Thermionic energy converters (TECs) offer a direct method for converting heat into electricity, providing potential applications in waste heat recovery and renewable energy generation. While extensive research has focused on developing low work function materials, the performance of vacuum-based converters remains fundamentally hindered by space-charge effects, necessitating improved theoretical characterization of the space-charge limited current (SCLC). In this study, we derive exact theories for SCLC for multidimensional diodes with nonzero initial velocity (approximating high cathode temperatures) to demonstrate how to design TECs with higher steady-state currents to enhance the conversion of heat to electricity. We show that injected currents exceeding the SCLC limit result in a sharp decrease in the collector current, defining the bifurcation condition. Simulations using the two-dimensional particle-in-cell codes XOOPIC and VSim for both the SCLC and bifurcation regimes yield SCLC within 7% of the theoretical predictions. Finally, the sharp knee characteristic of the transition from one-dimensional thermionic emission to SCLC, known as the Miram curve, is extended to multidimensional diodes characterized by a single sharpness parameter sigma, and its implications are discussed.

Crossed-field amplifiers are known for being noisy; however, the mechanism of noise generation remains poorly understood. This article identifies the spurious emission noise generation mechanism by using simulation and spatial-temporal, spatial-spectral, and spatial-tonal visualizations of the electron population. The VSim simulation model is based on the L-4953 crossed-field amplifier (CFA) from Stellant Systems, a approximate to 5 -MW peak power, approximate to 11.2 -dB, L-band, re-entrant, backward-wave device. The electron spokes are characterized for low-noise, typical stable, and unstable operation, where the spurious emission amplitudes are - 47 , - 37 , and - 15 dB, respectively. The simulation spectrum for typical stable operation matches the available physical device spectrum data, demonstrating the ability of simulation to model the spurious emission mechanism. Simulations show high sensitivity of the spectrum to operation parameters, where a relatively small shift in dc voltage from 91.6 to 93.1 kV causes a transition from typical stable to low-noise operation. The dispersion of the circuit was calculated and demonstrates the "hard" limit to bandwidth where mode competition occurs. Newly developed electron population visualizations identify noise generation mechanisms well within the band. Using these electron population visualizations, three conclusions are made: phase/frequency modulations (PMs/FMs) of the spokes cause many of the spurious emission sidebands on the output spectrum; the modulations of the spokes only couple to the output if the modulations in each spoke are in phase with each other; and the spurious emission amplitude is higher when the modulations in the spokes are a harmonic of a subharmonic of the transit frequency.

The electron spokes for stable operationin the L-4953 crossed-field amplifier (CFA) from StellantSystems are characterized via particle-in-cell (PIC) codesimulations in VSim (TechX). The CFA is a pulsed, re-entrant, backward wave device with a peak output power P-out(peak)approximate to 5 MW, gain G approximate to 11.2 dB, and a bandwidth from f=1.28 to 1.35 GHz. Spatial, spatial-temporal, spatial-spectral, and spatial-tonal visualizations of the electrondensity in both the lab and rotating frames of refer-ence were developed to characterize the spokes. Thespatial visualizations for simulations at the operation fre-quencyfop=1.3 GHz identify the Brillouin and cycloidalelectron flow within the spoke for space-charge lim-ited emission (SCLE) and non-SCLE, respectively. Thespatial-temporal/spectral visualizations identify an oscil-lation (transit wobble) within the spoke at a third of theoperation frequency (ftransit=fop/3=0.43 GHz) causedby the spoke transiting 360(degrees) in the re-entrant design. Thisfundamental spoke oscillation, though, does not directlyappear on the output. However, a much lower amplitudeoscillation at f(sideband)=0.18 GHz identified on the frontof the spoke directly appears as sidebands on the output.While the mechanisms that initiate sideband oscillations with in the spoke and generate noise on the output are relatively unknown, spatial-tonal visualizations show that the phase difference of the oscillations between spokes iscritical to this process. The ability of the visualizations todirectly connect oscillations within the spoke to the output is demonstrated, but strategies are still needed to interpretthe visualizations to identify and characterize noise generation mechanisms.

Particle-in-cell simulations are used to showcase the transit wobble in electron spokes observed in a re-entrant crossed-field amplifier (CFA). The transit wobble period corresponds to the time for a spoke to transit 360 degrees. This introduces a strong frequency component readily observable within the spoke, but not on the output signal. While the effects on the output are relatively unclear, a correlation between transit wobble and prominent side-bands is identified. The separation of the prominent side-bands from the operation frequency is often a harmonic of a sub-harmonic of the transit wobble frequency. This observation is important because it indicates possible avenues to reduce side-bands, such as designing CFAs to encourage a purely sinusoidal wobble to minimize sub-harmonics.

Inductively Coupled Plasmas (ICPs) are extensively used for materials processing, particularly in the semiconductor industry [1]. A typical ICP has an external RF antenna that couples power into a low-pressure chamber, forming a plasma. Antennas used for this purpose are typically coils; the electrical current induces an azimuthal electric field in the chamber, heating electrons and ionizing gas through electron-impact collisions. ICPs generally operate at tens of mTorr and can generate plasma densities up to 1×10 18 m −3 , Simulations of ICPs have been extensively done, typically using fluid-based models for the plasma species and a power deposition profile for the antenna [2]. For lower pressures, the assumptions in these models may break down, necessitating a fully-kinetic approach.

The recently available design specifications for the L-4953 crossed-field amplifier (CFA) from Stellant Systems provides an excellent high-power CFA simulation model for studying basic physics of crossed-field devices to improve performance. The L-4953 was recently modeled using VSim and validated against actual device specifications [1]. The maximum gain in the device is ~12 dB, limited by a loss of lock of the main amplifying mode and the onset of an oscillation. Using the VSim simulation model, the parameter space of magnetic field, DC voltage, emission current, frequency, and drive power was characterized with regards to gain, stability, and newly developed diagnostics. These diagnostics and visualizations are used in both the stationary coordinate system and a rotating coordinate system synchronized with the electron spokes. The new diagnostics include electron spoke angle, spoke width, spoke wobble, beat frequency, and electric field spoke alignment comparison. The new visualizations include electron population statistics and electron trajectories. Preliminary results show a 9 kV DC voltage range of stable operation for each magnetic field within the band. The spoke angle in the rotating frame of reference shows a $\square 45 \square^{\wedge} \circ$ shift from the lowest to the highest stable DC voltages. Unstable operation is distinguished by a modulation of the output power that resembles a beat frequency and often higher gain during the peaks of modulation.

The L-4953 Cross-Field Amplifier (CFA) is a high-power (≈5MW), moderate gain (11.2 dB), pulsed, L-band (1.28 to 1.35 GHz), reentrant, backward wave, thermionic cathode amplifier. We have developed a model of this CFA using the VSim particle-in-cell software and validated it with operating specifications [1]. Because crossed-field devices are noisier than traveling wave tubes, various studies indicate that very high electron emission (primary or secondary) would cause them to transition a low-noise state [2], [3]. The goal of this research is to develop a secondary electron emission (SEE) model for this CFA to study the various operating advantages in reentrant and non-reentrant geometries, noise degeneration, and power saturation. This requires a thorough characterization of the SEE model, which we present here. A VSim simulation of the SEE model will determine the gain, bandwidth, dispersion, resonant modes, zero-drive operation, and particle statistics. Preliminary results from the SEE reentrant version of the simulation model utilize a primary emission source extending across a 44° arc on the cathode to provide the seed current. This injected current uses a space-charge limited model and has demonstrated amplification with three stable spokes at a peak anode current of 80 A. The SEE current is based on a Vaughan emission model with $\delta\max=2.1$ and $\mathrm{W}_{\max}=400$ 2V. This work will show the device performance under reentrant and non-reentrant operation, minimizing the injection current and tailoring the SEE parameters to match the product performance to create a more realistic emitting sole CFA.

The ponderomotive force has previously been identified as a possible driver of observed density modifications close to radio frequency actuators during operation. This nonlinear force redistributes density in regions of gradients in the magnitude of an oscillating electric field and describes the influence of the fast time scale RF wave dynamics on slow time scale plasma transport. Depletion of the saturation current (a proxy for the density) measured at the Large Plasma Device (LAPD) was 30–35% during ion cyclotron range of frequencies operation. A coupled 1D plasma transport and cold plasma frequency domain wave solver was developed to self-consistently describe ponderomotive effects and was used to compare with results obtained from the LAPD experiment. The scaled current density driver for the wave model yielded an RF B field in close agreement with two components of the experimental data. However, the 1D parallel model did not accurately reproduce the amplitude or spatial distribution observed in experimental measurements of By. Within the limitations of the 1D model, initial simulation results showed that the ponderomotive force depleted up to 8% for high power (1 MW) and around 1% for the experimental power of 120 kW. This could suggest that the ponderomotive force is not the main driver of density modification for the LAPD experiments presented in this paper. Higher fidelity tools of at least 2D will be required to give a more realistic description of the RF E fields and the effect of the ponderomotive force on the LAPD.

The RF-Transpond code couples a fluid plasma transport solver with a frequency domain cold plasma RF wave solver in a 1D domain parallel to a strong background magnetic field. A ponderomotive force term proportional to parallel gradients in the electric field strength is included in the transport model in order to describe ponderomotive effects in the scrape-off layer (SOL) of fusion plasmas. The transport and wave codes are verified independently and a coupled case corresponding to experimental parameters from the LArge Plasma Device (LAPD) is presented. The density perturbation ratio R-n, calculated to describe ponderomotive force driven modifications, is up to 20% for the simulation inputs used. Program summary Program Title: rf-transpond CPC Library link to program files: https://doi.org/10.17632/xn3y2yx9wj.1 Developer's repository link: https://github.com/rhealbarnett/rf-transpond.git Licensing provisions: MIT Programming language: Matlab Nature of problem: Self consistent coupled model describing ponderomotive force driven density modification in the near field of RF antennas. Solution method: The density and velocity solutions are calculated from the continuity and momentum transport equations, solved using a finite difference time domain method, which include a ponderomotive force term that depends on the radio frequency electric field. The frequency domain electric field solution is calculated from the cold plasma wave equation, solved using a finite difference frequency domain method, where the cold plasma dielectric tensor is a function of the density. The electric field and density couple the two models, providing self consistency. (C) 2022 Published by Elsevier B.V.

Simulations are performed on the Stellant Systems, L-4953 crossed-field amplifier (CFA) in VSim. This is a high peak power $(P_{out}^{peak}\approx 5 {\mathrm{M}}\mathrm{W}, P_{o\tau,t}^{avg}\approx 3.2\text{kW})$ , moderate gain $(G=11.2\text{dB})$ , pulsed $(t_{pulse}=1.8\mu \mathrm{s},\ f_{pulse}=360\ \text{Hz})$ L-band ( $f = 1.28$ to 1.35 GHz), reentrant, backward wave, thermionic cathode CFA. Preliminary simulations predict $P_{out}^{peak} \approx 7.5\ \text{MW}$ and $\text{Gain} = 11.7$ dB at operation parameters in great agreement with specifications disclosed b y S tellant Systems. A new Child-Langmuir emission model recently introduced by TechX is tested on this crossed-field device, a nd predicts a n a node current of $I_{a} = 120\ \mathrm{A}$ , which matches relatively well with the the specified anode current of 100 A.

This paper uses field theory to derive the exact dispersion relation of space charge waves in a two-dimensional electron gas (2DEG) located in a dielectric or a dissimilar dielectric waveguide. It is found that the dispersion of a 2DEG can be modeled accurately using the free-electron sheet model, which is further confirmed by the almost identical polarizability of a 2DEG and of a free-electron sheet with zero drift velocity. Transitions among the well-known 2DEG dispersion, the beam mode in vacuum electronics, and Gould–Trivelpiece mode in plasma physics are demonstrated by varying the 2DEG density and direct current drift velocity. The effects of waveguide dimensions are also presented. Our method is general and can be applied to find the dispersion relation of 2DEG with arbitrary drift velocity (governed by electric field and scattering) in more complex circuits. Our study provides insight into the design of electromagnetic wave devices and circuits involving a 2DEG.

The micro-fabrication of small planar or rectangular waveguide components for use at very high frequencies in millimeter and up to THz wave ranges has attracted a lot of attention in recent decades due to advanced semiconductor manufacturing technologies. A homogenous metallic waveguide is a fast wave structure while a slow wave structure (SWS) can be obtained with employing a corrugation or dielectric filling in the waveguide. For a dielectric loaded waveguide, the normal modes are not, in general, either pure transverse electric (TE) or transverse magnetic (TM) modes, but rather combinations of these modes, namely longitudinal section electric (LSE) and longitudinal section magnetic (LSM) modes having no E and H components normal to the interface, respectively. It had been proposed to use a dielectric-loaded rectangular waveguide as an accelerating structure. In this work, we propose to use the partially filled rectangular waveguide as a SWS for THz wave generation (reversed acceleration) since the same beam wave interaction can be employed. The field analysis of the SWS is conducted using a conformal finite-difference time-domain (CFDTD) method and the corresponding dispersion relations of TE, TM, LSE, and LSM modes are calculated. The beam wave interaction for THz generation is studied using the 3-D CFDTD particle-in-cell simulations. The detailed simulation model and calculation results will be presented.

It is critical to have a standard reference model for crossed-field amplifiers (CFAs) for the research community. We use the TechX 3-D particle-in-cell (PIC) code TechX to model the Stellant Systems L-4953 CFA. This CFA is a pulsed, reentrant, backward wave device with a thermionic cathode operating in the space-charge limited regime. The basic operating parameters are: peak output power ${P}_{\text {out}}^{\text {peak}}\approx 5 \text {MW}$ , gain ${G}\approx 11.2 \text {dB}$ , pulse duration ${t}_{\text {pulse}}={1.8} \mu \text {s}$ , pulse rate ${f}_{\text {pulse}}={360} \text {Hz}$ , duty cycle $\text {Du}={0.06}8\%$ , and a frequency bandwidth from ${f}={1.28} \text {to} {1.35} \text {GHz}$ . This work will present device dimensions, the dc and radio frequency (RF) connection assemblies, and characterize the device performance. Simulations in VSim are used to determine the gain, bandwidth, and transmission characteristics. With the specified anode current of 98 A, a stable 3-electron spoke operation is observed with the simulated gain matching the device within 1 dB. The simulation model is directly compared with supplied device data from 13 devices and accurately predicts the operating voltages within 3% and output power within 10% except for an outlier at 1.28 GHz.

Simulation and characterization of the L-4953 Cross-Field Amplifier (CFA) has begun. This is a high power (3.2 kW), moderate gain (11.2 dB), pulsed (1.8 μs), L-band (1.28 to 1.35 GHz), reentrant, backward wave, thermionic cathode amplifier. The goal of this research is to develop a model based on this CFA to study the gain-limiting factors caused by mode interference and test various methods to retain lock on the amplifying mode such as a modulated cathode. This requires a thorough characterization of the device operating under specification, which we present here. Simulations in VSim are used to determine the gain, bandwidth, dispersion, resonant modes and frequencies, zero-drive operation, and particle statistics. At an anode current of, a stable 3 electron spoke operation is observed with the simulated gain matching specification within 1 dB. The dispersion shows backward wave device operation in-between a pair of eigenmodes resembling the TE31 mode. TE41 and TE21 eigenmode pairs are also observed but have lower frequency separation, making these regions less ideal for amplifier operation. Zero-drive simulations show 2, 3, 4, and even 9 electron spoke operation at the previously determined eigenfrequencies. This work will show the device performance, electron population analysis, and results of electron modulation.

On the electronic (RF) side of the THz gap, both solid-state transistors and vacuum electronic devices struggle to reach 1mW at 1THz largely due to the diminishing wavelength. Transistors scaled for THz operation have gate lengths << 100nm and cannot support sufficient width to produce appreciable power at this frequency. Vacuum beam traveling wave amplifiers are electrically large, but still struggle with fabrication and magnetic field tolerances at the required circuit dimensions. We combine the best attributes from both these fields of research into a solid-state traveling wave amplifier. We have derived an extension to the classical Pierce theory [1] to couple high density 2DEG plasma waves present at certain semiconductor heterostructure interfaces to a generic slow wave circuit. In this work, we present possible slow wave structures based on planar semiconductor fabrication techniques. EM simulations are shown, including losses in the THz regime, and the resulting gain from a numerical Pierce-style calculation. A brief discussion about the challenges of a full ‘hot tube’ style simulation is also included.

The interaction of two-dimensional electron gas (2DEG) in a solid-state heterostructure with a surrounding slow wave circuit holds the potential for high power THz generation and amplification. The dense 2DEG formed at material interfaces will provide an ideally confined beam of high-density electrons, where problems pertinent to the vacuum electron beams, such as strong external magnetic field needed for beam confinement and the stringent manufacturing and alignment tolerances at shorter wavelengths, can be eliminated. To utilize 2DEG in a wave amplifier, it is important to understand the behavior of space charge waves in a 2DEG [1] . In this work, we provide the exact dispersion relation for the space charge waves (or plasma waves) in a 2DEG located inside a dielectric waveguide. The effects of dissimilar dielectric materials, waveguide dimensions, and 2DEG density are analyzed. The results are compared to those of an ideal free-electron sheet beam with infinite axial magnetic field [2] . The transition to the Gould-Trivelpiece mode is demonstrated [3] .