Particle-in-cell Research Articles

Gain and Bandwidth Improvement Studies of Millimeter Wave Periodically Dielectric Loaded Gyro-Twystron Amplifier

In this article, the spurious oscillations in the output section of gyro-twystron have been analyzed and the design and modeling of its various subassemblies also been presented. The periodic dielectric loading (PDL) technique has been adapted in the output waveguide section to improve the device gain by suppressing the backward wave oscillations (BWOs). Further, to improve the performance of the amplifier all the cavities were staggered tuned. The particle-in-cell (PIC) simulation of the present PDL gyro-twystron predicted an RF output power of ~120 kW in the fundamental TE01 mode at 94 GHz. The conversion efficiency, 3-dB bandwidth, and saturated gain were calculated as ~34%, ~2.2 GHz, and ~51 dB, respectively. A triode magnetron injection gun (MIG) was designed for 60 kV and 6 A gyrating electron beam and optimized for the velocity spread of ~2.2% with a velocity ratio of 1.6. A single-stage depressed (SSD) collector has also been designed to enhance the efficiency of the amplifier to ~57%. A double-disk window was designed and optimized for the broader bandwidth of ~8 GHz.

Comparison of Material Point Method and Finite Element Method for Post-Failure Large Deformation Geotechnical Analysis

Finite Element Method (FEM) has been the state-of-the-art method in geotechnical analysis since it first formulated in the 40s. It capable to handle Multiphysics simulation, soil-structure and soil-water interaction, and time history analysis. Though powerful, the standard Lagrangian FEM suffers mesh distortion when handling large strain deformation problem. This mesh entanglement problem makes post-failure analysis is considerably challenging to model if not impossible to do using FEM. The Material Point Method (MPM) then later introduced to solve these large strain deformation problems. Adapted from the Particle in Cell (PIC) method, MPM is a hybrid method that combines Eularian and Lagrangian approach by utilizing moving material points which are moving over spatially fixed computational mesh. This approach enables MPM to calculate not only fluid mechanics such in PIC but also solid mechanics and its intermediatory states. To demonstrate the capability of MPM and its consistency with FEM in geotechnical analysis, this article presents a comparison of FEM and MPM analysis on a hypothetical slope using Mohr-Coulomb constitutive model. The simulation shows that both FEM and MPM analyses are consistent to each other especially in small strain scheme. However, in large strain deformation, MPM is still able to get convergent result while FEM is not. The MPM simulation is also able to animate post failure behavior clearly, calculate post-failure strains and stresses distribution, and present final geometry of the model.

Numerical study of viscosity and heat flux role in heavy species dynamics in Hall thruster discharge

A two- and three-dimensional velocity space axisymmetric hybrid-PIC model of Hall thruster discharge called Hybrid2D has been developed. The particle-in-cell (PIC) method was used for neutrals and ions (heavy species), and fluid dynamics on a magnetic field-aligned (MFA) mesh was used for electrons. A time-saving method for heavy species moment interpolation on a MFA mesh was developed. The method comprises using regular rectangle and irregular triangle meshes, connected to each other on a pre-processing stage. The electron fluid model takes into account neither inertia terms nor viscous terms and includes an electron temperature equation with a heat flux term. The developed model was used to calculate all heavy species moments up to the third one in a stationary case. The analysis of the viscosity and the heat flux impact on the force and energy balance has shown that for the calculated geometry of the Hall thruster, the viscosity and the heat flux terms have the same magnitude as the other terms and could not be omitted. Also, it was shown that the heat flux is not proportional to the temperature gradient and, consequently, the highest moments should be calculated to close the neutral fluid equation system. At the same time, ions can only be modeled as a cold non-viscous fluid when the sole aim of modeling is the calculation of the operating parameters or distribution of the local parameters along the centerline of the discharge channel. This is because the magnitude of the viscosity and the temperature gradient terms are negligible at the centerline. However, when a simulation’s focus is either on the radial divergence of the plume or on magnetic pole erosion, three components of the ion temperature should be taken into consideration. The non-diagonal terms of ion pressure tensor have a lower impact than the diagonal terms. According to the study, a zero heat flux condition could be used to close the ion equation system in calculated geometry.

Transient simulation of biomass combustion in a circulating fluidized bed riser

Interest in circulating fluidized bed (CFB) boilers as a power generation technology has sky-rocketed in recent years because of several advantages this technology offers over conventional boilers, such as increased gas-solid mixing, which results in higher combustion efficiency and the ability to use lower rank fuels. CFB combustors are operated at lower temperatures than conventional thermal power generation combustors, thus reducing NOx emissions, while SO2 emissions can be conveniently controlled through the addition of Ca-based sulfur sorbents within the combustor.This paper summarizes the modeling effort on a 50 kWth CFB combustor designed, built, and operated at CanmetENERGY in Ottawa, Canada. The numerical model employs the multiphase particle-in-cell (PIC) approach in the open-source Multiphase Flow with Interphase eXchanges (MFiX) Software Suite. The MFiX-PIC model parameters for the simulation are tuned against cold-flow experiments from CanmetENERGY using olivine sand as the inert bed material. It is shown that for the relatively coarse fluid meshes and large parcel sizes necessitated by the scale of the simulation, filter size dependent corrections to the drag law must be incorporated to ensure accuracy of the simulation results.The validated cold flow model is extended to simulate reacting flow with torrefied hardwood as the feedstock and to validate the combustion reaction scheme. The species concentrations at the riser outlet are compared against CanmetENERGY's experiments and show satisfactory agreement. The simulations demonstrate the ability of MFiX-PIC to accurately capture both the physics and chemistry of a CFB combustor at bench scales, which can be further extended to pilot- and industrial-scale systems.

On the control of electron heating for optimal laser radiation pressure ion acceleration

We study the onset of electron heating in intense laser–solid interactions and its impact on the spectral quality of radiation pressure accelerated ions in both hole boring and light sail regimes. Two- and three-dimensional particle-in-cell (PIC) simulations are performed over a wide range of laser and target parameters and reveal how the pulse duration, profile, polarization and target surface stability control the electron heating, the dominant ion acceleration mechanisms and the ion spectra. We find that the onset of strong electron heating is associated with the growth of the Rayleigh–Taylor-like instability at the front surface and must be controlled to produce high-quality ion beams, even when circularly polarized lasers are employed. We define a threshold condition for the maximum duration of the laser pulse that allows mitigation of electron heating and radiation pressure acceleration of narrow energy spread ion beams. The model is validated by three-dimensional PIC simulations, and the few experimental studies that reported low energy spread radiation pressure accelerated ion beams appear to meet the derived criteria. The understanding provided by our work will be important in guiding future experimental developments, for example for the ultrashort laser pulses becoming available at state-of-the-art laser facilities, for which we predict that proton beams with $\sim$ 150–250 MeV, $\sim$ 30% energy spread, and a total laser-to-proton conversion efficiency of $\sim$ 20% can be produced.

Taylor particle-in-cell transfer and kernel correction for material point method

The material point method (MPM) has been extensively used to solve problems involving large displacements and deformations. The standard MPM formulation, which adopts fluid-implicit-particle (FLIP) transfer, is less dissipative but also less stable than particle-in-cell (PIC) transfer. The affine PIC (APIC) transfer introduces the affine velocity and was developed to realize stable simulations while overcoming dissipations of the angular momentum in PIC. This paper presents Taylor-PIC (TPIC) transfer, which is a type of APIC transfer that combines the affine velocity based on the first-order Taylor series approximation and PIC transfer. TPIC is simple (only the particle velocity gradient is required) and inherits the key advantages of the original APIC, such as less dissipation and stability. Although TPIC does not conserve angular momentum, in contrast to APIC, the velocity gradient is preserved in the transfer between particles and the grid. This velocity gradient contains the angular information in its skew-symmetric component, which allows TPIC to adequately describe angular motion, similar to APIC.Furthermore, the MPM can cause stress oscillations near boundaries when boundary conditions are explicitly imposed, e.g., when the boundary grid velocity (or momentum) is set to zero. When affine-type transfers are used, this instability is exacerbated, and simulations can easily fail. Therefore, we propose a kernel correction method based on the weighted least squares for particles near boundaries. The proposed TPIC transfer and kernel correction are validated through five types of simulations, each using a different material—linear elastic, von Mises, Newtonian fluid, and Drucker–Prager. In the simulations, incorrect results due to stress oscillations are observed even for small deformations. Applying the corrected kernels successfully removes these spurious oscillations, and the results are consistent with the analytical solutions. Moreover, the numerical results confirm the accuracy and robustness of the proposed TPIC transfer.

Cascading parametric decay coupling between whistler and ion acoustic waves: Darwin particle-in-cell simulations

We present the results of numerical studies of the whistler wave parametric decay instability in the system with the suppressed Landau damping of ion acoustic waves (IAWs) based on the self-consistent Darwin particle-in-cell (PIC) model. It has been demonstrated that a monochromatic whistler wave launched along the background magnetic field couples to a counter-propagating whistler mode and co-propagating ion acoustic mode. The coupling of the electromagnetic mode to the electrostatic mode is guided by a ponderomotive force that forms spatio-temporal beat patterns in the longitudinal electric field generated by the counter-propagating whistler and the pump whistler wave. The threshold amplitude for the instability is determined to be δBw/B0 = 0.028 and agrees with a prediction for the ion decay instability: δBw/B0 = 0.042 based on the linear kinetic damping rates, and δBw/B0 = 0.030 based on the simulation derived damping rates. Increasing the amplitude of the pump whistler wave, the secondary and tertiary decay thresholds are reached, and cascading parametric decay from the daughter whistler modes is observed. At the largest amplitude (δBw/B0 ∼ 0.1) the primary IAW evolves into a short-lived and highly nonlinear structure. The observed dependence of the IAW growth rate on the pump wave amplitude agrees with the expected trend; however, quantitatively, the growth rate of the IAW is larger than expected from theoretical predictions. We discuss the relevant space regimes where the instability could be observed and extensions to the parametric coupling of whistler waves with the electron acoustic wave (EAW).

Kinetic modeling and experiments of a pulsed-bias plasma in a multipole plasma chamber

A pulse of electron timescale applied to a planar electrode immersed in a homogeneous plasma in a multipole plasma chamber (MPC) is modeled using a fully kinetic particle-in-cell (PIC) approach. In the time-explicit PIC simulations, we observed that the ion-sheath expansion is accompanied by electron timescale harmonic plasma oscillations at the sheath edge that decay after applying the pulse. First, we validate our PIC approach by comparing it with previous analytical and semi-empirical sheath expansion studies. Then, we compare our PIC results with experiments conducted in the MPC where similar electron frequency oscillations were excited when an electron timescale pulse was applied to a flat-conductor plate. In both PIC simulations and experiments, we find that the shape of the applied pulse dictates the amplitude of the sheath edge oscillations. In the PIC simulations, we observe that Landau damping has no discernible effect on these oscillations. However, in the experiments, the presence of a hot electron population results in a higher damping of electron oscillations. In both PIC simulations and experiments, the amplitude of the electron frequency oscillations decreases with the applied pulse width and these oscillations disappear for a linear pulse of a longer timescale of tpulse=1 μs (ωpetpulse=178), in the PIC simulations.

Isolated ultra-bright attosecond pulses via non-collinear gating

When light with relativistic intensity is incident on a solid target, bright attosecond pulses of extreme ultraviolet and x-ray radiation can be generated in the reflected beam. Unfortunately, the use of multi-cycle laser pulses results in trains of these attosecond pulses. Here we investigate a non-collinear gating scheme applied to surface high-harmonic generation to allow for the extraction of a single intense attosecond pulse from this train. Using 3D and 2D particle in cell (PIC) simulations we demonstrate that it is possible to angularly isolate a single attosecond pulse from the main driving laser pulse using this interaction geometry with intensities I > 1020 W cm−2. This result opens the door to generating bright attosecond pulses from relativistic plasmas without the need to spectrally filter the driving laser pulse.

Advanced Theoretical Models for Broadband Klystron Development

Broadband klystrons (BBKs) offer the potential of both high power and broad-bandwidth performance as microwave amplifiers. Staggered tuned bunching circuit and filter-loaded output cavity are the mainstream techniques adopted for developing such devices. However, in the design and optimization stage, the accurate and fast theoretical models are still missing before final particle-in-cell (PIC) simulations are conducted. In this article, the small-signal theory of klystron has been derived from accurate large-signal models used in KlyC, where complex mode field distribution, relativistic effects, mode coupling, and precise space charge model are fully considered in the final analytic formulas compared with existing simplified models. Furthermore, mode coupling theory with partially beam-loading conditions has been developed in KlyC to analyze the filter-loaded output cavity and overall klystron performance in the large-signal domain. An example of the retrofit design of 100-kW five-cavity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${X}$ </tex-math></inline-formula> -band klystron is then presented to demonstrate the advanced design methodology based on the above fast theoretical models. The 3-D PIC simulation finally verifies this BBK design, showing −1-dB bandwidth of 200 MHz is attainable with output power over 100 kW, where the maximum discrepancy between theoretical models and PIC is within 2% in the whole bandwidth.

Investigation of a Bifrequency Magnetically Insulated Line Oscillator With Ridged-Disk-Loaded Vanes

In this article, a bifrequency magnetically insulated line oscillator (BFMILO) with ridge-disk-loaded vanes has been investigated in order to increase the device efficiency. The influence of ridged slow wave structure (RSWS) on electromagnetic (EM) characteristics of the BFMILO has been studied in the absence of an electron beam with CST Eigenmode solver. Cold (without electron beam) EM simulation demonstrates the impact of the ridge at the disk tip on the resonance frequency, phase velocity, and coupling impedance of the ridged BFMILO (RBFMILO). It shows that the RSWS can significantly enhance the coupling impedance of the RBFMILO, improving overall power efficiency. The CST particle-in-cell (PIC) simulation has been carried out to assess the RF performance of the RBFMILO. For the input dc voltage of 500 kV and the current of 45 kA, the PIC simulation detects a high-power microwave (HPM) with two frequencies of 3.35 and 3.60 GHz, generating a collective peak RF power of 4.2 GW. The peak power conversion efficiency of the device is 18.7%.

Investigation of Half Rectangular-Ring Helix Slow Wave Structure for W-Band Wide Bandwidth High-Efficiency TWTs

The half rectangular-ring helix (HRRH) slow wave structure (SWS), which evolves from the rectangular helix (RH), is proposed to develop a high-efficiency wide bandwidth millimeter-wave traveling-wave tube (TWT). The comprehensive advantages of the HRRH SWS are lower phase velocity and higher interaction impedance in comparison with the RH and the planar helix with straight-edge connections (PH-SECs) SWS with the same dimensions. The particle-in-cell (PIC) simulation shows that, at a beam voltage of 6450 V, a beam current of 0.03 A, the maximum output power of 42.2 W, corresponding to a differential small-signal gain of 1.43 dB/mm, and an electron efficiency of 21.8% can be obtained for the HRRH TWT at 95 GHz. The output power, differential small-signal gain, and electron efficiency of the HRRH TWT are considerably enhanced compared with the RH TWT in a wide frequency range of 60–115 GHz under the same electrical parameters.

Study of the Frequency Self-Modulation in Gyro-TWT Based on Two -Band Amplifiers

Periodical radiation spectrum with a frequency difference of ~160 MHz is observed in hot-test experiments of Ku-band gyrotron traveling-wave tubes (gyro-TWTs). By the means of eigenmode analyses and particle-in-cell (PIC) simulation considering the whole output transition section from the interaction circuit end to the output window, we found that the circuit oscillation is pronounced because of frequency self-modulation (FSM). As a comparison, the cutoff taper contributing to the FSM is removed and a new amplifier has been developed; hot-test results indicate that the periodical property has been greatly alleviated as expected and the stability of the amplifier is well improved.

Design and Simulation for 100-Watt-Class 340-GHz Extended Interaction Klystron

An extended interaction klystron (EIK) working at the frequency of 340 GHz is designed in this present article. The characteristic impedance, coupling coefficient, and normalized electron conductance of the cold cavities are analyzed and optimized. To improve the output power, the EIK adopts a prebunching (PB)-cavity high-frequency structure (HFS). Compared with the conventional terahertz (THz) EIK, the coherence of PB-cavity EIK is enhanced, and the output power is improved. The 3-D particle-in-cell (PIC) simulation predicts the EIK, driven by a 0.20-A, 22.4-kV electron beam confined in a 0.2-mm-diameter beam tunnel, and generates an output power of 138.3 W at the frequency of 339.7 GHz. The gain, electronic efficiency, and 3-dB bandwidth are 39.6 dB, 3.1%, and 500 MHz, respectively. The proposed EIK can be applied to the THz high-resolution radar.

Verification of the Standard Theory of Plasma Emission with Particle-in-cell Simulations

The standard theory of plasma emission is based on kinetic couplings between a single beam of energetic electrons and unmagnetized thermal plasmas, involving multistep nonlinear wave–particle and wave–wave interactions. The theory has not yet been completely verified with fully kinetic electromagnetic particle-in-cell (PIC) simulations. Earlier studies, greatly limited by available computational resources, are controversial regarding whether the fundamental emission can be generated according to the standard theory. To resolve the controversy, we conducted PIC simulations with a large domain of simulations and a large number of macroparticles, among the largest ones of similar studies. We found significant fundamental emission if the relative beam density is small enough (say, ≤0.01), in line with an earlier study with a much smaller domain; the relative intensity (normalized by the total initial beam energy) of all modes, except the mode associated with the beam-electromagnetic Weibel instability, decreases with the increasing relative density of the beam. We also found a significant transverse magnetic component associated with the superluminal Langmuir turbulence, which has been mistakenly regarded as evidence of the F emission in the earlier study. Further investigations are required to reveal their origin.

Two modes of vacuum flashover process under pulsed voltage

Vacuum flashover process can be influenced by various factors, such as gap length, applied voltage form, electric and magnetic field structures, and so on, leading to different flashover voltages and flashover times under a pulsed voltage. Particle-in-cell (PIC) simulation results in this paper show two typical vacuum flashover modes: (a) the area of high space charge density appears after electrons run across the gap and extends from the anode to cathode and (b) the area of high space charge density appears before electrons run across the gap and extends from the middle to both ends of the gap. In order to verify the PIC simulation results, a probe that measures the change in the electric field between the gap is embedded in the anode, the experimental waveform of which shows different features when the shape of insulator is different. Simulation results and experimental waveforms indicate that the flashover process of certain cylindrical insulators corresponds to the first mode, while the flashover process of certain conical insulators with an acute angle between the cathode and dielectric corresponds to the second mode.

Relativistic Multivircator With Two Magnetic Mirrors on Underlimit Electron Beam: Concept and PIC-Simulation Results

A relativistic magneto-isolated vircator on the underlimit electron beam is studied. It contained two serial magnetic mirrors and a coaxial output of microwave radiation. Its 2.5-D particle-in-cell (PIC)-simulation is carried out. Space and phase dynamics of electrons are calculated. The mode is found at which several virtual cathodes (VCs) exist simultaneously in an electron beam, i.e., the multivircator mode is realized in the device. Spectral and power characteristics of the multivircator generation with two magnetic mirrors are calculated. The dependence of the average output microwave radiation and wave resistance of the radiation coaxial output is also calculated. The spectrogram of microwave radiation is provided.

Design and Analysis of Truncated Velocity Tapered Sine-Waveguide Structure for Traveling-Wave Tube in THz Band

A truncated sine-waveguide traveling-wave tube (SWGTWT) is studied to obtain wideband amplification at 600 GHz. The cold test parameters are obtained and finalized through simulation to achieve minimum dispersion coupled with a high interaction impedance. The interaction impedance at various points of the beam tunnel cross section area is evaluated to choose the right shape of the electron beam for the TWT. The effect of velocity tapering on the SWG structure is studied. Particle-in-cell (PIC) simulation is carried out using cylindrical as well as sheet beams. The velocity-tapered structure exhibits higher power and efficiency. The maximum output power and 3-dB bandwidth are estimated to be 7 W and 40 GHz, respectively. The corresponding gain and electronic efficiency of the truncated SWGTWT are 25.4 dB, and 1.88%, respectively.

Susceptibility of multipactor discharges near a dielectric driven by a Gaussian-type transverse rf electric field

Multipactor discharge near an rf window is a key limiting factor in high power microwave systems. In this work, we report special features of dielectric multipactor susceptibility under a Gaussian-type waveform as a function of the rf power density of the transverse rf electric field (P¯rf) and normal restoring field (Edc) via particle-in-cell (PIC) and multiple particle Monte Carlo (MC) simulations. The MC simulations show that, for a Gaussian waveform of a half peak width (Δτ), larger than Δτ/T=0.15 with T = 1 ns the rf repetition period, the susceptibility boundary is similar to that of the conventional sinusoidal waveform-driven multipactor, i.e., two inclined lines in the plane of (P¯rf,Edc). However, by decreasing Δτ, the susceptibility boundary converts to be a closed curve at Δτ/T=0.11 in the plane of (P¯rf,Edc) and further shrinks at Δτ/T=0.05. PIC simulations with a self-consistent surface and space charge effects also show a reduced Edc with increasing P¯rf when P¯rf exceeds a critical value, resulting in a closed curve in the plane of (P¯rf,Edc), and the maximum time-averaged Edc (multipactor strength) also decreases significantly with further decreasing Δτ in agreement with MC simulations. Accordingly, the fraction of the rf power density absorbed by the multipactor discharges also decreases nonlinearly with Δτ from the order of 10−2 to 10−3 (even 10−4), implying a significant improvement compared to the conventional sinusoidal waveform. The simulations also show that the multipactor susceptibility under a transverse Gaussian-type waveform for different frequencies follows the same scaling law in terms of the ratio of the electric field to the rf repetition rate.

Resolving multi-dimensional plasma phenomena in Hall thrusters using the reduced-order particle-in-cell scheme

Plasma in Hall thrusters exhibits a complex behavior, characterized by the interplay between various dominant processes in each of the thruster’s coordinates. The emergence of high-power Hall thrusters in the recent years and the design modifications intended to extend the lifetime of these devices have further amplified the three-dimensional nature of the plasma behavior. In this regard, the novel reduced-order particle-in-cell (PIC) scheme provides the possibility to resolve the multi-dimensional interactions in a Hall thruster at a computational cost up to two orders of magnitude lower than current multi-dimensional PIC simulations. To demonstrate this point, we present in this article the results from a series of pseudo-two-dimensional simulations we performed in three configurations: axial-azimuthal, azimuthal-radial, and axial-radial. We show that, in each configuration, the pseudo-2D PIC scheme provides a significantly improved picture of the involved physics compared to a one-dimensional PIC simulation and captures self-consistently the coupling between the plasma processes in different directions, notably similar to the observations from full-2D kinetic simulations.