Rising Sun Magnetron Research Articles

A new class of spatial harmonic magnetrons with potentials for CW and sub-THz operation

AbstractA strictly physically based design theory of a new class of Spatial Harmonic Magnetrons (SHM) is thoroughly derived which leads to analytically evaluable expressions. Thus two advantages are obtained: (1) The design parameters appear grouped into two separate categories – one just containing geometrical and material parameters, the other one exclusively containing beam current-related ones, which are in product-form determining performance. The influence of each parameter can thus easily be discovered and investigated. (2) Numerical efforts for any new design will be reduced by at least one order of magnitude. Subsequently and based on feature (1) it is derived that loading the anode structure by a suitably selected meta-material will increase output power and efficiency, will pave the way to CW operation, and can extend oscillation frequency well into the sub-THz range. Finally, it is shown that the Rising Sun Magnetron is a first step toward a meta-material loaded SHM offering the same but quantitatively reduced features and less stringent requirements to fabrication technology.

High-Efficiency Phase-Locking of Millimeter-Wave Magnetron for High-Power Array Applications

We introduced a phase-locking mechanism of millimeter-wave magnetrons coupled through a carefully designed coupling bridge. For such a structure, two Ka-band 22-vane rising-sun magnetron circuits operated in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pi $ </tex-math></inline-formula> -mode were phase-locked tightly as a whole through a double-ridged coupler. Moreover, the double-ridged coupler was optimized to suppress mode competition between zero-phase and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pi $ </tex-math></inline-formula> -phase difference mode, which achieved high-efficiency phase-locking. Total output power of the two identical magnetrons nearly doubled the output power of a free-running magnetron and efficiencies of them were nearly the same. Extension of this phase-locking mechanism to high-power applications appears feasible with more elements in an array of the millimeter-wave magnetrons.

Design and development of field emission based magnetron for industrial applications using conformal finite-difference time-domain particle-in-cell simulations

The magnetron is a high-efficiency high-power vacuum tube that generates microwaves based on the interaction of a stream of moving electrons under crossed electric and magnetic fields with a series of open coupled cavity resonators. They are widely used as a low-cost microwave source for industrial heating. Traditionally, a thermionic cathode is used as the electron source and a heater is needed to increase the temperature of the cathode up to about 1000 K. In this work, a field emission-based magnetron has been investigated for industrial applications as an easier and more robust configuration. The design and development were performed using a conformal finite-difference time-domain particle-in-cell simulation as implemented in the VSim code. A rising-sun configuration has been optimized and the corresponding operating condition has been determined to achieve an efficiency of up to ∼80%. The rising-sun magnetron operating at a frequency of 2.45 GHz can give an output power of 3 kW, serving as a good replacement of existing industrial magnetrons.

Machine Learning Investigation of the Rising Sun Magnetron Design and Operation

Many emerging applications of high-power microwave sources require operation at new and higher frequencies. Computer modeling is the main tool for the design and optimization of these sources, such as magnetrons. However, when designing a new source, the parameter space to scan can be too large to study with traditional techniques. We apply machine learning (ML) (supervised learning in particular) to search this parameter space automatically. We demonstrate this technique by optimizing the operation of a magnetron at 4 GHz, investigating selected parameters tradeoff and predicting operation space characteristics for the discovered device based on a limited amount of measurements. The combination of ML and optimization techniques that we demonstrate here has wide applicability for virtual prototyping and design of problems with sophisticated computer models and allows us to fundamentally reimagine the role of the human in the design workflow.

Numerical Assessment of Secondary Electron Emission on the Performance of Rising-Sun Magnetrons With Axial Output

Particle-in-cell simulations are performed to analyze the role of secondary electron emission (SEE) on the efficiency, the output power and the leakage currents of 12-cavity, 12-cathode Rising-Sun magnetrons with diffraction output. The simulation results seem to indicate that the role of SEE would be fairly negligible. Small changes are predicted, linked to deviations in the starting trajectories of secondary electrons following their generation and the lower fraction of electrons in clusters with a synchronized rotational velocity. Overall, a peak power output of about 2.48 GW is predicted at a magnetic field of 0.45 T, with efficiencies as high as 75%. Furthermore, deviations in the output power with SEE are predicted to occur at shorter times, but would not be an issue for pulses greater than 25 ns in duration.

Publisher's Note: “Investigation of the operating characteristics of a 12-cavity rising-sun relativistic magnetron with diffraction output using particle-in-cell simulations” [Phys. Plasmas 23, 052104 (2016)

Publisher's Note: “Investigation of the operating characteristics of a 12-cavity rising-sun relativistic magnetron with diffraction output using particle-in-cell simulations” [Phys. Plasmas <b>23</b>, 052104 (2016)

Investigation of the operating characteristics of a 12-cavity rising-sun relativistic magnetron with diffraction output using particle-in-cell simulations

We report on the performance of a 12-cavity rising-sun relativistic magnetron with diffraction output (12-cavity rising-sun RMDO). Particle-in-cell simulations show an electronic efficiency of 70% for a gigawatt output power 12-cavity rising-sun RMDO with a transparent cathode operating in the π mode for an applied voltage of U∼400 kV ±50 kV. When the RMDO is driven by the “F” transparent cathode, which is a coaxial transparent cathode, the axial leakage current can be reduced by about 50%.

Dynamic phase-control of a rising sun magnetron using modulated and continuous current

Phase-control of a magnetron is studied via simulation using a combination of a continuous current source and a modulated current source. The addressable, modulated current source is turned ON and OFF at the magnetron operating frequency in order to control the electron injection and the spoke phase. Prior simulation work using a 2D model of a Rising Sun magnetron showed that the use of 100% modulated current controlled the magnetron phase and allowed for dynamic phase control. In this work, the minimum fraction of modulated current source needed to achieve a phase control is studied. The current fractions (modulated versus continuous) were varied from 10% modulated current to 100% modulated current to study the effects on phase control. Dynamic phase-control, stability, and start up time of the device were studied for all these cases showing that with 10% modulated current and 90% continuous current, a phase shift of 180° can be achieved demonstrating dynamic phase control.

Particle-in-cell based parameter study of 12-cavity, 12-cathode rising-sun relativistic magnetrons for improved performance

Particle-in-cell simulations are performed to analyze the efficiency, output power and leakage currents in a 12-Cavity, 12-Cathode rising-sun magnetron with diffraction output (MDO). The central goal is to conduct a parameter study of a rising-sun magnetron that comprehensively incorporates performance enhancing features such as transparent cathodes, axial extraction, the use of endcaps, and cathode extensions. Our optimum results demonstrate peak output power of about 2.1 GW, with efficiencies of ∼70% and low leakage currents at a magnetic field of 0.45 Tesla, a 400 kV bias with a single endcap, for a range of cathode extensions between 3 and 6 centimeters.

Theoretical Investigation and Simulation of Resonant System of Sector and Hole-and-Slot Resonator Type Rising-Sun Magnetron

In this paper, a sector-step approximation (SSA) model is introduced. With step admittance recurrence and field matching relation, the dispersion equation of rising-sun magnetron (RSM) with arbitrary resonators is derived. By this model, resonant frequencies of a 10-resonator sector and hole-and-slot resonator type RSM (SHSRSM) are theoretically calculated. In addition, computer simulation is performed to verify the accuracy of the theory. Besides, the effects of the hole radius on magnetron’s main characteristic parameters are analyzed, such as $\pi$ -mode resonant frequency, mode separation, and quality factor. The optimized SHSRSM is compared with two common kinds of RSMs, such as sector resonator type RSM (SRSM) and sector-and-slot resonator type RSM (SSRSM). The results show that the theoretical results are well consistent with the simulation results, and the maximum relative error is less than 3%, which verifies the accuracy and feasibility of the SSA model. Compared with SRSM and SSRSM, SHSRSM has greater mode separation and quality factor, which improves the stability and the energy storage of RSM.

Phase-control of a rising sun magnetron using a modulated, addressable, current source

It has been proposed that the use of gated field emitters with a faceted cathode in place of the conventional thermionic cathode could be used to control the current injection in a magnetron, both temporally and spatially. In this work, this concept is studied using the particle-in-cell code VORPAL. The magnetron studied is a ten-cavity, rising sun magnetron, which can be modeled easily using a 2D simulation. The magnetron has a ten-sided faceted cathode. The electrons are injected from three emitter elements on each of the ten facets. Each emitter is turned ON and OFF in sequence at the oscillating frequency with five emitter elements ON at once to obtain the five electron spokes of the π-mode. The simulation results show that the modulated, addressable cathode reduces startup time from 100 to 35 ns, increases the power density, controls the RF phase, and allows active phase control during oscillation.

Simulation of a rising sun magnetron employing a faceted cathode with a continuous current source

It has been proposed that gated field emitters could be used in place of conventional thermionic cathodes to control the current injection in a magnetron, both temporally and spatially. Since gated field emitters have to be fabricated on flat surfaces, a faceted cathode would be used to implement this approach. A 2D ten cavity, rising sun magnetron has been modeled using the particle-in-cell code vorpal. Cylindrical, five-sided, and ten-sided faceted cathodes were modeled to study the variation of magnetron operation due to the cathode shape. This work shows the results of the device performance employing three different cathode geometries with a typical continuous current source. The cathode voltage is −22.2 kV; magnetic field is 0.09 T; and linear current density is 326 A/m. The three models oscillated at the π-mode, at a frequency of 960 MHz for the cylindrical cathode and 957 MHz for the faceted cathodes. Simulations show a faster start up time for the ten-sided faceted cathode. This resulted in a reduced overall startup time of the device from 200 to 110 ns. A strong current instability was observed in the five-sided cathode case with a periodicity range from 250 to 350 ns. This instability was limited to the start-up period of the ten-sided cathode model; hence the ten-sided case was more stable.

Phase control and fast start-up of a magnetron using modulation of an addressable faceted cathode

The use of an addressable, faceted cathode has been proposed as a method of modulating current injection in a magnetron to improve performance and control phase. To implement the controllable electron emission, five-sided and ten-sided faceted planar cathodes employing gated field emitters are considered as these emitters could be fabricated on flat substrates. For demonstration, the conformal finite-difference time-domain particle-in-cell simulation, as implemented in VORPAL, has been used to model a ten-cavity, rising sun magnetron using the modulated current sources and benchmarked against a typical continuous current source. For the modulated, ten-sided faceted cathode case, the electrons are injected from three emitter elements on each of the ten facets. Each emitter is turned ON and OFF in sequence at the oscillating frequency with five emitters ON at one time to drive the five electron spokes of the π-mode. The emitter duty cycle is then 1/6th the Radio-Frequency (RF) period. Simulations show a fast start-up time as low as 35 ns for the modulated case compared to 100 ns for the continuous current cases. Analysis of the RF phase using the electron spoke locations and the RF magnetic field components shows that the phase is controlled for the modulated case while it is random, as typical, for the continuous current case. Active phase control during oscillation was demonstrated by shifting the phase of the electron injection 180° after oscillations started. The 180° phase shift time was approximately 25 RF cycles.

Derivation and generalization of the dispersion relation of rising-sun magnetron with sectorial and rectangular cavities

Field analysis method is used to derive the dispersion relation of rising-sun magnetron with sectorial and rectangular cavities. This dispersion relation is then extended to the general case in which the rising-sun magnetron can be with multi-group cavities of different shapes and sizes, and from which the dispersion relations of conventional magnetron, rising-sun magnetron, and magnetron-like device can be obtained directly. The results show that the relative errors between the theoretical and simulation values of the dispersion relation are less than 3%, the relative errors between the theoretical and simulation values of the cutoff frequencies of π mode are less than 2%. In addition, the influences of each structure parameter of the magnetron on the cutoff frequency of π mode and on the mode separation are investigated qualitatively and quantitatively, which may be of great interest to designing a frequency tuning magnetron.

Theoretical analysis and numerical simulation of rising sun magnetron with sector cavities

Field analysis method is used to deduce the dispersion relation of rising-sun magnetron with sector cavities, which is proved correct by the high frequency field analysis software, and the influence of each structure parameter of the magnetron on the cutoff frequency of π mode and the mode isolation is investigated. The results show that the relative errors between the theoretical values and the simulation values of the dispersion relation are less than 3%, and the relative errors between the theoretical and simulation cutoff frequencies of π mode are less than 1%. Cutoff frequency of π mode is in direct proportion to the cathode radius Rc, anode radius Ra and big cavity angle 2θ1, but in inverse proportion to small cavity radius Rd0, big cavity radius Rd1 and small cavity angle 2θ0. However, these qualitative relationships are not entirely consistent with those of the same cavity magnetron. In radial orientation, the structure parameters, the influence of which on frequency is sorted in descending order, are as follows: anode radius, big cavity radius, small cavity radius and cathode radius. In angular orientation, the influence of big cavity angle on frequency is greater than that of small cavity angle. In addition, mode isolation γ is in direct proportion to big cavity radius Rd1, but in inverse proportion to cathode radius Rc, small cavity radius Rd0, and small cavity angle 2θ0, and it increases first and then decreases with the increase in anode radius Ra or big cavity angle 2θ1.

Faceted magnetron concept using field emission cathodes

A magnetron concept using field emission cathodes has been modeled with the Air Force Research Laboratory particle-in-cell code ICEPIC and the two-dimensional particle trajectory simulation Lorentz2E. In this approach, field emitters are used to provide a distributed cathode in place of a traditional thermionic cathode. The emitters are placed below the interaction space in a shielded structure. The cathode is comprised of facet plates with slits to protect the emitters. Simulation of an L-band rising sun magnetron shows that the faceted magnetron will oscillate using both five and ten facet cathodes. The startup times are very similar to that of a cylindrical cathode magnetron. The electron trajectories of the shielded slit structure have been modeled, and the results indicate that electrons can be injected through the slits and into the interaction space using lateral edge emitters and a pusher electrode design.

Sidney Millman

Sidney Millman

Particle-in-cell code simulations on a rising-sun magnetron oscillator

A high-power rising-sun magnetron oscillator (AX-9) operating at 9.50 GHz is examined by the use of a three-dimensional particle-in-cell (PIC) code, MAGIC3D. A mode spectrum of the 18 vanes rising-sun magnetron cavity is obtained from both an analytic field theory and the numerical code MAGIC3D. A large mode separation in the vicinity of a /spl pi/-mode is observed in the rising-sun configuration. A time evolved electron flow exhibits nine space charge spokes in the PIC simulations, which confirms the /spl pi/-mode oscillation in the 18 vanes rising-sun magnetron. When space charge spokes build up in the interaction region, a single frequency RF oscillation starts to grow and the leakage current escaping from the interaction region reduces to zero. Simulations predict that the saturated radiation power measured at the output waveguide is 250 kW at 9.50 GHz, corresponding to a magnetron efficiency of 53% where the external magnetic field is 0.52 T and the beam voltage and current are 28 kV and 17 A, respectively.

Operation of a relativistic rising-sun magnetron with cathodes of various diameters

This paper presents results of an experimental investigation of a relativistic L-band (1.3 GHz) 10-cavity rising-sun magnetron with cathodes of various diameters. A major goal was to investigate the effect of the cathode diameter on the overall performance, mode stability and pulse shortening of this magnetron when operating at voltages of 100-500 kV and microwave peak power of P/sub /spl mu// /spl sim/ 100-700 MW. The largest levels of P/sub /spl mu// /spl sim/ 700 MW have been achieved, as expected, with cylindrical velvet cathodes. Mode structure and mode competition/switching for each cathode has been investigated in the entire range of operating magnetic fields. A cathode plasma expansion was found to be not the primary factor in a mode instability and pulse shortening of the magnetron investigated. Experimental results on effective magnetron diode gap, uniformity of electron emission, variation of the peak microwave power and microwave pulse duration with the cathode diameter and a correlation between the magnetron operating point and Buneman-Hartree curves are also presented and discussed.

Effects that limit efficiency in relativistic magnetrons

This work is an attempt to elucidate effects that may limit efficiency in magnetrons operated at relativistic voltages (V/spl sim/500 kV). Three-dimensional (3-D) particle-in-cell (PIC) simulation is used to investigate the behavior of 14- and 22-cavity, cylindrical, rising-sun magnetrons. Power is extracted radially through a single iris located at the end of every other cavity. Numerical results show that in general output power and efficiency increase approximately linearly with increasing iris width (decreasing vacuum Q) until the total Q becomes too low for stable oscillation in the /spl pi/-mode to be maintained. Beyond this point, mode competition or switching occur and efficiency decreases. Results reveal that the minimum value of Q (maximum efficiency) that can be achieved prior to the onset of mode competition is significantly affected by the magnitude of the 0-space-harmonic of the /spl pi/-mode, a unique characteristic of rising-suns, and by the magnitude of the electron current density (space-charge effects). When these effects are minimized, numerical simulation predicts that gigawatt-level power production at 55% efficiency may be possible at relativistic voltage.