Jack Watrous

3D PIC simulations of the Relativistic Klystron Oscillator

Summary form only given. The Relativistic Klystron Oscillator (RKO) is a gigawatt class microwave source that is being investigated within the Air Force Research Laboratory (AFRL). In this talk, results of 3D simulations of the AFRL RKO using the particle-in-cell software ICEPIC (Improved Concurrent Electromagnetic Particle-In-Cell) are presented. Full 3D simulations of the RKO are challenging for a number of reasons, not the least of which is the sheer size of the problem. ICEPIC is unique in its ability to perform very large simulations and is an appropriate tool for solving problems related to the RKO. Other challenges include the correct treatment of emission from the knife-edge cathode and proper modeling of the Q of the RKO cavities.

Three-dimensional Particle-In-Cell (PIC) simulations of a conventional, strapped, oven magnetron, including the effect of periodic variations in the insulating magnetic field

Summary form only given. We report on three-dimensional simulations of a conventional oven magnetron, operating at near 2.5 GHz, performed with the parallel Particle-In-Cell (PIC) code ICEPIC. Including the details of strapping, thermionic emission, and output power extraction, the calculations produce excellent agreement with experimentally observed quantities such as frequency, anode current, and output power. The self-oscillation condition, mode competition, and growth rate of the pi mode is examined as a function of cathode current, and found to agree with experimental results. Specifically, the details of spoke formation under various emission assumptions (thermionic and space charge limited emission) discussed. Finally, the inclusion of permanent magnets to produce a periodic variation in the strength of the confining magnetic field is shown to greatly reduce the time to steady-state operation in the pi mode, even at very low levels of cathode current. The physics of this situation, and the implications on the noise production of the device, discussed.

Generation, propagation and diagnostics of a long pulse annular electron beam for an HPM source

We are in the process of re-assembling the injection-locked relativistic Klystron oscillator to increase the duration of the high power microwave pulse. This HPM source is designed to use a 500 kV, 10 kA annular electron beam and generate /spl sim/1.5 GW microwave pulse. Previously we published that the microwave pulse length was experimentally observed to be limited to a finite change in the beam current. These initial experiments focus on controlling the total variation of the emitted beam current. That is, our goal is to have the vacuum diode behave as a resistive load at the desired voltage. We will be presenting results of experiments on the materials used to fabricate the cathode and its emission surface, results from X-ray and optical diagnostics of the unmodulated electron beam position and thickness, and finally results from X-ray and optical diagnostics of the modulated electron beam position and thickness. These results will be compared with different time dependent and steady state computational tools.

Simulation of a faceted magnetron using discrete modulated current sources

Summary form only given. Simulation of a 2-D model of a ten cavity rising sun magnetron was developed using the 3-D particle-in-cell (PIC) code VORPAL 5.21. The cathode structure is comprised of field emitters, designed with facet plates with slits to protect the emitters2. A cylindrical and faceted (five and ten sided) cathode was modeled to study the variation of results due to the cathode shape. Discrete current sources were modeled to come from each facet of the five and ten sided cathode to study its effect on the magnetron operation. Each plate on the five sided cathode structure contains 5 emitters that can be addressed spatially and modulated temporally. Similarly the ten sided cathode contains 3 emitters per facet. The simulations were run with the discrete current sources and then compared with the reference continuous current source model. The discrete current sources allow control in space and time of the current injection. Each ON emitter represents the location of the electron spoke. By using this technique, the startup of oscillations and its location can be controlled. Simulations demonstrating this concept are presented in this work. This technique was implemented in both the five sided and ten sided cathode structure. Startup times from each model were obtained from the simulation. The ten sided, modulated cathode resulted in the fastest start up at 35 ns. After analyzing each model, it was found that there is an instability in the five sided cathode oscillations. This instability results in a current “spike” to the anode and a subsequent collapse of the spokes. An analysis of the total current injected was completed to address this problem. This was observed in both the continuous and the modulated current source models. The problem was minimized by implementing the ten sided cathode geometry. These results and comparisons will be presented in this work. Finally, by using the modulation technique, a phase shift of 180° was simulated by changing the timing of the modulated current injection. This work and additional observations will be also presented.

Simulation of a phase controlled magnetron using a modulated, addressabel cathode

A 2-D model of a ten cavity rising sun magnetron was developed using the 3-D particle-in-cell (PIC) code VORPAL 5.21. A 10-sided cathode structure was modeled to represent gated field emitters on the facet plates2. Each plate contains 3 emitters that can be addressed spatially and modulated temporally. The simulations were initially run to compare a cylindrical, 5-sided, and 10-sided cathode with continuous current emission (DC). Then the simulations were run with the modulated electron sources. For the rising sun magnetron, the π-mode is the primary mode, so the 10 cavity device has 5 spokes in π-mode. Therefore, a single spoke rotates past 2 cathode facet plates (6 total emitters) every RF period. This magnetron oscillates at 957 MHz. Hence, 1 out of 6 emitters per 2 adjacent facets was turned on at a frequency of 957 MHz with a 1/6 duty cycle. Therefore, 5 emitters are on at one time for the entire magnetron; each ON emitter represents the location of the electron spoke. This approach then controls the startup of oscillation and location of the spokes (phase). Simulations demonstrate this effect. A decreased start-up time is observed, falling from 100 ns for the continuous current source cases to 35 ns using modulation. The spokes are always located at the same locations in simulation time for different simulations runs while without source modulation control, the spoke locations vary randomly. Finally, during a simulation run, the spoke locations were shifted by 180° by changing the timing of the modulated current injection to generate the electron spokes 180° out of phase. This demonstration of phase control as well as other observations from the simulations will be presented.

Use of distributed cathode in crossed-field amplifiers

Summary form only given. Crossed-Field Amplifiers (CFAs) use thermionic emission or secondary electron emission for their current sources. These sources do not allow spatial or temporal modulation of the current. One limit in the gain of CFAs is the input current. Too much injected electron current can swamp the RF input signal. One way to increase the device gain is by using the emitting-sole design. This design uses secondary electron emission along the sole electrode of the device to provide high current density. This approach is, in effect, a distributed cathode, but there is no control over the electron current along the device. The use of distributed Field Emission Arrays (FEAs) in CFAs has been proposed. FEAs may allow active temporal and spatial control in CFAs. By having control over the distributed sources, it is possible that the gain can be increased. Also, a distributed cathode allows for a method to study the physics of the device in great detail. The way in which noise propagates can be studied by perturbing the emitted current from various locations. A distributed source CFA is studied both experimentally and computationally. The CFA device uses a meander line slow wave circuit and operates somewhere in the 600 to 900 MHz range. Simulations of the slow wave circuit using VORPAL, ICEPIC, and COMSOL will be presented. The wave pattern of the meander slow wave circuit will be mapped spatially, and the traveling wave components of the field will be measured with a high speed oscilloscope. These results will be compared with the simulations. The relationship between the gain and the number of sources, placement of the sources, and timing of the sources will all be studied both experimentally and by simulation.

Simulation of a faceted magnetron device using discrete current sources

Summary form only given. A 2-D model of a ten cavity rising sun magnetron was developed using the 3-D particle-in-cell (PIC) code VORPAL 5.21. The cathode structure is comprised of field emitters, designed with facet plates with slits to protect the emitters. A cylindrical and faceted (pentagon shaped) cathode was modeled to study the variation of results due to the cathode shape. Discrete current sources were also modeled to come from each facet of the pentagon-shaped cathode to study its effect on the magnetron operation. Appropriate spatial and velocity distributions of the electrons for the VORPAL input are developed with results obtained from the electron trajectory modeling generated with Lorentz2E2. Since the discrete current sources can be turned on and off, this part of the work will allow control in space and time of the current injection. Preliminary results of the implementation of this technique will be presented in this work. The final goal is to have control over the device oscillations. By setting adequate diagnostics, the phase at which the magnetron oscillates at certain periods of time will be controlled and determined using the simulation. It is expected to have full control over the magnetron operation. Therefore, changes in startup time, hub thickness, power and efficiency will be study under these conditions.

Simulation of a faceted magnetron device using field emission arrays

Summary form only given. A magnetron structure 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 Lorentz2E1. For the particle trajectory modeling the cathode has a distributed structure comprised of field emitters instead of the traditional thermionic cathode. The cathode is designed with facet plates with slits to protect the emitters. In this work the electron trajectories of the slit structure were modeled with Lorentz2E to study the sensitivity of the device.

Simulations of a 95 GHz, 100 kW CW gyrotron interaction cavity using 3D PIC

Summary form only given. We show ICEPIC (Improved Concurrent Electromagnetic Particle-in-cell) simulations of the interaction cavity operation of a 95 GHz, 100 kW CW gyrotron. Such devices are extremely challenging to simulate with PIC because of the combination of large device size and very small electromagnetic wavelength, which must be well-resolved by the computational mesh. Nevertheless, PIC simulations are desired because they are self-consistent, full-physics models and include all electromagnetic modes. We present comparisons of device mode of operation, frequency, and power output with experiment, and the simulated effect of varying various design parameters, including magnetic field, simulated geometry, beam energy, beam radius, and alpha.

Multi-dimensional effects in space-charge-limited emission: an improved voltage-current relation for parallel plate geometry

Summary form only given. Previous analysis (Luginsland, Yau, Gilgenbach, Phy. Rev. Lett., vol. 77, no. 2, p. 4668) of space-charge-limited emission in simple two-dimensional parallel plate geometry indicated that the current-voltage relationship in this geometry was not well approximated in all cases by the simple one-dimensional Child-Langmuir Law. This previous analysis used particle-in-cell code calculations to determine the limiting current for a given voltage and given beam width. This analysis assumed that the beam current density was uniform. A new analysis, based upon numerical solution of the Poisson equation, makes no assumption about the current density, but leaves the current density distribution as an unknown function to be determined. The numerical approach that has been developed to simultaneously determine the electrostatic potential and the beam current density will be described. The numerical method is used to generate a current-voltage relationship for the two-dimensional parallel plate geometry. These results are compared against particle-in-cell code calculations based upon two different approaches to modeling space-charge-limited emission.