3D Particle-in-cell Simulations Research Articles

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

Abstract 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.

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.

Addressing key aspects of J × B driven MeV fast electron generation in ultra-short ultra-intense laser foil interaction

Applicability of J × B mechanism of MeV fast electron generation is clearly demonstrated through observation of directed electron beam along laser propagation direction (simultaneous emission also along laser polarization/transverse directions) in the interaction of ∼25 fs laser pulse with thin foil target at an intensity of 1–7 × 1019 W/cm2. Fast electron temperature is found to be lower (higher) than ponderomotive for shorter (longer) preplasma scale lengths. Role of pre-acceleration of electrons in the rising part of the laser pulse is suggested for observed efficient J × B acceleration for p-polarization case. 2D particle in cell simulation also supports the above-mentioned observations.

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.

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.

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.

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.

Relativistically transparent magnetic filaments: scaling laws, initial results and prospects for strong-field QED studies

Relativistic transparency enables volumetric laser interaction with overdense plasmas and direct laser acceleration of electrons to relativistic velocities. The dense electron current generates a magnetic filament with field strength of the order of the laser amplitude (>105 T). The magnetic filament traps the electrons radially, enabling efficient acceleration and conversion of laser energy into MeV photons by electron oscillations in the filament. The use of microstructured targets stabilizes the hosing instabilities associated with relativistically transparent interactions, resulting in robust and repeatable production of this phenomenon. Analytical scaling laws are derived to describe the radiated photon spectrum and energy from the magnetic filament phenomenon in terms of the laser intensity, focal radius, pulse duration, and the plasma density. These scaling laws are compared to 3D particle-in-cell (PIC) simulations, demonstrating agreement over two regimes of focal radius. Preliminary experiments to study this phenomenon at moderate intensity (a 0 ∼ 30) were performed on the Texas Petawatt Laser. Experimental signatures of the magnetic filament phenomenon are observed in the electron and photon spectra recorded in a subset of these experiments that is consistent with the experimental design, analytical scaling and 3D PIC simulations. Implications for future experimental campaigns are discussed.

Computational study of simultaneous positive and negative streamer propagation in a twin surface dielectric barrier discharge via 2D PIC simulations

The propagation mechanisms of plasma streamers have been observed and investigated in a surface dielectric barrier discharge (SDBD) using 2D particle in cell simulations. The investigations are carried out under a simulated air mixture, 80% N2 and 20% O2, at atmospheric pressure, 100 kPa, under both DC conditions and a pulsed DC waveform that represent AC conditions. The simulated geometry is a simplification of the symmetric and fully exposed SDBD resulting in the simultaneous ignition of both positive and negative streamers on either side of the Al2O3 dielectric barrier. In order to determine the interactivity of the two streamers, the propagation behavior for the positive and negative streamers are investigated both independently and simultaneously under identical constant voltage conditions. An additional focus is implored under a fast sub nanosecond rise time square voltage pulse alternating between positive and negative voltage conditions, thus providing insight into the dynamics of the streamers under alternating polarity switches. It is shown that the simultaneous ignition of both streamers, as well as using the pulsed DC conditions, providing both an enhanced discharge and an increased surface coverage. It is also shown that additional streamer branching may occur in a cross section that is difficult to experimentally observe. The enhanced discharge and surface coverage may be beneficial to many applications such as, but are not limited to: air purification, volatile organic compound removal, and plasma enhanced catalysis.

Investigation of dual-frequency effect on the ion energy and flux in Torr-regime plasma by a two-dimensional GPU-PIC simulation

Dual frequency (DF) capacitively coupled plasma (CCP) equipment has been widely used in semiconductor processing and requires particle-in-cell (PIC) simulations to investigate the nonlinear particle dynamics. It is believed that DF driving controls the electron density and ion energy separately, but a strong coupling exists between the two frequencies in reality. The two-dimensional (2D) PIC simulation of DF CCPs under deposition process conditions has not yet been reported due to the heavy computational load that can be resolved with a graphics processing unit (GPU) computation. This study quantitatively investigates the Torr-regime DF CCP using a 2D GPU-PIC simulation. The increase of the low-frequency (LF) power enhances ion transport, which results in the rise of plasma potential, the increase of sheath thickness, and the reduction of the electron density. The ions exhibit the Maxwellian distribution due to the frequent charge-exchange collisions. The ion flux keeps uniformity while electron density becomes abruptly nonuniform with the increase of the LF power, which is suitable to maintain the quality of deposited films.

Formation and evolution of post-solitons following a high intensity laser-plasma interaction with a low-density foam target

The formation and evolution of post-solitons has been discussed for quite some time both analytically and through the use of particle-in-cell (PIC) codes. It is however only recently that they have been directly observed in laser-plasma experiments. Relativistic electromagnetic (EM) solitons are localised structures that can occur in collisionless plasmas. They consist of a low-frequency EM wave trapped in a low electron number-density cavity surrounded by a shell with a higher electron number-density. Here we describe the results of an experiment in which a 100 TW Ti:sapphire laser (30 fs, 800 nm) irradiates a TMPTA foam target with a focused intensity . A third harmonic ( nm) probe is employed to diagnose plasma motion for 25 ps after the main pulse interaction via Doppler-Spectroscopy. Both radiation-hydrodynamics and 2D PIC simulations are performed to aid in the interpretation of the experimental results. We show that the rapid motion of the probe critical-surface observed in the experiment might be a signature of post-soliton wall motion.

Analysis Design and Simulation of an Axially partitioned Dielectric loaded Bi frequency MILO

In this paper, a bi-frequency magnetically insulated line oscillator (MILO) was proposed and designed. The bi-frequency MILO proposed has two axially partitioned slow-wave interaction structures (SWS) and the second SWS is dielectric-loaded to create the frequency shift in the resonant frequency. The conventional MILO device design methodology was followed along with two SWSs separated by a segregation cavity. The dispersion relation of the dielectric-loaded SWS was calculated using an equivalent circuit approach. Furthermore, the cold analysis was carried out to find the energy stored in the different SWSs to validate the device oscillation frequency. The beam wave interaction behaviour and device RF output performance were investigated through 3D PIC (Particle-in-cell) simulation for typical diode voltage of 550 kV, and current 48 kA, respectively. Simulation results illustrate that the proposed MILO generates RF peak power of ~3.5 GW at frequencies 3.62 GHz and 3.72 GHz. The conversion efficiency of the device was ~13.25%.

Microinstabilities in the Transition Region of Weak Quasi-perpendicular Intracluster Shocks

Abstract Microinstabilities play important roles in both entropy generation and particle acceleration in collisionless shocks. Recent studies have suggested that in the transition region of quasi-perpendicular (Q ⊥) shocks in the high-beta (β = P gas/P B) intracluster medium (ICM), the ion temperature anisotropy due to the reflected-gyrating ions could trigger the Alfvén ion cyclotron (AIC) instability and the ion-mirror instability, while the electron temperature anisotropy induced by magnetic field compression could excite the whistler instability and the electron-mirror instability. Adopting the numerical estimates for ion and electron temperature anisotropies found in the particle-in-cell (PIC) simulations of Q ⊥ shocks with sonic Mach numbers, M s = 2–3, we carry out a linear stability analysis for these microinstabilities. The kinetic properties of the microinstabilities and the ensuing plasma waves on both ion and electron scales are described for wide ranges of parameters, including β and the ion-to-electron mass ratio. In addition, the nonlinear evolution of the induced plasma waves are examined by performing 2D PIC simulations with periodic boundary conditions. We find that for β ≈ 20–100, the AIC instability could induce ion-scale waves and generate shock surface ripples in supercritical shocks above the AIC critical Mach number, M AIC * ≈ 2.3 . Also, electron-scale waves are generated primarily by the whistler instability in these high-β shocks. The resulting multiscale waves from electron to ion scales are thought to be essential in the electron injection to diffusive shock acceleration in Q ⊥ shocks in the ICM.

Bright betatron x-rays generation from picosecond laser interactions with long-scale near critical density plasmas

Our previous experimental and three-dimensional (3D) particle-in-cell (PIC) simulation results demonstrated that a well-directed electron beam with space charge of about μC and maximum energy of 100 MeV can be generated via a sub-petawatt, picosecond laser pulse interacting with a long-scale near-critical-density plasma. Effective laser energy coupling into hot electrons occurs in the presence of strong self-generated quasistatic electric and magnetic fields that confine fast electrons in relativistic ion channels. Here, we report results of 3D PIC simulations, which show that this direct laser accelerated electron beam can work as a compact high-brightness source of x rays. The relativistic electrons make betatron oscillations in the transverse fields of the ion channel and emit a bright broadband x-ray radiation with the critical energy of about 5 keV. Due to the huge number of accelerated electrons, our simulation shows that with a picosecond, 20 J laser pulse, an x-ray spectrum with a photon number of 7×1011 (>1 keV) can be generated, resulting into a peak flux of 2 ×108 photons/eV and a brilliance of 3.3×1020 photons/s/mm2/mrad2/0.1%BW.