Search

VPIC is a general purpose particle-in-cell simulation code for modeling plasma phenomena such as magnetic reconnection, fusion, solar weather, and laser-plasma interaction in three dimensions using large numbers of particles. VPIC's capacity in both fidelity and scale makes it particularly well-suited for plasma research on pre-exascale and exascale platforms. In this article, we demonstrate the unique challenges involved in preparing the VPIC code for operation at exascale, outlining important optimizations to make VPIC efficient on accelerators. Specifically, we show the work undertaken in adapting VPIC to exploit the portability-enabling framework Kokkos and highlight the enhancements to VPIC's modeling capabilities to achieve performance at exascale. We assess the achieved performance-portability trade-off through a suite of studies on nine different varieties of modern pre-exascale hardware. Our performance-portability study includes weak-scaling runs on three of the top ten TOP500 supercomputers, as well as a comparison of low-level system performance of hardware from four different vendors.

Particle-in-cell (PIC) simulations of a microwave oven free-running 2.45 GHz “cooker” ten-vane magnetron operating with a “cold” explosive-emission cathode in a uniform axial magnetic field are performed with two computer codes, improved concurrent electromagnetic PIC (ICEPIC), and CST Particle Studio (CST-PS). PIC simulations are done to compare results obtained by these two codes to each other and, in such a way, identify all possible advantages and disadvantages of each code performance as a reliable tool allowing to predict all important characteristics of the magnetron operation. Results of the PIC simulations show that the range of applied voltages within which the magnetron is able to operate in the $\pi $ -mode at an external uniform axial magnetic field 0.19 T is much broader as it is predicted by the CST-PS code, from 4.00 to 4.70 kV, than as it predicted by the ICEPIC code, from 3.90 to 4.10 kV. It is also shown that while the magnetron startup time gradually decreases, as it is predicted by the ICEPIC code, from about 700 ns (3.90 kV) to about 100 ns (4.20 kV) with the applied voltage increase, it initially chaotically varies, as it is predicted by the CST-PS code, between about 1000 ns (4.03 kV) and about 300 ns (4.01 kV) and only then gradually decreases down to 10–20 ns (4.40–4.60 kV) with the applied voltage increase. Additional PIC simulation with MAGIC or VORPAL codes would be interesting to perform as well to compare the obtained with these codes simulation results with results described in this article.

This article presents the derivation of semianalytic solutions to a new 1-D photoelectron sheath model near the lunar surface. The plasma species include the cold solar wind protons, drifting Maxwellian solar wind electrons, and Maxwellian photoelectrons emitted from the surface. The semianalytic model is then numerically solved to obtain profiles of quantities of interest as functions of the vertical distance from the surface. A fully-kinetic 3-D finite-difference (FD) particle-in-cell (PIC) code is then utilized to simulate the 1-D photoelectron sheath and the results agree well with the numerical solution to the semianalytic model. A $\kappa $ -distribution for solar wind electrons is also implemented to the FD-PIC code to compare with the Maxwellian distribution. Results show that photoelectron sheath may reach as high as close to 100 m above the illuminated flat lunar surface near the terminator region and up to about 50 m near the equator region. Our results show that under average solar wind condition, the photoelectron sheath profiles obtained with Maxwellian and $\kappa $ -distribution (with $\kappa = 4.5$ ) are very close for 1-D numerical results.

Theory and simulations predict the metamaterial-enhanced resistive wall amplifier (MERWA) may offer improvements to megawatt-level high-power microwave (HPM) amplifiers in terms of combined bandwidth and gain rates. A low-power proof-of-concept test prototype has been designed using a metamaterial (MTM) consisting of a linear array of periodically spaced thin lossy meandered wires. Direct simulations of these arrays of thin meandering wires using typical 3-D particle-in-cell (PIC) solvers are inaccurate, creating significant challenges for obtaining trustworthy hot test simulations of the prototype device. This work enables predictive PIC simulations of the experimental MERWA prototype by replacing the thin lossy wire structure with an equivalent effective-medium model. We find that a finite-width rod having an anisotropic Drude–Lorentz permittivity is a suitable model to replace the lossy wire MTM structure. We detail our modeling process and assumptions, fitting procedures, and model fitting results. The model is validated by comparing PIC simulations to experimental results.

Kinetic particle-in-cell (PIC) method is a reliable technique for the laser–plasma interactions simulation based on particles’ statistical behavior. This method can be applied in simulating physical phenomena involved in optical diagnostics tools, such as the interferometry-polarimetry (IP) system. IP is one of the significant laser diagnostic methods suggested in the large tokamaks, such as international thermonuclear experimental reactor (ITER), as to improve the accuracy of density and magnetic field measurements. In this article, two separate simulations of the poloidal IP system are run by applying a 2-D/3-V XOOPIC code to observe the phase-shift and Faraday effect in a magnetized plasma with input density and poloidal magnetic field of ${n}_{e} =3.00\times 10^{19}\,\,\mathrm {m}^{-3}$ and ${B}_{p}=1.00$ T, respectively. For this purpose, a gaseous $\mathrm {(CO}_{2})$ linear-polarized far-infrared laser beam of $\boldsymbol {\lambda }_{i}=118\,\,\mu \text{m}$ wavelength, and about ${30}~{\text {W}}/ {\text {m}}^{2}$ intensity is passed through the plasma, parallel to the magnetic field. The density and poloidal magnetic field are computed from laser phase-shift and Faraday rotation theories, at ${n}_{e,\text {com}}=2.99\times {10}^{19}\,\,\text {m}^{-3}$ and ${B}_{p,\text {com}}=0.99$ T, which correspond to the input values of these simulations. The obtained results indicate the competence and potency of the PIC method in simulating role-playing phenomena in ITER diagnostic devices like the IP system.

The influences of parameters on the emission performance of a novel multipacting cathode are numerically investigated by using particle-in-cell (PIC) method in this article, including cathode length, material secondary electron yield (SEY), and the magnitude values of external magnetic field, applied axial and radial electric field. The numerical results demonstrate that the effective way of improving the emission performance of the novel multipacting cathode is synchronously increasing the magnitude values of applied axial electric field, radial electric field, and external magnetic field. Through this way, the output current could be notably increased. Meanwhile, the output electrons are with low energy spread and good emittance.

The proper orthogonal decomposition technique is applied to a finite-element time-domain particle-in-cell (PIC) algorithm for the simulation of kinetic plasmas, resulting in a reduced-order system. The reduced model is tested with representative examples involving an accelerated electron beam and a plasma ball expansion and compared with full-order simulations. The strengths and weakness of this type of model order reduction when applied to PIC algorithms are discussed through the analysis of the results. In particular, the method allows for a major reduction in the field degrees of freedom necessary to capture the relevant physics, but it can also lead to spurious results if proper care is not taken when assembling the reduced-order system.

This paper presents a 3-D, fully kinetic particle-in-cell (PIC) simulation study of plasma charging for small, irregularly shaped, composite asteroids in the solar wind. Three types of asteroid internal structures are considered: 1) a homogeneous composition of regolith; 2) a single hard rock; and 3) a composite of hard rock core covered with a regolith outer layer. The simulation model resolves the plasma flow field, asteroid surface differential charging, and asteroid internal electric field self-consistently. The results show that while the ambient plasma condition and surface property determine surface charging, the internal composition substantially affects the subsurface electric field inside an asteroid.

In this paper, an accurate time-domain model was established to calculate the ion-flow field of ultrahigh-voltage direct current transmission line. First, the influence of corona layer thickness is considered in the model. Second, the ionic-flow field is calculated without using the traditional fluid model in which the mobility is set as a constant but based on the particle-in-cell iterative method, and the migration of charged particles is analyzed which considering different forces in motion. Therefore, the nonlinear migration of the electric charge can be considered by this calculation process, making the model closer to the actual situation. Third, coaxial cylinder model is used to verify this method. Finally, corresponding calculation results of −1100 kV transmission line were obtained by this method, and the impact of wind speed is also studied in this paper.

To overcome the shortcomings of the traditional staircased particle-in-cell (PIC) method, this paper presents the conformal PIC method to simulate the system-generated electromagnetic pulse (SGEMP) produced by the X-ray beam. One advantage of this method is to accurately simulate the electromagnetic response from the boundary of the object, and more importantly, it can be used to simulate the emission direction of the electrons accurately by properly handling the normal direction of the curved boundary. The numerical results show that the conformal PIC method can save much more computation time and memory than the staircased PIC technique to obtain the same accurate computational results.

We combine a novel finite-element-based electromagnetic particle-in-cell (EM-PIC) algorithm for the solution of Maxwell–Vlasov equations on irregular (unstructured) grids together with the Furman–Pivi probabilistic model governing the secondary electron emission process. The algorithm can be used for the analysis of resonant electron discharging phenomena (multipactor effects) in high-power radio frequency devices. In contrast to previous algorithms, the present EM-PIC algorithm yields a self-consistent time update of fields and particles on irregular grids with energy and charge conservation obtained from first principles. The use of unstructured grids enables local mesh refinement and simulation of complex geometries with minimal geometric defeaturing. We apply the algorithm to model multipactor effects on waveguides with flat or corrugated walls. We contrast the evolution of the electron population in various cases and investigate the respective saturation processes arising from self-field counterbalancing effects.

The configuration design of a novel high-current density cathode for producing a ring-like electron beam is briefly introduced. Due to the complicated physical process of this novel cathode, in this paper, only the temporal evolution of multipacting on this cathode surface is numerically simulated by using the particle-in-cell method. The simulation results indicate that the multipacting process could be successfully achieved on the surface of this cathode. In multipacting process, both the electron number and output current start rapid exponential increases in very short time and then tend to be saturation with slow decreases. The multipacting start point is not at the triple-junction (vacuum-metal-dielectric) region but has a distance to the region. The saturation region of multipacting will expand toward the outlet with the spreading speed on the order of 107 m/s, which agrees with the speed of the luminous front of the initial surface flashover measured by experiment, and the emission current density of the cathode could reach the level of kA/cm2. The region of multipacting electrons will first be lengthened and then will be shortened due to the region of deposited positive charges expanding to the outlet and the maximum value of deposited positive charges moving from the triple-junction region to the outlet side.

In this article, we describe a novel implementation of finite-size (super) particles described by polynomial-based spatial shape factors in electromagnetic particle-in-cell (EM-PIC) algorithms for kinetic plasma simulations based on unstructured meshes. The proposed implementation is aimed at mitigating (spurious) numerical Cherenkov radiation effects while preserving exact charge conservation. This is achieved by employing a representation of Maxwell's equations based on the exterior calculus of differential forms and a discretization of twisted differential forms associated with the primal mesh by Whitney forms, while ordinary differential forms are associated with the dual mesh. The set of full-discrete Maxwell's equations is then obtained by using a finite-element Galerkin method and a leap-frog time integration, leading to a mixed D-H finite-element time-domain Maxwell field solver. In the proposed EM-PIC implementation, the gather and scatter steps of the algorithm yield integrals of polynomials over polyhedral domains in 3-D space (or polygonal domains in 2-D space) that can be evaluated analytically. We provide numerical examples confirming charge conservation down to machine precision on an unstructured mesh.

A design for a high-power relativistic inverted magnetron oscillator (IMO) is presented and modeled numerically using the massively parallel electromagnetic particle-in-cell code, improved concurrent electromagnetic particle in cell (ICEPIC). The inverted magnetron presented here is designed to operate in the $L$ -band for magnetic fields ranging from 0.07 to 0.1 T with voltages ranging from ~250 to 480 kV. Simulations in that voltage/magnetic field range demonstrate that the inverted magnetron is capable of fast startup, $\pi $ -mode dominance with little-to-no mode competition, as well as high output power, exceeding 2.5 GW at the high end of voltages examined. End-loss current, a common source of energy loss in relativistic magnetrons, is not present for this IMO design. The IMO radiates RF energy axially through the use of a novel dual-ring radiator that excites the TM01 mode in the downstream waveguide. This approach yields nominal RF output power efficiencies near 20%. ICEPIC simulations predict that the above features combined with the IMO’s stable, robust, and reliable performance in the desired mode over a large voltage range yield a class of high-power microwave source notable for its inverted geometry and T-vane slow-wave structure.

Recent circuit driven electromagnetic particle in cell simulation of the United Nations University-International Centre for Theoretical Physics plasma focus device revealed regular oscillations in both the voltage and current profiles. The simulated voltage waveform agreed well with the experimental profile, where similar unaccounted oscillations were also observed. In this paper, the oscillations are attributed to the plasma inductance, whose value was calculated by circuit analysis and agreed reasonably well with the computed experimental value. A circuit simulation of the prebreakdown and postbreakdown phases, with the plasma inductance incorporated, reproduced with sufficiency accuracy the electromagnetic particle in cell generated waveforms and consequently confirmed our finding.

We have developed a circuit particle-in-cell (PIC) coupled model for simulating a pulsed power system, based on a circuit algorithm of a pulsed power supply and a PIC simulation for a magnetically insulated transmission line (MITL) system. The coupled algorithm comprises an external circuit algorithm based on BERTHA and a coupled algorithm for the PIC and circuit interface based on the Mur absorbing boundary condition. In this paper, a simple coaxial MITL with a single linear transformer driver (LTD) was simulated to validate the coupled model compared with PSPICE and BERTHA simulations. The numerical results show that the circuit–PIC coupled model achieved almost the same outputs on the load. The coupled model was then applied to an MITL system driven by ten LTD cavities. The simulation results and experimental results were in agreement, which confirms that the circuit–PIC coupled model could provide a reference for the structural design of experimental apparatuses.

We performed the 2-D particle-in-cell simulation of the laser wakefield in an inhomogeneous plasma to study the dependence of the speed of the wakes to the electron density of the background plasma to search the condition of “accelerating flying mirror”. Acceleration of the plasma wakes is not observed in the simulations with the parameters that we have tested.

The simulation of unbounded domains inevitably requires an artificial truncation of the computational domain and spurious reflections resulting from this procedure are a common problem. In this paper, a perfectly matched layer formulation for Maxwell’s equations in purely hyperbolic form is presented. The model is applied to standard wave attenuation problems and particle-in-cell simulations of electron beam devices.

The number of macroparticles increases dramatically during the particle-in-cell (PIC) simulations of an electron avalanche in high-pressure gas discharges, which always leads to a collapse of simulations. The use of macroparticle coalescing models dynamically decreases the number of macroparticles, but introduces computational errors destructing the conservations of momentum, kinetic energy, and phase-space distribution of the macroparticles. Two new macroparticle coalescing models for 3-D PIC simulations, namely, 2-to-1 and 4-to-2 models, are developed and presented here. Both the models classify macroparticles into eight groups in the velocity space and sort them separately according to the magnitude of the three velocity components. Numerical simulations show that the 4-to-2 model not only conserves the phase-space distribution of the macroparticles but also keeps the deviations of their momentum and kinetic energy at a very low level. The deviations even reduce when the total number of precoalesced macroparticles increases.

The metamaterial-enhanced resistive wall amplifier (ME-RWA) has been shown to be capable of producing large gains over wide bandwidths. Previous theoretical investigation of the ME-RWA focused on an idealized case using a homogenous dielectric with Drude dispersion to provide the negative permittivity required to achieve high gains. This paper reports the results of investigating practical metamaterial implementations with approximate Drude-type responses that enable the realization of a ME-RWA. Using these metamaterials, an architecture for a ME-RWA using periodically spaced inductive meandered lines is proposed. Our theoretical analyses and particle in cell simulations of this device predict that the proposed technique provides a practical method of implementing ME-RWAs, capable of providing a large gain over a substantial bandwidth.

The objective of this paper is to report findings based on the particle-in-cell (PIC) modeling of the axial and coaxial virtual cathode oscillators in order to validate the experiments already performed on these devices over the years. In addition to this, observations regarding validation and similarities between the simulations and the experiments have been reported, with an emphasis on analysis of device parameters such as e-beam voltage, current density, and microwave power. Theoretical aspects of a virtual cathode oscillator (vircator) and some of the key experimental works have been revisited. Investigation is done on the power generated in a coaxial vircator, and various cavity modifications have been tested for the coaxial vircator using the MAGIC3D, PIC tools suite, in order to search for improvement in the device efficiencies. Also, the axial vircator has been modeled to comment on the particle energies, device design, and beam quality associated with it.

A new method called tetrahedral fluid method is presented in this paper. It is developed based on the fluid behavior of plasmas, unlike particle-based models, such as particle in cell; this method serves the continuity of the charge regions. The modeling of a moving plasma is performed by a fluid segmentation, in which the interaction with plasma fields is treated by the finite-difference time-domain numerical technique. The development of the relation between two field and fluid lattices has been described. The important part of this relation is the determination of the common volumes in the two lattices. A comparison is made between the results obtained by this method and those using the nearest grid point method, which shows the increased accuracy and speed of the proposed technique in a sample problem.

We present a particle-in-cell (PIC) method using a nonhomogeneous immersed-finite-element (IFE) field solver for modeling dielectric surface charging of complex-shaped objects in plasmas. The IFE solver allows PIC codes using a Cartesian mesh applied to simulations involving arbitrarily shaped objects with a similar accuracy as that using a body-fitting mesh. The object surface is treated as an interface. Surface charging is calculated directly from charge deposition at the interface, and the electrostatic fields on both sides of the interface are resolved self-consistently. The capability of the nonhomogeneous IFE-PIC method is demonstrated by a simulation study of the charging of an irregular-shaped asteroid in the solar wind.

1-D particle-in-cell simulations are used to investigate the propagation and decomposition of the ion acoustic solitary waves (IASWs) in plasmas. Our results show that for small-amplitude conditions, IASWs are stable and the simulation results are consistent with the theoretical predictions of the reductive perturbation method. As the amplitudes of IASWs increase, the waves become unstable and trains of oscillating waves are emitted behind the main waves. When the amplitude is large enough, the wave cannot exist and will decay into a series of waves with a small amplitude. By comparing our simulations with the theoretical solutions of Kortewag–de Vries soliton, the upper limitation of the amplitude of IASWs in plasmas is found. Moreover, our results show that although the reductive perturbation method is valid only for small perturbations, the application scope of the reductive perturbation method can be expanded to describe the potential profiles of IASWs with any amplitude. Meanwhile, the application scope for the density profiles is still limited in the perturbation cases.

Conformal (or body-fitted) electromagnetic particle-in-cell (EM-PIC) numerical solution schemes are reviewed. Included is a chronological history of relevant particle physics algorithms often employed in these conformal simulations. Brief mathematical descriptions of particle-tracking algorithms and current weighting schemes are provided, along with a brief summary of major time-dependent electromagnetic solution methods. Several research areas are also highlighted for recommended future development of new conformal EM-PIC methods.

The behavior of a six-vane relativistic magnetron with a single radial output slot has been studied in detail by 3-D particle in cell simulations. It is found that a delicate power imbalance caused by the pulsed-power generator and magnetron impedance mismatch is responsible for the shortening of the radiated power pulse. Pulse shortening can be avoided completely, and the radiated power can be considerably increased by decreasing the emitted current when it is too large to be sustainable. When the magnetron current is too high, the voltage decreases, which causes the radiated power to drop and shortens the pulse. This relatively simple electrical power balance is the result of intricate dynamics involving the electron flow within the magnetron, out of the interaction cavity through the axial flow and the electromagnetic modes supported by the structure.

The resistive wall amplifier (RWA), a vacuum electron device, has been theoretically predicted to provide extremely high gain. However, the properties of practical, naturally available bulk materials for the resistive wall support structure significantly reduce achievable gain. This paper investigates the capabilities of a metamaterial-enhanced RWA (ME-RWA). We predict that using epsilon-negative metamaterials can yield high gains that closely approach the idealized performance limit. ME-RWAs may exhibit bandwidths and gains much higher than many commercially available vacuum electron devices.

An electrostatic particle-in-cell simulation code is developed to investigate the interaction between plasma and material surfaces in the presence of secondary electron emission. Kinetic ions are included into the numerical simulation to incorporate the process of ion bombardment on the material surfaces. The influences of the secondary electron emission on sheath dynamics are further investigated, which is induced by ions on top of electrons.

This paper evaluates the performance and reliability of a commercially available 3-D conformal finite-difference time-domain particle-in-cell (PIC) code, VSim, for cold test simulations of a gyrotron cavity. An interaction cavity for a 95-GHz gyrotron is simulated and optimized using the VSim PIC code to achieve TE6,2 mode excitation. The optimized cavity design is also studied and compared using the commercially available numerical code, CASCADE, and PIC code, MAGIC. A rigorous analysis of the simulation results obtained through VSim and MAGIC is performed using the CASCADE results as a reference. The performance of VSim is also compared with MAGIC based on its accuracy for calculating the resonant frequency and quality factor. Finally, the optimized cavity is fabricated and experimentally tested to measure the resonant frequency and the quality factor. The experimental results confirm the reliability and accuracy of the VSim cold cavity results.

A parallelized particle-in-cell (PIC) simulation and direct simulation of Monte Carlo (DSMC) are combined to simulate low-pressure discharges. A two-dimensional (2-D) PIC simulation parallelized with graphics processing units is used to examine the discharge characteristics of a capacitively coupled plasma device at pressures

This paper presents electromagnetic and particle-in-cell (PIC) simulation studies of ring strapped vane resonator of a 2.45 GHz 1-kW magnetron using Computer Simulation technology microwave studio and MAGIC-3-D. The aim was to gain design understanding through the analysis of constituent parts of the resonant system and to deduce results having significant engineering value. The electromagnetic analysis includes modeling the effect of the end-gap length, the straps, the coupling antenna, and the surface roughness of cavity wall on resonant frequency. It was found that a clearance of 4 mm and beyond between cavity resonator and end plate have negligible effect on resonance frequency. Straps influence the resonant frequency of the \(\pi \) mode maximum, and can be used to control and fine tune the resonant frequency of the desired \(\pi \) mode. A surface roughness of 1 \(\mu \) m or more affects the unloaded \(Q\) of the resonator cavity adversely. Coupling antenna height is found to play an important role to achieve desired \(Q_{l}\) and \(Q_{\rm ext}\) for the segment loaded axial extraction of power. The PIC simulation study predicted that the hot resonant frequency differ from cold resonant frequency by \(\sim 9\) MHz. The computed frequency, power, and efficiency were found to be 2.462 GHz, 1.3 kW, and 70%, respectively.

To study the nonlinear beam-wave interaction for sheet beam klystron (SBK), a 2-D simulation code of SBK2D, based on the 2-D rod macroparticle model, has been designed and realized thoroughly in this paper. In our physical model, the sheet beam is simulated by a series of rods with nonzero thickness and length in \(y\) and \(z\) directions, respectively ( \(y\) is the direction of sheet beam’s narrow dimension, and \(z\) is the direction of beam motion). Then, the space-charge forces between the rod macroparticles are calculated by Green’s functions approach, and the port-approximation methods are employed to simulate high-frequency fields for each cavity. Furthermore, the relativistic Lorentz motion equation is solved to obtain the parameters for further macroparticle motion, and the specific criterions are introduced to deal with the sheet beam interception problem by the tunnel and cavities. To verify our simulation code, an eight-cavity W-band SBK has been designed, calculated, and analyzed by SBK2D in detail. The good consistency between SBK2D and 3-dimensional Particle in Cell (3-D PIC) program indicates the reliability of the physical model and simulation code for our program. In addition, the calculation time of SBK2D is only about 1% of that of the 3-D PIC, which makes it more feasible and efficient to calculate and optimize the initial physical parameters for the design of complicated SBK.

Time-domain modeling of vacuum tubes is important for theoretical analysis of spurious oscillation, amplification and generation of short pulses and complex multifrequency, or chaotic signals. In this paper, a time-domain model of a klystron delayed feedback oscillator is presented. The model is based on the nonstationary Vainshtein theory of cavity excitation and the 1-D particle-in-cell method for simulation of electron beam dynamics. The results of simulation are presented for an S-band four-cavity klystron with delayed feedback, as well as for a miniaturized sub-terahertz reflex klystron. The developed code allows sufficiently fast and accurate calculation of output characteristics of klystron-type oscillators.

Particle-in-cell (PIC) methods first made it feasible to simulate plasmas and microwave devices in two dimensions on 1960s computers. In this approach, the electromagnetic interactions between charged particles are mediated by a spatial mesh, on which currents and field are defined. The dominance of long-range forces in weakly coupled plasma means that the mesh and time-step do not have to resolve nearest neighbor interactions. Advances in algorithms and parallel computers have greatly expanded the applicability of PIC. We review this evolution, with particular emphasis on the contributions of Prof. Ned Birdsall and those he influenced.

The Warp code (and its framework of associated tools) was initially developed for particle-in-cell simulations of space-charge-dominated ion beams in accelerators, for heavy-ion-driven inertial fusion energy, and related experiments. It has found a broad range of applications, including nonneutral plasmas in traps, stray electron clouds in accelerators, laser-based acceleration, and the focusing of ion beams produced when short-pulse lasers irradiate foil targets. We summarize novel methods used in Warp, including: time-stepping conducive to diagnosis and particle injection; an interactive Python-Fortran-C structure that enables scripted and interactive user steering of runs; a variety of geometries (3-D $x$ , $y$ , $z$ ; 2-D $r$ , $z$ ; 2-D $x$ , $y$ ); electrostatic and electromagnetic field solvers; a cut-cell representation for internal boundaries; the use of warped coordinates for bent beam lines; adaptive mesh refinement, including a capability for time-dependent space-charge-limited flow from curved surfaces; models for accelerator lattice elements (magnetic or electrostatic quadrupole lenses, accelerating gaps, etc.) at user-selectable levels of detail; models for particle interactions with gas and walls; moment/envelope models that support sophisticated particle loading; a drift-Lorentz mover for rapid tracking through regions of strong and weak magnetic field; a Lorentz-boosted frame formulation with a Lorentz-invariant modification of the Boris mover; an electromagnetic solver with tunable dispersion and stride-based digital filtering; and a pseudospectral electromagnetic solver. Warp has proven useful for a wide range of applications, described very briefly herein. It is available as an open-source code under a BSD license. This paper describes material presented during the Prof. Charles K. (Ned) Birdsall Memorial Session of the 2013 IEEE Pulsed Power and Plasma Science Conference. In addition to our overview of the computational methods used in Warp, we summarize a few aspects of Ned's contributions to plasma simulation and to the careers of those he mentored.

In this paper, a multigap extended output cavity was designed by 3-D simulations, which served as the output cavity for a W-band sheet-beam extended interaction klystron (SBEIK). In our numerical design, the circuit dimensions were systematically optimized by parametric finite-difference time-domain simulations, and the equivalent circuit for the output cavity was also analyzed. The proper external loading was selected by using a region of loss in 3-D, and the output power was optimized. The results were verified by using the coupler and the waveguide. The 2π mode of the optimized five-gap extended output cavities had an ohmic Q (Q0) of 1343.5, an external Q (Qe) of 501.6, and a loaded Q (QL) of 365.2 at 94.5 GHz. The 3-D particle-in-cell simulations predict that the output cavity of the SBEIK (75 kV and 4 A) can stably produce more than 50 kW of output power using a prebunched beam.

The radiation enhancement of a relativistic backward-wave oscillator (RBWO) driven by two annular electron beams is demonstrated in this paper. The slow-wave structure of RBWO is composed of a cylindrical grating with rectangular corrugation. The concentric electron beams are maintained with a velocity difference to initiate two-stream instability (TSI). The dispersion equations of the RBWO are derived and solved numerically for the growth rate of microwave signal. Compared with the single beam device, an enhancement in the growth rate is observed for the two beam case and that is attributed by the TSI. This theoretical observation is verified by 2-D particle in cell simulation and experiment. The experimental results show that the output power of 150 MW for a signal-beam device is enhanced to 200 MW for the two beam case and duration of microwave pulse is also enlarged from 10.6 to 16.8 ns. The efficiency of the devices is ~ 6%.

The particle-in-cell (PIC) algorithm for the simulation of charged-particle kinetics in plasmas is a very resource consuming method, and high-performance parallel computing is required for practical problems. Graphics processing units (GPUs) are powerful low-cost parallel systems that can be used for intensive computations. We have developed a PIC Monte Carlo collision (MCC) model of a low temperature magnetized plasma using GPUs. We describe how each part of the PIC MCC model is implemented on the GPU and show how particles are dynamically managed. The computational cost of the PIC MCC model on the GPU is compared with a standard PIC MCC model running on a single central processing unit (CPU). We show that speedup can reach from 10 to 20 times compared with a sequential code running on a CPU, depending on the number of cells and particles considered. The results are illustrated with the example of plasma transport across a magnetic filter similar to that of a negative-ion source for the neutral beam injector of fusion devices.

A 16-vane millimeter-wave spatial-harmonic magnetron (SHM) with a cold secondary emission cathode is examined by the use of a 3-D particle-in-cell (PIC) code embedded in CST Particle Studio. Simulations of the SHM are performed without artificial RF priming and without assuming restrictive assumptions on the mode of operation or on the number of harmonics to be considered. Thus, in our simulations, the electromagnetic oscillations grow naturally from noise. Time-evolved space-charge simulations and gradual formation of a single-frequency RF oscillation are presented. Examination of space-charge profiles at saturation time reveals the presence of two different space-charge distributions that depend on the amount of primary emission current. This current is employed to model a bombarding current, which is used to initialize the cold cathode. It is shown that a small primary emission density results in nonperiodic distribution of space charge at saturation time, which is in accordance with the previously reported space-charge distribution in SHMs. The simulated current, power, and efficiency indicate good correlation with the experimental results.

Recently, we have reported a microwave plasma jet at atmosphere in argon, capable of generating filamentary streamer discharges within the entire quartz tube, while several bifurcations yield at the end of the copper wire immediately in the quartz tube when incident power reaches 20 W. However, the ionization process for the discharges is still not very well clarified. This paper shows a numerical study of the proposed plasma jet by means of the 2D3V particle in cell with Monte Carlo collision method. The detailed information about the distributions of plasmas and electromagnetic fields is obtained by sampling the simulated results at different time steps. The simulation results suggest that the production of the proposed plasma jet is attributed to the seed plasmas triggered by the enhanced electric field of surface plasmon polaritons and its interaction with plasmas.

A 3-D particle-in-cell (PIC) code MAGIC 3-D has been used to examine the output performance of a relativistic magnetron operating under the effect of electric priming by protrusions and recessions on the inner surface of the anode vanes. Electric priming has been implemented and demonstrated using the PIC code for electron prebunching in A6 relativistic magnetron. When N-fold perturbation of the radial electric field is imposed in the azimuthal direction along anode-vane inner surfaces, the electron initially develops into the desired 2π-mode, resulting in fast oscillation startup. The startup time is reduced by 46%, the output power is increased by 30%, and the efficiency is increased by 30% for three protrusions alternating with three recessions along the anode-vane inner surfaces in comparison with the A6 basic model. Simulations have been also carried out for different combinations of protrusions and recessions. All the studies have been carried out for 2π -mode of operation.

This paper discusses simulation and modeling of the slow wave structure of a folded-waveguide terahertz traveling wave tube (TWT) using the Improved Concurrent Electromagnetic Particle In Cell (ICEPIC) software. This is the first time ICEPIC has been used for simulation of a TWT amplifier. Cold test simulations compare favorably with analytical models; at 368 GHz, the on-axis interaction impedance is 7.8 $\Omega$. Hot test (beam included) ICEPIC simulations were used to determine the effects of space charge on the gain calculations. At 368 GHz, the normalized beam plasma frequency from ICEPIC simulations is ${\mit\Omega}{p}=0.56$. Analysis of our ICEPIC simulations at 368 GHz indicates a normalized beam plasma frequency 75% larger than an analytical model we improvised from a sheath helix model taken from the literature. The hot test ICEPIC simulations at 368 GHz for a 64 periods long slow wave structure and a 10 mA, 25 kV electron beam produce small signal gain of 27 dB. The small-signal fractional 3-dB bandwidth of the TWT is 2.9%. The saturated fractional 3-dB bandwidth is 3.2%. Large signal simulations indicate that the saturated power at 368 GHz is 39.4 dBm and the saturated gain is 21.8 dB. A snapshot of a cross section of the electron beam shows bunching in space and a corresponding modulation in the velocity of the electron beam. © 2011 IEEE.

A model is presented to numerically simulate the time-dependent interaction of satellites with space plasma. The approach is based on a fully kinetic description of the plasma using particle in cell modeling for all plasma species with physical charges and masses. The model also relies on a discretization of space with an unstructured tetrahedral mesh that is capable of representing complex boundaries and realistic spacecraft geometries. The code solves for the self-consistent electric fields, given calculated volume charges and charge deposition on the various satellite components. The model is purely electrostatic, but it does account for the effects of a possible constant and uniform background magnetic field.

An electrometer circuit is designed and developed to measure the ion-space charge created during HVDC corona events. The interpretation of the electrometer output and visualization of various discharge processes are facilitated by a particle-in-cell computational code. The time it takes for the space charge to be created during a single monopolar corona event to reach the ground electrode in a corona test method is computed for a small corona cage, a short test line, as well as a large corona cage. This complements results obtained by the authors in another paper where it is shown that a small corona test cage cannot be used to predict the RI performance of HVDC conductors due to the space charge buildup in the small electrode gap.

The folded-waveguide slow-wave structure (SWS) is a robust beam-wave interaction circuit for millimeter-wave traveling-wave tubes. We applied a particle-in-cell solver (Computer Simulation Technology Particle Studio) to analyze and optimize a 220-GHz folded-waveguide SWS. The beam-wave interaction and the electron beam dynamics were studied based on simulation results. The influence of the beam tunnel, with respect to its transverse shape and size, on the circuit performance was investigated in detail. A beam tunnel with a square cross section exhibits lower gain and efficiency and similar bandwidth compared with a beam tunnel with a circular cross section. With a proper phase-velocity taper employed in the nonlinear region of the circuit, the small-signal gain, peak saturated output power, and efficiency were significantly improved, increasing from 21.5 to 27.8 dB, 41 to 70.5 W, and 4.5% to 8%, respectively, for a 36-mm-long loss-free circuit. A simulated 3-dB bandwidth of ~ 15 GHz is demonstrated.

Accepted: 2010-11-27, 資料番号: SA1003250000

Plasma structure and electron ring formation in a magnetic mirror trap under electron cyclotron resonance (ECR) conditions is studied numerically through a simulation of the Newton-Lorentz equation by a particle-in-cell method. The plasma self-generated electric field is calculated through a numerical solution of the Poisson equation with the help of the fast Fourier transform technique. The zone where the ECR conditions are fulfilled is almost of a one-sheet hyperboloid shape. It is shown that in the middle transversal plane of the trap, a stable gyrating electron ring is formed. Some trajectories of the hot and superhot electrons comprising the ring are visualized.

The relativistic dynamics of an electron beam which is accelerated by a circular polarized standing electromagnetic wave in an axisymmetric steady-state magnetic field under cyclotron-resonance conditions is studied. The profile of the inhomogeneous magnetic field is chosen such as to maintain the beam electrons in the space cyclotron autoresonance regime. The influence of the self-consistent field under space-autoresonance conditions is simulated by using the particle-in-cell method. The electric potential produced by electron beams on each time step is found by solving the Poisson equation under the Dirichlet boundary conditions through the fast Fourier transform technique. The axisymmetric magnetic field and the self-consistent electric field are found in the particle positions through bilinear and trilinear interpolations of the mesh node data, which are extensions of the linear interpolation to dimensions D = 2 and D = 3. The beam trajectory and its energy evolution are obtained by solving the relativistic Newton-Lorentz equation employing the Boris leapfrog procedure. The 6-kV/cm TE112 microwave mode of 2.45-GHz frequency is used for the numerical simulations. It is shown that an electron beam of an initial longitudinal energy of 10 keV injected into the axisymmetric magnetic field is found in the resonance phase band, and it is accelerated up to an energy of 0.2 MeV. The main purpose of this paper is to determine the optimum parameters for an electron beam acceleration via the spatial autoresonance mechanism using a numerical modeling.

The Monte Carlo collision (MCC) model is widely adopted to simulate discharge plasmas using the particle-in-cell (PIC) method; however, it has low efficiency in high-pressure plasmas because of the small time steps required due to the constraint of high collision frequency. To relax this time step constraint, a compensated Monte Carlo collision model (CMCC) is proposed which considers multiple collisions in a time step as a series of single collisions to compensate for the neglected collisions. The electron motion in a high-pressure He gas for various reduced electric fields E/N and the streamer formation process in a laser-triggered spark gap were simulated using the CMCC model. Simulation results showed that the CMCC model with long time step obtained reasonable electron velocity distribution, temperature, drift velocity, plasma density, and space-charge field. It was demonstrated that the CMCC model had high accuracy and high efficiency, particularly for PIC simulation in high-pressure plasmas.

In order to efficiently study the complex nonlinear beam-wave interaction in high-power klystrons, we have developed a 2.5-D code, named, KLY2D, based on a theoretical model combining particle-in-cell (PIC) method and finite-difference time-domain (FDTD) algorithm together. In the model, the particle charge and the beam current are properly assigned onto the grids based on the PIC method; the FDTD algorithm is introduced to solve Maxwell's equations so that the space charge of the electron beam can be accurately calculated, and the port-approximation method is employed to simulate high-frequency cavity fields; finally, the Lorentz motion equation is solved to further advance particle motion. This 2.5-D model is more accurate than the simple 1-D nonlinear code. For the cylindrical structure of a normal klystron, the port-approximation cavity model is accurate enough to model field-to-beam effect and saves much more computer resource than the full 3-D PIC model. This code is benchmarked on an S-band 50-MW high-peak-power klystron. The good consistency between the theoretical results and the experimental data indicates the reliability of the theoretical model and the simulation code, which is of importance for further promoting the design and the development of high-power klystrons.