3D Particle-in-cell Research Articles

Effect of plasma initialization on 3D PIC simulation of Hall thruster azimuthal instability

The lack of understanding of the azimuthal instability and the resulting electron anomalous transport limits further improvement of Hall thrusters. Compared to theoretical and experimental approaches, the numerical particle-in-cell (PIC) simulation is a suitable and powerful tool, which has been widely applied to investigate the azimuthal instability, and great progress has been made in the past decades. However, PIC simulations are intrinsically computationally expensive, and it is realized that the Hall thruster azimuthal instability has a three dimensional nature. Therefore, massive 3D PIC simulation must be carried out to completely reveal the mechanism of the instability. In this paper, the effect of plasma initialization on 3D PIC simulation of Hall thruster azimuthal instability is studied as a starting point. It is found that by initializing with ion density and velocity fitting functions to the steady-state simulation results, a faster convergence can be obtained and the computational time can be reduced by about 1.5 times. Typical fitting functions of ion density, drifting velocity, and temperature are given, and the influence of different initialization profiles is presented.

Rescattering of stimulated Raman side scattering in nonuniform plasmas

Rescattering of stimulated Raman side scattering (SRSS) is observed for the first time via two-dimensional (2D) particle-in-cell (PIC) simulations. We construct a theoretical model for the rescattering process, which can predict the region of occurrence of mth-order SRSS and estimate its threshold. The rescattering process is identified by the 2D PIC simulations under typical conditions of a direct-drive inertial confinement fusion scheme. Hot electrons produced by second-order SRSS propagate nearly perpendicular to the density gradient and gain nearly the same energy as in first-order SRSS, but there is no cascade acceleration to produce superhot electrons. Parametric studies for a wide range of ignition conditions show that SRSS and associated rescatterings are robust and important processes in inertial confinement fusion.

Stabilization and correction of aberrated laser beams via plasma channelling.

High-power laser applications, and especially laser wakefield acceleration, continue to draw attention through various research topics, and may bring many industrial applications based on compact accelerators, from ultrafast imaging to cancer therapy. However, one main step towards this is the arch issue of stability. Indeed, the interaction of a complex, aberrated laser beam with plasma involves a lot of physical phenomena and non-linear effects, such as self-focusing and filamentation. Different outcomes can be induced by small laser instabilities (i.e. laser wavefront), therefore harming any practical solution. One promising path to be explored is the use of a plasma channel to possibly guide and correct aberrated beams. Complex and costly experimental facilities are required to investigate such topics. However, one way to quickly and efficiently explore new solutions is numerical simulations, especially Particle-In-Cell (PIC) simulations if, and only if, one is confidently implementing such aberrated beams which, contrary to a Gaussian beam, do not have analytical solutions. In this research, we propose two new advancements: the correct implementation of aberrated laser beams inside a 3D PIC code, showing a great consistency, under vacuum, compared to the calculations with Fresnel theory); and the correction of their quality via the propagation inside a plasma channel. We demonstrate improvements in the beam pattern, becoming closer to a single plasma mode with less distortions, and thus suggesting a better stability for the targeted application. Through this confident calculation technique for distorted laser beams, we are now expecting to proceed with more accurate PIC simulations, closer to experimental conditions, and obtained results with plasma channels indicate promising future research.

Simple 3D PIC Analysis for Beam Phase Space Oscillation in RF Driven Negative Hydrogen Ion Source

Temporal oscillation of the negative hydrogen ion (H−) beam in the Radio Frequency (RF) ion source is investigated by a simple 3D3V Particle-In-Cell (PIC) model. The model solves electron, proton, and H− transport processes in the extraction region. The calculation domain is from the vicinity of the beam aperture to the ground electrode. To understand the relation between the plasma density oscillation and the extracted H− beam characteristics, the input electron and proton fluxes from the driver region are varied parametrically with the fundamental J-PARC RF frequency (2 MHz). The numerical results give an idea of the main physical processes between the oscillations of the plasma parameters and the extracted H− ion trajectories depending on the plasma meniscus shape in the different RF phases.

Multi-GeV wakefield acceleration in a plasma-modulated plasma accelerator.

We investigate the accelerator stage of a plasma-modulated plasma accelerator (P-MoPA) [Jakobsson et al., Phys. Rev. Lett. 127, 184801 (2021)0031-900710.1103/PhysRevLett.127.184801] using both the paraxial wave equationand particle-in-cell (PIC) simulations. We show that adjusting the laser and plasma parameters of the modulator stage of a P-MoPA allows the temporal profile of pulses within the pulse train to be controlled, which in turn allows the wake amplitude in the accelerator stage to be as much as 72% larger than that generated by a plasma beat-wave accelerator with the same total drive laser energy. Our analysis shows that Rosenbluth-Liu detuning is unimportant in a P-MoPA if the number of pulses in the train is less than ∼30, and that this detuning is also partially counteracted by increased red-shifting, and hence increased pulse spacing, towards the back of the train. An analysis of transverse mode oscillations of the driving pulse train is found to be in good agreement with 2D (Cartesian) PIC simulations. PIC simulations demonstrating energy gains of ∼1.5GeV (∼2.5GeV) for drive pulse energies of 2.4J (5.0J) are presented. Our results suggest that P-MoPAs driven by few-joule, picosecond pulses, such as those provided by high-repetition-rate thin-disk lasers, could accelerate electron bunches to multi-GeV energies at pulse repetition rates in the kilohertz range.

Numerical thermalization in 2D PIC simulations: Practical estimates for low-temperature plasma simulations

The process of numerical thermalization in particle-in-cell (PIC) simulations has been studied extensively. It is analogous to Coulomb collisions in real plasmas, causing particle velocity distributions (VDFs) to evolve toward a Maxwellian as macroparticles experience polarization drag and resonantly interact with the fluctuation spectrum. This paper presents a practical tutorial on the effects of numerical thermalization in 2D PIC applications. Scenarios of interest include simulations, which must be run for many thousands of plasma periods and contain a population of cold electrons that leave the simulation space very slowly. This is particularly relevant to many low-temperature plasma discharges and materials processing applications. We present numerical drag and diffusion coefficients and their associated timescales for a variety of grid resolutions, discussing the circumstances under which the electron VDF is modified by numerical thermalization. Though the effects described here have been known for many decades, direct comparison of analytically derived, velocity-dependent numerical relaxation timescales to those of other relevant processes has not often been applied in practice due to complications that arise in calculating thermalization rates in 1D simulations. Using these comparisons, we estimate the impact of numerical thermalization in several examples of low-temperature plasma applications including capacitively coupled plasma discharges, inductively coupled plasma discharges, beam plasmas, and hollow cathode discharges. Finally, we discuss possible strategies for mitigating numerical relaxation effects in 2D PIC simulations.

High-energy synchrotron flares powered by strongly radiative relativistic magnetic reconnection: 2D and 3D PIC simulations

ABSTRACT The time evolution of high-energy synchrotron radiation generated in a relativistic pair plasma energized by reconnection of strong magnetic fields is investigated with 2D and 3D particle-in-cell (PIC) simulations. The simulations in this 2D/3D comparison study are conducted with the radiative PIC code OSIRIS, which self-consistently accounts for the synchrotron radiation reaction on the emitting particles, and enables us to explore the effects of synchrotron cooling. Magnetic reconnection causes compression of the plasma and magnetic field deep inside magnetic islands (plasmoids), leading to an enhancement of the flaring emission, which may help explain some astrophysical gamma-ray flare observations. Although radiative cooling weakens the emission from plasmoid cores, it facilitates additional compression there, further amplifying the magnetic field B and plasma density n, and thus partially mitigating this effect. Novel simulation diagnostics utilizing 2D histograms in the n-B space are developed and used to visualize and quantify the effects of compression. The n-B histograms are observed to be bounded by relatively sharp power-law boundaries marking clear limits on compression. Theoretical explanations for some of these compression limits are developed, rooted in radiative resistivity or 3D kinking instabilities. Systematic parameter-space studies with respect to guide magnetic field, system size, and upstream magnetization are conducted and suggest that stronger compression, brighter high-energy radiation, and perhaps significant quantum electrodynamic effects such as pair production, may occur in environments with larger reconnection-region sizes and higher magnetization, particularly when magnetic field strengths approach the critical (Schwinger) field, as found in magnetar magnetospheres.

Effect of Surface Produced H<sup>- </sup>Ion on the Plasma Meniscus in Negative Hydrogen Ion Sources

To extract intense ion beams with good beam optics from ion sources, controlling the distance deff between the plasma meniscus (i.e., beam emission surface) and the beam extraction grid is important. This study conducts a novel investigation into the dependence of the effective distance deff on the amount of surface H- production SH-. For this purpose, a 3D PIC (three dimensional Particle-in-Cell) simulation is conducted to obtain a model geometry of the extraction region for a H- ion source with SH- as a parameter. Based on results, deff significantly depends on SH- and the H--electron density ratio (α = nH-/ne) in front of the extraction aperture for the same plasma density; as SH- increases, deff decreases. The results suggest that SH- is critical for controlling deff and the resultant beam optics extracted from the negative ion source.

3D particle-in-cell study of the electron drift instability in a Hall Thruster using unstructured grids

In a Hall Thruster, the E×B current generates a strong electron drift with respect to the ions, which can trigger plasma instabilities, such as the electron drift instability (EDI), also called the electron cyclotron drift instability. The EDI has drawn a great deal of attention in the E×B community as previous one- and two-dimensional Particle-In-Cell (PIC) studies suggest it plays a major role in the anomalous transport of electrons across the magnetic barrier. However, experiments showed that the EDI has an inherent three-dimensional nature, which cannot be accurately described in a 1D or 2D configuration. Unfortunately, due to their prohibitive computational cost, needed 3D PIC simulations remained inaccessible without scaling plasma parameters, which inevitably modified the physics in a Hall Thruster. Thanks to recent computational developments, this paper presents a 3D fully kinetic investigation of the EDI in a typical Hall Thruster channel and near plume region. The study was conducted using an unstructured grid, thus demonstrating the feasibility to model more complicated geometries in the future. The growth and development of the EDI are described along with other plasma fluctuations, possibly the signature of another plasma instability, the modified-two-stream-instability. 3D effects on the anomalous transport are also assessed and found to be lower than in an analogous 2D simulation. This is due to lower losses in 2D, which lead to the saturation of the EDI occurring at higher energy levels.

Formation and Reconnection of Electron Scale Current Layers in the Turbulent Outflows of a Primary Reconnection Site

Abstract We simulate with 3D particle in cell, the spontaneous formation of turbulent outflows in an initially laminar 3D reconnecting current layer. We observe the formation of many secondary current layers and reconnection sites in the outflow. The approach we follow is to study each individual feature within the turbulent outflow. To identify all clusters of current in the outflow we use a clustering technique widely used in unsupervised machine learning: density-based spatial clustering of applications with noise. Once the clusters are identified we measure their size and compute reconnection indicators to establish which are undergoing reconnection. With this analysis we establish that the size of the current clusters reaches all the way from its initial system scale down to subelectron skin depth scale. We observe that the smaller current clusters are more prone to reconnecting and to releasing energy. We then find the process of reconnection of the smaller current cluster to be of the recently observed electron-only type that leaves the ions essentially unaffected.

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.

Electron beam energy slicing performance in laser wakefield acceleration

The first stage of electron acceleration, the plasma cathode, is a key part of LWFA. Output parameters of this stage such as beam charge, mean energy, energy spread, and emittance can be varied in a rather broad range depending on laser pulse and gas target conditions. These parameters are usually evaluated via particle-in-cell (PIC) simulations. However, if an essential improvement of the beam quality could be further performed with a conventional beamline, the selection of an acceleration regime, including laser pulse and gas target characteristics, should be done taking into account not only PIC simulations but also beam transport simulations. Here is shown that improvements of electron beam quality via energy slicing using magneto-optics (MO) may become an important step in developing full-optical electron accelerators and radiation devices. Since the typical energy of electrons presently achieves sub-GeV in a single acceleration stage, the elaboration of slicing techniques for quasi-mono-energetic, high density LWFA beams is of particular interest. Depending on the efficiency of beam slicing the reverse problem of initial beam energy distribution and, therefore, a proper acceleration regime can be solved. An efficient slicing may allow operation with broader beam energy spreads, higher charges, and getting better stability in contrast to narrower beam energy spreads requiring far more precise control over laser and gas target parameters. Even though this technique has been used in classical particle accelerators, its limitations have not been well studied in LWFA with their less stable beams. MO slicing is explored numerically with use of realistic LWFA electron beams obtained from 3D PIC simulations at various target parameters.

Evidence of the Alfvén Transition Layer and Particle Precipitation in the Cusp Region: 3D Global PIC Simulation of the Solar Wind–Earth Magnetosphere Interaction

A transition layer, named the Alfvénic transition layer (or ATL), has been clearly evidenced near the outer boundary of the cusp by experimental observations from the Cluster mission. This layer characterized by a local value of Log M A ∼ 1, where M A is the Alfvén Mach number, allows the bulk flow to transit from super-Alfvénic to sub-Alfvénic from the exterior to the interior side of the outer cusp. The ATL has been observed during northward interplanetary magnetic field orientation, and mainly within the meridian plane. Currently, 3D Particle In Cell (PIC) global simulations of the solar wind–magnetosphere interaction are being performed in order to analyze the cusp region and this layer in detail. Present results stress the following points: (i) the ATL has a 3D structure; (ii) within the meridian plane, the ATL appears as a sublayer within a much more extended slow-mode pattern, and it is almost adjacent and located above the upper edge of the stagnant exterior cusp (SEC); and (iii) the plasma deceleration through the ATL is not uniform in the region located above the cusp. In addition, present preliminary results stress that (a) the spiraled streamlines of ion/electron fluxes converge when approaching the cusp, and their intensity strongly increases; and (b) ion and electron energetic fluxes penetrating the cusp region strongly differ in terms of their penetration depths and are issued from different regions of the magnetosphere/magnetosheath. Our results illustrate the importance of 3D effects used with a PIC simulation approach allowing the analysis of each population simultaneously.

Fully Kinetic Shearing-box Simulations of Magnetorotational Turbulence in 2D and 3D. I. Pair Plasmas

The magnetorotational instability (MRI) is a fundamental mechanism determining the macroscopic dynamics of astrophysical accretion disks. In collisionless accretion flows around supermassive black holes, MRI-driven plasma turbulence cascading to microscopic (i.e., kinetic) scales can result in enhanced angular-momentum transport and redistribution, nonthermal particle acceleration, and a two-temperature state where electrons and ions are heated unequally. However, this microscopic physics cannot be captured with standard magnetohydrodynamic (MHD) approaches typically employed to study the MRI. In this work, we explore the nonlinear development of MRI turbulence in a pair plasma, employing fully kinetic particle-in-cell (PIC) simulations in two and three dimensions. First, we thoroughly study the axisymmetric MRI with 2D simulations, explaining how and why the 2D geometry produces results that differ substantially from 3D MHD expectations. We then perform the largest (to date) 3D simulations, for which we employ a novel shearing-box approach, demonstrating that 3D PIC models can reproduce the mesoscale (i.e., MHD) MRI dynamics in sufficiently large runs. With our fully kinetic simulations, we are able to describe the nonthermal particle acceleration and angular-momentum transport driven by the collisionless MRI. Since these microscopic processes ultimately lead to the emission of potentially measurable radiation in accreting plasmas, our work is of prime importance to understand current and future observations from first principles, beyond the limitations imposed by fluid (MHD) models. While in this first study we focus on pair plasmas for simplicity, our results represent an essential step toward designing more realistic electron–ion simulations, on which we will focus in future work.

Laser ion acceleration from tailored solid targets with micron-scale channels

Laser ion acceleration is a promising concept for the generation of fast ions using a compact laser-solid interaction setup. In this study, we theoretically investigate the feasibility of ion acceleration from the interaction of petawatt-scale laser pulses with a structured target that embodies a micron-scale channel filled with relativistically transparent plasma. Using 2D and 3D particle-in-cell (PIC) simulations and theoretical estimates, we show that it is possible to generate GeV protons with high volumetric charge and quasimonoenergetic feature in the energy spectrum. Optimal parameters of the target are obtained using 2D PIC simulations and interpreted on a basis of an analytical two-stage ion acceleration model. 3D PIC simulations and realistic preplasma profile runs with 2D PIC show the feasibility of the presented laser ion acceleration scheme for the experimental implementation at the currently available petawatt laser facilities.

Integrating a ponderomotive guiding center algorithm into a quasi-static particle-in-cell code based on azimuthal mode decomposition

High fidelity modeling of plasma based acceleration (PBA) requires the use of three dimensional, fully nonlinear, and kinetic descriptions based on the particle-in-cell (PIC) method. In PBA an intense particle beam or laser (driver) propagates through a tenuous plasma whereby it excites a plasma wave wake. Three-dimensional PIC algorithms based on the quasi-static approximation (QSA) have been successfully applied to efficiently model the interaction between relativistic charged particle beams and plasma. In a QSA PIC algorithm, the plasma response to a charged particle beam or laser driver is calculated based on forces from the driver and self-consistent forces from the QSA form of Maxwell's equations. These fields are then used to advance the charged particle beam or laser forward by a large time step. Since the time step is not limited by the regular Courant-Friedrichs-Lewy (CFL) condition that constrains a standard 3D fully electromagnetic PIC code, a 3D QSA PIC code can achieve orders of magnitude speedup in performance. Recently, a new hybrid QSA PIC algorithm that combines another speedup technique known as an azimuthal Fourier decomposition has been proposed and implemented. This hybrid algorithm decomposes the electromagnetic fields, charge and current density into azimuthal harmonics and only the Fourier coefficients need to be updated, which can reduce the algorithmic complexity of a 3D code to that of a 2D code. Modeling the laser-plasma interaction in a full 3D electromagnetic PIC algorithm is very computationally expensive due the enormous disparity of physical scales to be resolved. In the QSA the laser is modeled using the ponderomotive guiding center (PGC) approach. We describe how to implement a PGC algorithm compatible for the QSA PIC algorithms based on the azimuthal mode expansion. This algorithm permits time steps orders of magnitude larger than the cell size and it can be asynchronously parallelized. Details on how this is implemented into the QSA PIC code that utilizes an azimuthal mode expansion, QPAD, are also described. Benchmarks and comparisons between a fully 3D explicit PIC code (OSIRIS), as well as a few examples related to laser wakefield acceleration, are presented.

Particle-in-cell modeling of plasma jet merging in the large-Hall-parameter regime

The merging process of magnetized plasma jets with parameters relevant to the plasma-jet-driven magneto-inertial fusion (PJMIF) design and the plasma liner experiment (PLX) is modeled by fully kinetic particle-in-cell (PIC) simulations in one and two spatial dimensions. The modified two-stream instability is identified to be the main mechanism responsible for stopping the plasma jets and preventing species interpenetration. The electron and ion Hall parameters of the merged plasma are greater than unity, and the plasma β is close to unity, which is the desired characteristic of planned experiments at PLX. Our 2D PIC simulations validate the results of the radiation magneto-hydrodynamics code FLASH, which will be the primary tool for modeling various stages of future PJMIF experiments.

Two‐dimensional analysis for the transition from nonlocal to local electron kinetics and its effect on the spatial uniformity of a capacitively coupled plasma

AbstractIn capacitively coupled plasmas (CCPs) operated under various pressure conditions in semiconductor manufacturing processes, the transition in discharge characteristics is observed depending on local or nonlocal electron kinetics. A two‐dimensional (2D) particle‐in‐cell (PIC) simulation is required because the one‐dimensional PIC method cannot capture the effect of device structures and because fluid models cannot treat the self‐consistent change in the energy distributions. Using a 2D PIC simulation parallelized with a graphics processing unit, we investigated the transition of electron kinetics for the variation of the driving voltage, gas pressure, the gap distance between upper and lower electrodes, and the sidewall condition. Moreover, the mechanism for electron energy relaxation in a CCP is elucidated to develop a method to improve the process uniformity.

Study of post-arc residual plasma dissipation process of vacuum circuit breakers based on a 2D particle-in-cell model

In order to get an insight into residual plasma radial motion during the post-arc stage, a two-dimensional (2D) cylindrical particle-in-cell (PIC) model is developed. Firstly, influences of a virtual boundary condition on the residual plasma motion are studied. For purpose of validating this 2D cylindrical particle-in-cell model, a comparison between one-dimensional particle-in-cell model is also presented in this paper. Then a study about the influences of the rising rate of transient recovery voltage on the residual plasma radial motion is presented on the basis of the 2D PIC model.

Particle-in-cell simulations of THz emission from plasma by oblique collision of two-electron beams

We studied the THz radiation generated by a beam-plasma system using two-dimensional (2D) particle-in-cell (PIC) simulations. The Langmuir waves excited by two counterpropagating electron beams, via two-stream instability, collide with each other at an oblique angle, which forms a high beam-density modulation near the collision region, where both beam electrons become trapped. As a result, spatially localized Langmuir wave packets with large longitudinal-electric field amplitudes are formed, which give rise to bursts of electromagnetic radiation. Our 2D PIC simulations of the two thin, low-density, asymmetric, electron beams colliding obliquely show that a strong THz emission is obtained at the second harmonic of the plasma frequency (f = 1.0 THz), with a narrow spectral width (∼0.80%) in vacuum and significantly higher efficiency than the head-on-collision case. The efficiency of power conversion from electron beams to THz radiation measured in vacuum reaches around ∼0.0289, for a continuous injection of beams into the plasma, making it suitable for applications requiring high-power narrow-band THz radiation sources.