gilgenbach, R. M., Jones, M. C., Frese, M. H., &amp; Watrous, J. J. (2004). Three-dimensional particle-in-cell simulations of rapid start-up in strapped oven magnetrons due to variation in the insulating magnetic field. Applied Physics Letters, 84(26), 5425-5427. 
     Referring specifically to  FIG. 7 , utilizing the anode radii of 10.0 cm and 7.1 cm respectively, as well as the frequency of the π mode at 2 GHz, a non-interacting fluid model (single particle) of charged particles employing the Buneman-Hartree resonance condition and the Hull Cut-off condition in a smooth bore geometry yields the region in voltage-magnetic space over which the IMO  100  may oscillate in the π mode. Oscillations in the π mode typically occur right above the Buneman-Hartree π mode curve. Consequently, the presented simulations target this region of the voltage-magnetic field parameter space. Referencing the graph in  FIG. 7 , a resolution of one grid cell length equals 0.05 cm on a uniform Cartesian grid. With the cathode radius at 10 cm and the vane tips located at 7.1 cm, the simulated interaction region is well resolved at 58 grid cells. At this resolution, the grid volume as simulated was 668, 662, and 1758 cells in the x, y, and z directions, respectively, yielding a total of approximately 777 million grid points. Adding to this computational burden are the charged particle dynamics. Simulations produced about 330 million charged macro-particles. 
     Simulations of the presented magnitude may only be performed on large high performance computing resources. The presented simulations were carried out on a parallel computing platform using 256 Intel Xeon E5-2697 2.7 GHz cores. Each simulation required approximately 2.0 days to reach 200 ns of simulation time at which time saturation was well established. 
     A pulsed power device was used to provide the diode voltage (i.e., DC radial electric field) between the field emission cathode  107  and the anode block  150 . The circuit and switches that constitute the pulsed power device were not modeled. Rather, a time dependent voltage function was used to emulate the behavior of the pulsed powered source. The voltage function was continuous and consisted of two parts. The first part was a 50 ns linear ramp up followed by a second part that was a constant voltage amplitude which lasted for the duration of the simulation. This amplitude was a free parameter that was manipulated in the presented simulations. Input voltages used in the presented simulations ranged from 200-400 kV. 
     A uniform axial magnetic field existed for the duration of the presented simulations. This field represented the insulating magnetic field that current carrying coils may generate. The coils may produce a magnetic field that may be uniform in the interaction region  108  and throughout most of the IMO  100 . 
     The IMO  100  was simulated at magnetic fields of 0.05 T, 0.06 T, 0.07 T, 0.08 T, and 0.09 T. The voltage, V=375.0 kV, at B=0.07 T simulation served as the reference simulation for this IMO  100  embodiment. The dynamics of the IMO  100  presented are representative of all performed simulations. 375 kV was the dial up voltage and the resultant voltage was 353 kV. 
       FIG. 8  illustrates the time evolution of the simulated magnetron modes. The simulation exhibited a transient period of mode competition primarily due to the 7π/8 mode during the ascent of the π mode. However, by 75 ns, the 7π/8 mode tended toward dissipation and the T mode was dominant. After this, time mode competition was confined to amplitudes less than 1 kV for each competing mode with the amplitude of the 7π/8 mode quickly decaying. The π mode remained the dominant mode at a frequency of approximately 2 GHz for the duration of the simulation. 
       FIG. 9  displays the spoking pattern of particles in a sample slice of the interaction region  108  slice in the xy-plane of 2 dx thickness, and as simulated at 150 ns. For example, and without limitation, the IMO  100  was operating in π mode at saturation for input parameter, voltage=375 kV and magnetic field=0.07 T. Each particle is represented by a dot  901 . Eight particle spokes  902 , characteristic of the π mode in a sixteen-vane IMO  100 , are evident. 
     RF output power is evaluated via the area integral of the outward Poynting flux. This integral covers the downstream cylindrical waveguide  110 . The plane of integration was located downstream of the interaction region  108  and covered the entire surface area whose normal is the z-axis. RF output power at saturation was approximately 560 MW. 
     Output power efficiency is defined as the ratio of radiated power to system input power. Input power is given by P=IV, where I is the input current supplied to the field emission cathode  107  and V is the upstream diode voltage. This current is calculated by performing a closed path line integral of the magnetic field around the area in which the current is flowing. The voltage is determined by integrating the electric field radially. For the presented simulation, RF Power efficiency was 12.6% with an input current of 12.5 kA and a measured voltage of 353 kV. The operating IMO  100  exhibited no downstream leakage current. 
     An examination of critical areas within the IMO  100  with sufficiently high electric fields was conducted. Concern in high-power magnetron design included breakdown due to field stress. The Kilpatrick limit for breakdown in a magnetron operating at 2 GHz is approximately 390 kV/cm. Kilpatrick W. D., (September 1953),  Criterion for Vacuum Sparking Designed to Include Both RF and DC , UCRL-2321. A survey of electrical field data at saturation throughout the volume of the IMO  100  indicated that the critical location for breakdown may be the downstream taper  109  just before the start of the cylindrical waveguide  110 . Consequently, a thorough examination of field stresses at this location was carried out. Field stress data at the downstream taper  109  was produced during saturation over six oscillatory periods. Results indicated that the magnitude of the electric field component peaks near 300 kV/cm. Thus, RF breakdown was not problematic for the presented simulation. Furthermore, the axial magnetic field of B=0.07 T may act to insulate any charge flow along this direction, thus easily mitigating breakdown. 
       FIG. 10  is a graph of oscillation in π mode of the IMO  100  at approximately 50 kV increments for specifically sampled magnetic fields. This simulation is representative of the battery of runs performed from B=0.05 T to B=0.09 T. A minor period of mode competition present at startup, which may occur between 40-60 ns, tended toward decay once π mode saturation was reached. The IMO  100  operated in accordance with the Buneman-Hartree resonance condition. Operation was robust and predictable over the range of magnetic fields and voltages sampled. The voltage window for π mode oscillation for a given magnetic field was approximately 50 kV which advantageously may provide for advanced performance stability. 
       FIG. 11  displays the RF output power generated for all simulations. Every simulation tested successfully operated in the π mode. At approximately 350 kV and B=0.07 T the IMO  100  surpassed 0.5 GW in RF output power, thus demonstrating high power low voltage, low magnetic field performance. The IMO  100  exhibited significant RF generation over the range of voltages and magnetic fields examined. By 440 kV the IMO  100  was approaching a GW. 
       FIG. 12  plots the efficiency of the IMO  100 . As shown, operation of the IMO  100  exhibited a general increase in RF efficiency as the magnetic field was increased. However, for a given magnetic field, efficiency declined as voltage was raised. Efficiency ranged from 5-37.0% with the highest values of efficiency occurring for the highest voltages sampled. Notably, for a given magnetic field, peak efficiency did not correspond with the voltage that produced peak output power. 
     The IMO  100  presented in the first embodiment consistently oscillates in the π mode across a wide range of magnetic fields and voltages. The IMO  100  operated in a predictable fashion obeying the Buneman-Hartree resonance condition. The π mode resonance curve was used to successfully predict where the magnetron would oscillate in voltage/magnetic field space (i.e., oscillations tracked well with the curve). Therefore, this embodiment of the present invention advantageously proved stable and reliable. 
       FIG. 13  illustrates a second embodiment of the inverted magnetron, defined as IMO-B  1300 . IMO-B  1300  may have the same dimensions and specifications as the IMO  100 , but with an added annular shaped torus, defined as a second excitation ring  1302  and a second plurality of connecting rods  1303  extending from the anode block second end  153 . In one embodiment, the second plurality of connecting rods  1303  may be eight (8) in number. 
     The second excitation ring  1302  may be mounted to the remaining vane panels  156  of the anode block  150  via the second plurality of connecting rods  1303  that do not include the first plurality of connecting rods  161  and the mounted first excitation ring  162 . Thus, the second excitation ring  162  will have opposite polarity to the first excitation ring  162 . Because the second excitation ring  1302  is approximately half a wavelength downstream of the first excitation ring  162 , the TM 01  mode that the second excitation ring  1302  induces may interfere constructively with the mode generated by the first excitation ring  162  and thus boost the amplitude of the wave. 
     For example, and without limitation, the second excitation ring  1302  may be positioned 7.56 cm away from the anode block second end  153 . The second excitation ring  1302  may measure a major radius of 1.99 cm and a minor radius of 0.45 cm. The second excitation ring  1302  may be smaller in diameter than the first excitation ring  162  and may extend distally from the anode block second end  153  by the distance of the second plurality of connecting rods  1303 . In some embodiments, the distance of the second plurality of connecting rods  1303  may be greater than the distance of the first plurality of connecting rods  161 . 
     The second plurality of connecting rods  1303  may be connected to alternating vane panels  156 , proximate the inner perimeter  170  of the anode block second end  153  relative to the first plurality of connecting rods  161 . The second plurality of connecting rods  1303  may be located on vane panels  156  not inclusive of the first plurality of connecting rods  161 . Therefore, the first plurality of connecting rods  161  and the second plurality of connecting rods  1303  may be alternated, respectively. For example, and without limitation, the second plurality of connecting rods  1303  may be located at the base  175  of the vane panels  156  on the anode block second end  153  before the vane panels  156  become defined by the resonant holes  401  and resonant channels  159 . The second plurality of connecting rods  1303  may form an angle other than 90 degrees with the anode block second end  153  to accommodate the smaller diameter of the second excitation ring  1302  relative to the positioning of the second plurality of connecting rods  1303  on the anode block second end  153 . 
       FIG. 14  is a side-sectional view of the IMO-B  1300  that illustrates the second plurality of connecting rods  1303  measuring longer than the first plurality of connecting rods  161  and forming an angle between the anode block second end  153  and the second excitation ring  1302 . In one embodiment, the second plurality of connecting rods  1303  may connect to the anode block second end  153  at one portion, may pass through an inner perimeter established by the first excitation ring  162 , and may connect to the second excitation ring  1302  at a positioning distal to the anode block second end  153  relative to the first excitation ring  162 . 
     As illustrated by the graphed simulation data presented in  FIGS. 16-18 , addition of the second excitation ring may increase the RF output power of the IMO-B  1300  as compared to the IMO  100 . The following three fields were used to test the IMO-B  1300 : 0.06 T, 0.065 T and 0.07 T. For the IMO-B  1300 , the reference simulation was chosen at input voltage=305 kV and B=0.065 T. This simulation is reflective of the battery of simulations that were carried out for the IMO-B  1300 . The 305 kV was the dial up voltage and the resultant voltage was 307 kV. 
       FIG. 16  plots the mode dynamics of the IMO-B  1300  as a function of time. A small period of mode competition existed as the π mode underwent rapid growth. However, by 60 ns, all competition had dissipated and the π mode was dominant at 2 GHz for the length of the simulation. 
       FIG. 17  shows IMO-B  1300  RF Output power performance across a range of voltages. RF output power at saturation was approximately 496 MW. Output power efficiency was 17.8% with an input current of 9 kA and a measured voltage of 307 kV. The IMO so configured exhibited no downstream leakage current. As with the IMO  100 , peak electric field amplitudes remained well below the Kilpatrick limit for RF breakdown. As with the IMO  100 , the IMO-B  1300  proved to be advantageously stable and reliable over the voltage and magnetic fields sampled. 
       FIG. 18  shows that efficiencies for the IMO-B  1300  behave in a similar manner as the IMO, although average efficiency is slightly less. 
     Some of the illustrative aspects of the present invention may be advantageous in solving the problems herein described and other problems not discussed which are discoverable by a skilled artisan. 
     While the above description contains much specificity, these should not be construed as limitations on the scope of any embodiment, but as exemplifications of the presented embodiments thereof. Many other ramifications and variations are possible within the teachings of the various embodiments. While the invention has been described with reference to exemplary embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed as the best or only mode contemplated for carrying out this invention, but that the invention will include all embodiments falling within the scope of the appended claims. Also, in the drawings and the description, there have been disclosed exemplary embodiments of the invention and, although specific terms may have been employed, they are unless otherwise stated used in a generic and descriptive sense only and not for purposes of limitation, the scope of the invention therefore not being so limited. Moreover, the use of the terms first, second, etc. do not denote any order or importance, but rather the terms first, second, etc. are used to distinguish one element from another. Furthermore, the use of the terms a, an, etc. do not denote a limitation of quantity, but rather denote the presence of at least one of the referenced item. 
     Thus, the scope of the invention should be determined by the appended claims and their legal equivalents, and not by the examples given.