Particle-in-cell Research Articles

GW-Level Ku-Band Compact Coaxial TTO With Permanent Magnet Packaging Potential

When the O-type high-power microwave (HPM) sources are extended to the high band, the current density of the intense relativistic electron beam will increase, which requires a higher intensity of the guiding magnetic field. The coil of the excitation system will be bulkier, which is not conducive to the development of the device toward the direction of light and small. The transit time oscillator (TTO) has attracted much attention due to its ability to output GW-level HPMs in the small number of cavities. In order to replace solenoid with permanent magnet, the compact coaxial TTO with a low magnetic field is designed in this article. The coaxial structure reduces the need for magnetic field strength. In addition, the familiar reflector is removed and the axial size of the beam-wave interaction region is reduced, which not only reduces the risk of electron beam diffusion under low magnetic field, but helps to reduce the weight of permanent magnets in the future. In particle-in-cell (PIC) simulation, the proposed coaxial TTO can output more than HPMs of 1.0 GW under the magnetic field less than 0.4 T with the efficiency is over 30%. Therefore, it is feasible to use permanent magnet packaging for the device.

Diagnosis of fast electron transport by coherent transition radiation

Transport of fast electrons in overdense plasmas is of key importance in high energy density physics. However, it is challenging to diagnose the fast electron transport in experiments. In this article, we study coherent transition radiation (CTR) generated by fast electrons on the back surface of the target by using 2D and 3D first-principle particle-in-cell (PIC) simulations. In our simulations, aluminum targets of 2.7 g cc−1 are simulated in two different situations by using a newly developed high order implicit PIC code. Comparing realistic simulations containing collision and ionization effects, artificial simulations without taking collision and ionization effects into account significantly underestimate the energy loss of electron beams when transporting in the target, which fail to describe the complete characteristics of CTR produced by electron beams on the back surface of the target. Realistic simulations indicate the diameter of CTR increases when the thickness of the target is increased. This is attributed to synergetic energy losses of high flux fast electrons due to Ohm heating and colliding drags, which appear quite significant even when the thickness of the solid target only differs by micrometers. Especially, when the diagnosing position is fixed, we find that the intensity distribution of the CTR is also a function of time, with the diameter increased with time. As the diameter of CTR is related to the speed of electrons passing through the back surface of the target, our finding may be used as a new tool to diagnose the electron energy spectra near the surface of solid density plasmas.

Ion effects on the scaling of magnetic field amplification in plasmas with the system size

Magnetic field amplification during the nonlinear stage of the current filamentation instability excited by ultra-relativistic electron beams is investigated with a two-dimensional electromagnetic particle-in-cell (PIC) simulation code, with special attention paid to the effects of plasma ions and the system size. The effect of plasma ions is shown to be significant and enhanced magnetic field amplification and beam energy deposition are found due to plasma cavity expansion and merger. When the system size in the transverse direction (perpendicular to the beam propagation direction) is enlarged by a factor of m, the transverse magnetic field energy is found to increase by a factor of m 2 in the case of the plasma with movable ions, in contrast to m with immovable ions. The results are also confirmed by three-dimensional PIC simulations.

Efficient parallelization for 3D-3V sparse grid Particle-In-Cell: Single GPU architectures

In the present paper, an efficient General Purpose Graphical Processing Unit (GPGPU)-based implementation of sparse grid Particle-In-Cell (PIC) methods is proposed. The parallelization, implementing novel strategies specific to sparse-PIC methods and tailored to GPU architectures, provides speed-ups1 as large as 100 on a single Tesla V100 GPU, with respect to sequential Computing Processing unit (CPU) execution; and a four order of magnitude reduction of the computational time in comparison with a standard PIC sequential CPU simulation. In addition, the simple implementation of the parallelization with the OpenACC framework offers portability to a large class of accelerators.

Electrode plasma formation and melt in Z -pinch accelerators

Recent studies of power flow and particle transport in multi-MA pulsed-power accelerators demonstrate that electrode plasmas may reduce accelerator efficiency by shunting current upstream from the load [Bennett et al., Phys. Rev. Accel. Beams 24, 060401 (2021)]. The detailed generation and evolution of these electrode plasmas are examined here using fully relativistic, Monte Carlo particle-in-cell (PIC) and magnetohydrodynamic (MHD) simulations over a range of peak currents (8--48 MA). The PIC calculations, informed by vacuum science, describe the electrode surface breakdown and particle transport prior to electrode melt. The MHD calculations show the bulk electrode evolution during melt. The physical description provided by this combined study begins with the rising local magnetic field that increases the local electrode surface temperature. This initiates the thermal desorption of contaminants from the electrode surface, with contributions from atoms outgassing from the bulk metal. The contaminants rapidly ionize forming a ${10}^{15}--{10}^{18}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}3}$ plasma that is effectively resistive while weakly collisional because it is created within, and rapidly penetrated by, a strong magnetic field ($>30\text{ }\text{ }\mathrm{T}$). Prior to melting, the density of this surface plasma is limited by the concentration of absorbed contaminants in the bulk ($\ensuremath{\sim}{10}^{19}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}3}$ for hydrogen), its diffusion, and ionization. Eventually, the melting electrodes form a conducting plasma (${10}^{21}--{10}^{23}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}3}$) that experiences $\mathbf{j}\ifmmode\times\else\texttimes\fi{}\mathbf{B}$ compression and a typical decaying magnetic diffusion profile. This physical sequence ignores the transport of collisional plasmas of ${10}^{19}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}3}$ which may arise from electrode defects and associated instabilities. Nonetheless, this picture of plasma formation and melt may be extrapolated to higher-energy pulsed-power systems.

Suppression of stimulated Raman scattering in plasma by an ultra-wideband stochastic phase low-coherence laser

Suppression of the stimulated Raman scattering (SRS) by a stochastic phase low-coherence laser (SPLL) in homogeneous plasma is investigated by theoretical analysis and one-dimensional particle-in-cell (PIC) simulation. A simple model is established, in which the SPLL is modelled as a combination of a monochromatic laser and a broadband laser. When the phase randomness increases, the bandwidth of the SPLL is broadened and the energy proportion of the monochromatic laser component is reduced. PIC simulation shows that the SPLL can effectively suppress SRS and hot electron generation. Various phenomena in the nonlinear process, such as the nonlinear frequency shift and the competition between forward-scattering and back-scattering modes, are explained in detail.

An elliptical beam-tunnel sine waveguide slow wave structure for G-band elliptical beam traveling wave tube

In order to improve the performance of sine waveguide (SW) traveling wave tube (TWT), an elliptical beam-tunnel sine waveguide (EBTSW) slow wave structure (SWS) is proposed. EBTSW-SWS not only has high interaction impedance in a relatively wide frequency band but also has an elliptical beam-tunnel. The simulation results of high-frequency characteristics show that, under the same dispersion, the passband of EBTSW-SWS increases by 30% compared to the SW-SWS, and the average interaction impedance of EBTSW-SWS is higher than that of SW-SWS in almost the whole passband. Moreover, the particle-in-cell (PIC) simulation results reveal that under the operating voltage of 20.8 kV and beam current of 150 mA, EBTSW-TWT can provide more than 70 W of saturated output power in the frequency range of 200-260 GHz, reaching the maximum power of 151 W at 220 GHz with the maximum electronic efficiency of 4.85%.

Integrating batched sparse iterative solvers for the collision operator in fusion plasma simulations on GPUs

Batched linear solvers, which solve many small related but independent problems, are increasingly important for highly parallel processors such as graphics processing units (GPUs). GPUs need a substantial amount of work to keep them operating efficiently and it is not an option to solve smaller problems one-by-one. Because of the small size of each problem, the task of implementing a parallel partitioning scheme and mapping the problem to hardware is not trivial. In recent history, significant attention has been given to batched dense linear algebra. However, there is also an interest in utilizing sparse iterative solvers in a batched form.An example use case is found in a gyrokinetic Particle-In-Cell (PIC) code used for modeling magnetically confined fusion plasma devices. The collision operator has been identified as a bottleneck, and a proxy app has been created for facilitating optimizations and porting to GPUs. The current collision kernel linear solver does not run on the GPU—a major bottleneck. As these matrices are sparse and well-conditioned, batched iterative sparse solvers are an attractive option.A batched sparse iterative solver capability has recently been developed in the Ginkgo library. In this paper, we describe how Ginkgo's batched solver technology can integrate into the XGC collision kernel and accelerate the simulation process. Comparisons for the solve times on NVIDIA V100 and A100 GPUs and AMD MI100 GPUs with one dual-socket Intel Xeon Skylake CPU node with 40 cores are presented for matrices from the collision kernel of XGC. Further, the speedups observed for the overall collision kernel are presented in comparison to different modern CPUs on multiple supercomputer systems. The results suggest that Ginkgo's batched sparse iterative solvers are well suited for efficient utilization of the GPU for this problem, and the performance portability of Ginkgo in conjunction with Kokkos (used within XGC as the heterogeneous programming model) allows seamless execution on exascale-oriented heterogeneous architectures.

Particle-in-Cell Modeling of Omega Experiments on Ablation of Plasmas

The large electric fields due to charge separation generated by a laser pulse propagating in a plasma can accelerate the electrons to very high energies. The hydrodynamics models that are based on the local thermodynamic equilibrium assuming a Maxwellian distribution of velocities cannot describe the evolution of groups of hot electrons of different energy ranges and kinetic particle-in-cell (PIC) simulations are required. The SMILEI PIC code is used to investigate the generation of hot electrons in plasmas produced by laser pulses in the Omega extended performance (EP) experiments. In 2-D PIC simulation using SMILEI code, a Gaussian-shaped laser pulse of 100-ps duration with the intensity of 10 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{15}$</tex-math> </inline-formula> W/cm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{2}$</tex-math> </inline-formula> and a wavelength of 351 nm impinges onto a plasma with the electron density and temperature profiles. The electromagnetic field, electron, and total energies of a plasma as a function of time are evaluated. The evolution of number density, electromagnetic fields, and energy spectra of electrons is studied. The time evolution of hot electrons in a plasma is investigated. These PIC results provide insights into the contribution and importance of the kinetic effects in the expansion dynamics of ablated plasmas, thereby helping to analyze and explain the Omega experimental data and computational fluid dynamics results.

Improved modellisation of laser–particle interaction in particle-in-cell simulations

A new method named B-TIS (Bourgeois &amp; Davoine, J. Comput. Phys., vol. 413, 2020, 109426) has recently been proposed for suppressing the influence of numerical Cherenkov radiation that appears in particle-in-cell (PIC) simulation of laser wakefield acceleration (LWFA). However, while this method provides good results when applied to the already accelerated electrons, we show here that it cannot model correctly most of the plasma electron bulk interacting with the laser field. We thus investigate in this paper the origins of this limitation and propose an improved method for which this limitation is removed. This new method, named B-TIS3, can now be applied to a much broader variety of problems and improve the performance in comparison with the standard PIC algorithm. We show that, for an electron interacting directly with a laser pulse, this new technique offers greater accuracy in terms of momentum and motion than the conventional scheme used in many PIC codes. These improvements translate into more faithful energy spectrum and electric charge for the accelerated beam in simulations of vacuum laser acceleration (VLA) or LWFA involving direct laser acceleration (DLA) at low plasma density. This new method, easy to implement and not computationally demanding, should then prove useful to study in depth and help develop novel VLA, DLA and LWFA techniques.

A Charge Conserving Exponential Predictor Corrector FEMPIC Formulation for Relativistic Particle Simulations

The state of art of charge conserving electromagnetic finite element particle-in-cell (EM-FEMPIC) has grown by leaps and bounds in the past few years. These advances have primarily been achieved for leap-frog time stepping schemes for Maxwell solvers, in large part, due to the method strictly following the proper space for representing fields, charges, and measuring currents. Unfortunately, leap-frog-based solvers (and their other incarnations) are only conditionally stable. Recent advances have made it possible to construct EM-FEMPIC methods built around unconditionally stable time-stepping methods while conserving charge. Together with the use of a quasi-Helmholtz decomposition, these methods were both unconditionally stable and satisfied Gauss’ laws to machine precision. However, this architecture was developed for systems with explicit particle integrators where fields and velocities were off by a time step. While completely self-consistent methods exist in the literature, they follow the classic rubric: collect a system of first-order differential equations (Maxwell and Newton equations) and use an integrator to solve the combined system. These methods suffer from the same side effect as earlier—they are conditionally stable. Here, we propose a different approach; we pair an unconditionally stable Maxwell solver to an exponential predictor corrector (PC) method for Newton’s equations. As we will show via numerical experiments, the proposed method conserves energy within a particle-in-cell (PIC) scheme, has an unconditionally stable electromagnetic (EM) solve, solves Newton’s equations to much higher accuracy than a traditional Boris solver, and conserves charge to machine precision. We further demonstrate benefits compared with other polynomial methods to solve Newton’s equations, like the well-known Boris push.

Research on a Highly Overmoded Slow Wave Circuit for 0.3-THz Extended Interaction Oscillator

Here, we present the complete design process of a highly overmoded slow wave circuit (SWC) stably operating in the quasi-TM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{\text{04}}$</tex-math> </inline-formula> mode for terahertz (THz) extended interaction oscillator (EIO). The developed interaction circuit emits THz frequency electromagnetic radiation through structural size of the engineered millimeter-wave (MMW) circuits, which provides a new technological horizon for overcoming the engineering challenges caused by the limitation of circuit size. Through careful engineering of the electron optical system, a cylindrical beam with a diameter of 0.38 mm and a current of 0.25 A is obtained at a bias of 14.8 kV. Through the particle-in-cell (PIC) simulation, these new design approaches have been shown to achieve an output power of 250 W at 0.3 THz in a cylindrical cavity with an inner diameter of 4.16 mm.

Application scope of the reductive perturbation method to derive the KdV equation and CKdV equation in dusty plasma

The application scopes of two different reductive perturbation methods to derive the Korteweg–de Vries (KdV) equation and coupled KdV (CKdV) equation in two-temperature-ion dusty plasma are given by using the particle-in-cell (PIC) numerical method in the present paper. It suggests that the reductive perturbation method (RPM) is valid if the amplitude of the CKdV solitary wave is small enough. However, for the KdV solitary wave, RPM is valid not only if the amplitude of the KdV solitary wave is small enough, but also if the nonlinear coefficient of the KdV equation is not tending to zero.

Modeling of very high frequency large-electrode capacitively coupled plasmas with a fully electromagnetic particle-in-cell code

Phenomena taking place in capacitively coupled plasmas with large electrodes and driven at very high frequencies are studied numerically utilizing a novel energy- and charge-conserving implicit fully electromagnetic particle-in-cell (PIC)/Monte Carlo code ECCOPIC2M. The code is verified with three model problems and is validated with results obtained in an earlier experimental work (Sawada et al 2014 Japan. J. Appl. Phys. 53 03DB01). The code shows a good agreement with the experimental data in four cases with various collisionality and absorbed power. It is demonstrated that under the considered parameters, the discharge produces radially uniform ion energy distribution functions for the ions hitting both electrodes. In contrast, ion fluxes exhibit a strong radial nonuniformity, which, however, can be different at the powered and grounded electrodes at increased pressure. It is found that this nonuniformity stems from the nonuniformity of the ionization source, which is in turn shaped by mechanisms leading to the generation of energetic electrons. The mechanisms are caused by the interaction of electrons with the surface waves of two axial electric field symmetry types with respect to the reactor midplane. The asymmetric modes dominate electron heating in the radial direction and produce energetic electrons via the relatively inefficient Ohmic heating mechanism. In the axial direction, the electron energization occurs mainly through an efficient collisionless mechanism caused by the interaction of electrons in the vicinity of an expanding sheath with the sheath motion, which is affected by the excitation of the surface modes of both types. The generation of energetic electron populations as a result of such mechanisms is shown directly. Although some aspects of the underlying physics were demonstrated in the previous literature with other models, the PIC method is advantageous for the predictive modeling due to a complex interplay between the surface mode excitations and the nonlocal physics of the corresponding type of plasma discharges operated at low pressures, which is hard to reproduce in other models realistically.

On the space-charge effects in the beam extraction process of ion thrusters: the roles of compensating electrons and changing beam radius

Space-charge effects limit the beam-extraction capability of the ion optics and thus hinder the miniaturization and other performance improvements of ion thrusters. This paper presents numerical studies of the space-charge effects in ion optics using hybrid and full particle-in-cell (PIC) simulations, and proposes a modified Child–Langmuir (CL) law. As the injected current increases, the parallel-plane electrode system which corresponds to the classical CL law will reach an unstable and oscillatory state, while the ion optics system remains stable because the electrons from the bulk plasma compensate for the space-charge effects. Furthermore, the radial expansion of the ion beam and the loss of ions on the grids can counteract the space-charge effects when the injected current increases. In general, the space-charge effects in ion optics are self-consistently adjusted by the compensating electrons and the variation of the beam radius. Accordingly, we identify a region in ion optics where, generally, no electrons exist to exclude the influence of electron compensation, and then we modify the CL law of this region by taking into account the effect of the change in the beam radius. We validate the modified CL law and demonstrate its effectiveness in predicting the operating points of the ion optics, such as the perveance-limit point.

Novel 0.22-THz Extended Interaction Oscillator Based on the Four-Sheet-Beam Orthogonal Interconnection Structure

Numerous terahertz vacuum electronic devices (TVEDs) have been proposed. Among these devices, extended interaction oscillators (EIOs) exhibit small-volume, lightweight, low-working-voltage, stable-working frequency, and high-power characteristics. The ladder-line slow wave structure exhibits strong coupling and can interact with the sheet beam to considerably improve the efficiency of beam–wave interaction. In this study, a novel high-frequency structure was proposed. Four conventional ladder-line slow wave structures were placed vertically to form a four-sheet-beam orthogonal interconnection structure (OIS) that considerably increased the coupling efficiency between the cavities, improved output power and efficiency, and interacted perfectly with the TM81 mode. In this study, the dispersion characteristics and field distribution were studied through numerical and simulation calculations, and the optimal working parameters and output structure were analyzed using particle-in-cell (PIC) software. Next, a 0.22-THz extended interaction oscillator based on four-sheet-beam OSI was designed. Simulation results have shown the achievement of the output power of 0.22-THz wave over 500 W with four sheet beams at 16.6 kV and each current of 0.8 A. Finally, preliminary processing and cold tests of the structure were performed. This novel structure provided an alternative for the development of terahertz EIOs.

Energy Coupling Mechanism of Electrodeless Plasma Thruster with Rotating Electric Field

The energy coupling process indicated by particle density, speed, current density, and power absorption in a thruster using a rotating electric field was simulated using a one dimension, three velocities electrostatic particle-in-cell (PIC) code under different external magnetic field strengths varying from 0 to 80 G. The longer interaction between electrons and the sheath layer due to the increased magnetic field results in a significant decrease in electron speed from at 0 G to at 80 G; a reduction in electron power absorption from at 0 G to at 80 G; and an increase in electron density, current density, and total current density about 69.48, 21.11, and 5.4%, respectively. While ions cannot respond to the changes in time because of their large mass. Three types of currents, namely, electron, ion, and displacement, are primarily present throughout the discharge process. Ion current is significantly less than the other two. The characteristics of plasma described exhibit a nonlinear change, dropping at first and then rising when the magnetic field is strengthened. The results have implications for both choosing the magnetic field for the thruster and thoroughly investigating the energy coupling inside the plasma.

Underdense plasma lens with a transverse density gradient

We explore the implications of a transverse density gradient on the performance of an underdense plasma lens and nonlinear plasma-based accelerator. Transverse density gradients are unavoidable in plasma sources formed in the outflow of standard gas jets, which are used heavily in plasma accelerator communities. These density gradients lead to longitudinal variations in the transverse wakefields, which can transversely deflect an electron beam within the blowout wake. We present a theoretical model of the fields within the plasma blowout cavity based on empirical analysis of 3D particle-in-cell (PIC) simulations. Using this model, the transverse beam dynamics may be studied analytically, allowing for an estimation of the net kick of a witness electron bunch from an underdense plasma lens and for density uniformity tolerance studies in plasma accelerators and plasma lenses. This model is compared to PIC simulations with a single electron bunch and constant density profile, and to PIC simulations with two bunches and a thin, underdense plasma lens density profile with density ramps.

A conservation law consistent updated Lagrangian material point method for dynamic analysis

The Material Point Method (MPM) is well suited to modelling dynamic solid mechanics problems undergoing large deformations with non-linear, history dependent material behaviour. However, the vast majority of existing material point method implementations do not inherit conservation properties (momenta and energy) from their continuum formulations. This paper provides, for the first time, a dynamic updated Lagrangian material point method for elasto-plastic materials undergoing large deformation that guarantees momenta and energy conservation. Sources of energy dissipation during point-to-grid and grid-to-point mappings for FLuid Implicit Particle (FLIP) and Particle In Cell (PIC) approaches are clarified and a novel time-stepping approach is proposed based on an efficient approximation of the Courant-Friedrich-Lewy (CFL) condition. The formulation provided in this paper offers a platform for understanding the energy conservation nature of future/existing features of material point methods, such as contact approaches.

An Angular Radial Extended Interaction Amplifier at the W Band

In this paper, an angular radial extended interaction amplifier (AREIA) that consists of a pair of angular extended interaction cavities is proposed. Both the convergence angle cavity and the divergence angle cavity, which are designed for the converging beam and diverging beam, respectively, are investigated to present the potential of the proposed AREIA. They are proposed and explored to improve the beam-wave interaction capability of W-band extended interaction klystrons (EIKs). Compared to conventional radial cavities, the angular cavities have greatly decreased the ohmic loss area and increased the characteristic impedance. Compared to the sheet beam (0°) cavity, it has been found that the convergence angle cavity has a higher effective impedance and the diverging beam has a weaker space-charge effect under the same ideal electron beam area; the advantages become more obvious as the propagation distance increases. Particle-in-cell (PIC) results have shown that the diverging beam (8°) EIA performs better at an output power of 94 GHz under the condition of lossless, while the converging beam (-2°) EIA has a higher output power of 6.24 kW under the conditions of ohmic loss, an input power of 0.5 W, and an ideal electron beam of 20.5 kV and 1.5 A. When the loss increases and the beam current decreases, the output power of the -2° EIA can be improved by nearly 30% compared to the 0° EIA, and the -2° EIA has a greatly improved beam-wave interaction capacity than conventional EIAs under those conditions. In addition, an angular radial electron gun is designed.