We design and develop a new Particle-in-Cell (PIC) method for plasma simulations using Deep-Learning (DL) to calculate the electric field from the electron phase space. We train a Multilayer Perceptron (MLP) and a Convolutional Neural Network (CNN) to solve the two-stream instability test. We verify that the DL-based MLP PIC method produces the correct results using the two-stream instability: the DL-based PIC provides the expected growth rate of the two-stream instability. The DL-based PIC does not conserve the total energy and momentum. However, the DL-based PIC method is stable against the cold-beam instability, affecting traditional PIC methods. This work shows that integrating DL technologies into traditional computational methods is a viable approach for developing next-generation PIC algorithms.
With an implicit Particle-in-cell/Monte Carlo model, capacitively coupled plasmas are studied in two-dimensional and axisymmetric geometry. Self-bias dc voltage effects are self-consistently considered. Due to finite length effects, the self-bias dc voltages show sophisticating relations with the electrode areas. Two-dimensional kinetic effects are also illuminated. Compare to the fluid mode, PIC/MC model is numerical-diffusion-free and thus finer properties of the plasmas are simulated.
Recent increases in supercomputing power, driven by the multi-core revolution and accelerators such as the IBM Cell processor, graphics processing units (GPUs) and Intel's Many Integrated Core (MIC) technology have enabled kinetic simulations of plasmas at unprecedented resolutions, but changing HPC architectures also come with challenges for writing efficient numerical codes. This paper describes the Plasma Simulation Code (PSC), an explicit, electromagnetic particle-in-cell code with support for different order particle shape functions. We focus on two distinguishing feature of the code: pat…
A new spectral particle-in-cell (PIC) method for plasma modeling is presented and discussed. In the proposed scheme, the Fourier-Bessel transform is used to translate the Maxwell equations to the quasi-cylindrical spectral domain. In this domain, the equations are solved analytically in time, and the spatial derivatives are approximated with high accuracy. In contrast to the finite-difference time domain (FDTD) methods that are commonly used in PIC, the developed method does not produce numerical dispersion, and does not involve grid staggering for the electric and magnetic fields. These featu…
Particle-in-cell codes are the most widely used simulation tools for kinetic studies of ultra-intense laser-plasma interactions. Using the motion of a single electron in a plane electromagnetic wave as a benchmark problem, we show surprising deterioration of the numerical accuracy of the PIC algorithm with increasing normalized wave amplitude for typical time-step and grid sizes. Two significant sources of errors are identified: strong acceleration near stopping points and the temporal field interpolation. We propose adaptive electron sub-cycling coupled with a third order temporal interpolati…
We formulate a possible description of the deflection of a relativistic $e^-$ beam in an inhomogeneous copper plasma, encountered by the beam when propagating through a accelerating cell that has undergone a high electric-field RF-breakdown. It is well known that an inhomogeneous plasma forms and may last for up to a few micro-seconds, until recombination in an accelerating structure where a field-emission triggers melting and ionization of RF-cell wall deformity. We present a preliminary model for the beam deflection due to collective plasma response based upon the beam density, plasma densit…
Incoherent Thomson scattering is a non-intrusive technique commonly used for measuring local plasma density. Within low-density, low-temperature plasma's and for sufficient laser intensity, the laser may perturb the local electron density via the ponderomotive force, causing the diagnostic to become intrusive and leading to erroneous results. A theoretical model for this effect is validated numerically via kinetic simulations of a quasi-neutral plasma using the Particle-in-Cell technique.
Comment on "Impact of particle number and cell-size in fully implicit charge- and energy-conserving particle-in-cell schemes" by N. Savard et al., Phys. Plasmas 32, 073903 (2025)
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
For simulating laser-plasma interactions, we developed a parallel, multi-dimensional, fully relativistically particle-in-cell (PIC) code, named YUNIC. The core algorithm is introduced, including field solver, particle pusher, field interpolation, and current interpolation. In addition to the classical electromagnetic interaction in plasmas, nonlinear Compton scattering and nonlinear Breit-Wheeler pair production are also implemented based on Monte-Carlo methods to study quantum electrodynamics (QED) processes. We benchmark YUNIC against theories and other PIC codes through several typical case…
This paper concerns development of a high-performance implementation of the Particle-in-Cell method for plasma simulation on Intel Xeon Phi coprocessors. We discuss suitability of the method for Xeon Phi architecture and present our experience of porting and optimization of the existing parallel Particle-in-Cell code PICADOR. Direct porting with no code modification gives performance on Xeon Phi close to 8-core CPU on a benchmark problem with 50 particles per cell. We demonstrate step-by-step application of optimization techniques such as improving data locality, enhancing parallelization effi…
The global electrostatic mode in pair-ion plasmas is discussed for cylindric geometry and for a radially inhomogeneous equilibrium density. In the case of a Gaussian radial density profile, exact analytical eigen solutions are found in terms of the Kummer confluent hypergeometric functions. The mode is identified as a convective cell propagating in the poloidal and axial direction, having at the same time a standing wave structure in the radial direction.
The paper provides a tutorial to the conceptual layout of a self-consistently coupled Particle-In-Cell/Test-Particle model for the kinetic simulation of sputtering transport in capacitively coupled plasmas at low gas pressures. It explains when a kinetic approach is actually needed and which numerical concepts allow for the inherent nonequilibrium behavior of the charged and neutral particles. At the example of a generic sputtering discharge both the fundamentals of the applied Monte Carlo methods as well as the conceptual details in the context of the sputtering scenario are elaborated on. Fi…
The propagation of intense laser pulses and the generation of high energy electrons from the underdense plasmas are investigated using two dimensional particle-in-cell simulations. When the ratio of the laser power and a critical power of relativistic self-focusing is the optimal value, it propagates stably and electrons have maximum energies.
This paper discusses temporally continuous and discrete forms of the speed-limited particle-in-cell (SLPIC) method first treated by Werner et al. [Phys. Plasmas 25, 123512 (2018)]. The dispersion relation for a 1D1V electrostatic plasma whose fast particles are speed-limited is derived and analyzed. By examining the normal modes of this dispersion relation, we show that the imposed speed-limiting substantially reduces the frequency of fast electron plasma oscillations while preserving the correct physics of lower-frequency plasma dynamics (e.g. ion acoustic wave dispersion and damping). We the…
A self-consistent fluid model developed for simulations of micro- gravity dusty plasma experiments has for the first time been used to model asymmetric dusty plasma experiments in a modified GEC reference cell with gravity. The numerical results are directly compared with experimental data and the experimentally determined dependence of global discharge parameters on the applied driving potential and neutral gas pressure is found to be well matched by the model. The local profiles important for dust particle transport are studied and compared with experimentally determined profiles. The radial…
Cold atmospheric plasma (CAP) was shown to affect cells not only directly, but also indirectly by means of plasma pre-treated solution. This study investigated a new application of CAP generated in deionized (DI) water for the cancer therapy. In our experiments, the CAP solution was generated in DI water using helium as carrier gas. We report on the effects of this plasma solution in breast (MDA-MD-231) and gastric (NCI-N87) cancer cells. The results revealed that apoptosis efficiency was dependent on the plasma exposure time and on the levels of reactive oxygen and nitrogen species (ROS and R…
Numerical simulations of beam-plasma instabilities may produce quantitatively incorrect results because of unrealistically high initial noise from which the instabilities develop. Of particular importance is the wakefield noise, the potential perturbations that have a phase velocity which is equal to the beam velocity. Controlling the noise level in simulations may offer the possibility of extrapolating simulation results to the more realistic low-noise case. We propose a novel method for generating wakefield noise with a controllable amplitude by randomly located charged rods propagating ahea…
We extend the simplex-in-cell (SIC) technique recently introduced in the context of collisionless dark matter fluids (Abel et al. 2012; Hahn et al. 2012) to the case of collisionless plasmas. The six-dimensional phase space distribution function $f(\mathbf x,\mathbf v)$ is represented by an ensemble of three-dimensional manifolds, which we refer to as sheets. The electric potential field is obtained by solving the Poisson equation on a uniform mesh, where the charge density is evaluated by a spatial projection of the phase space sheets. The SIC representation of phase space density facilitates…
The plasma force on grains of specified charge and height in a collisional DC plasma sheath are calculated using the multidimensional particle in cell code COPTIC. The background ion velocity distribution functions for the unperturbed sheath vary substantially with collisionality. The grain force is found to agree quite well with a combination of background electric field force plus ion drag force. However, the drag force must take account of the non-Maxwellian (and spatially varying) ion distribution function, and the collisional drag enhancement. It is shown how to translate the dimensionles…
Non-thermal atmospheric plasma (NTAP) can be applied to living tissues and cells as a novel technology for cancer therapy. Even though studies report on the successful use of NTAP to directly irradiate cancer cells, this technology can cause cell death only in the upper 3-5 cell layers. We report on a NTAP argon solution generated in DI water for treating human gastric cancer cells (NCl-N87). Our findings showed that the plasma generated in DI water during a 30-minute treatment had the strongest affect in inducing apoptosis in cultured human gastric cancer cells. This result can be attributed …
Ideally, binary-collision algorithms conserve kinetic momentum and energy. In practice, the finite size of collision cells and the finite difference in the particle locations affect the conservation properties. In the present work, we investigate numerically how the accuracy of these algorithms is affected when the size of collision cells is large compared with gradient scale length of the background plasma, a parameter essential in full-f fusion plasma simulations. Additionally, we discuss implications for the conserved quantities in drift-kinetic formulations when fluctuating magnetic and el…
Basic principles of particle-in-cell (PIC ) codes with the main application for plasma-based acceleration are discussed. The ab initio full electromagnetic relativistic PIC codes provide the most reliable description of plasmas. Their properties are considered in detail. Representing the most fundamental model, the full PIC codes are computationally expensive. The plasma-based acceler- ation is a multi-scale problem with very disparate scales. The smallest scale is the laser or plasma wavelength (from one to hundred microns) and the largest scale is the acceleration distance (from a few centim…
PIC-JR$_{ho}$m: a pseudo-spectral Particle-In-Cell formulation with arbitrary charge and current densities time dependencies for the modeling of relativistic plasmas
A new method that solves concurrently the multi-fluid and Maxwell's equations has been developed for plasma simulations. By calculating the stress tensor in the multi-fluid momentum equation by means of computational particles moving in a self-consistent electromagnetic field, the kinetic effects are retained while solving the multi-fluid equations. The Maxwell's and multi-fluid equations are discretized implicitly in time enabling kinetic simulations over time scales typical of the fluid simulations. The fluid-kinetic Particle-in-Cell solver has been implemented in a three-dimensional electro…
In this dissertation, a fully object-oriented, fully relativistic, multi-dimensional Particle-In-Cell code was developed and applied to answer key questions in plasma-based accelerator research. The simulations increase the understanding of the processes in laser plasma and beam-plasma interaction, allow for comparison with experiments, and motivate the development of theoretical models. The simulations support the idea that the injection of electrons in a plasma wave by using a transversely propagating laser pulse is possible. The beam parameters of the injected electrons found in the simulat…
The interaction of two lasers with a difference frequency near that of the ambient plasma frequency produces beat waves that can resonantly accelerate thermal electrons. These beat waves can be used to drive electron current and thereby embed magnetic fields into the plasma [D. R. Welch et al., Phys. Rev. Lett. 109, 225002 (2012)]. In this paper, we present two-dimensional particle-in-cell simulations of the beat-wave current-drive process over a wide range of angles between the injected lasers, laser intensities, and plasma densities. We discuss the application of this technique to the magnet…
SMILEI is a collaborative, open-source, object-oriented (C++) particle-in-cell code. To benefit from the latest advances in high-performance computing (HPC), SMILEI is co-developed by both physicists and HPC experts. The code's structures, capabilities, parallelization strategy and performances are discussed. Additional modules (e.g. to treat ionization or collisions), benchmarks and physics highlights are also presented. Multi-purpose and evolutive, SMILEI is applied today to a wide range of physics studies, from relativistic laser-plasma interaction to astrophysical plasmas.
Implicit particle-in-cell codes offer advantages over their explicit counterparts in that they suffer weaker stability constraints on the need to resolve the higher frequency modes of the system. This feature may prove particularly valuable for modeling the interaction of high-intensity laser pulses with overcritical plasmas, in the case where the electrostatic modes in the denser regions are of negligible influence on the physical processes under study. To this goal, we have developed the new two-dimensional electromagnetic code ELIXIRS (standing for ELectromagnetic Implicit X-dimensional Ite…
We present the Photon-Plasma code, a modern high order charge conserving particle-in-cell code for simulating relativistic plasmas. The code is using a high order implicit field solver and a novel high order charge conserving interpolation scheme for particle-to-cell interpolation and charge deposition. It includes powerful diagnostics tools with on-the-fly particle tracking, synthetic spectra integration, 2D volume slicing, and a new method to correctly account for radiative cooling in the simulations. A robust technique for imposing (time-dependent) particle and field fluxes on the boundarie…
When a charged particle moves through a plasma at a speed much higher than the thermal velocity of the plasma, it is subjected to the force of the electrostatic field induced in the plasma by itself and loses its energy. This process is well-known as the stopping power of a plasma. In this paper we show that the same process works in particle-in-cell (PIC) simulations as well and the energy loss rate of fast particles due to this process is mainly determined by the number of plasma electrons contained in the electron skin depth volume. However, since there are generally very few particles in t…
Based on the particle-in-cell (PIC) plasma simulation method, the speed-limited PIC (SLPIC) method delivers faster kinetic plasma simulation in cases where the particle distributions evolve slowly compared with the maximum stable PIC timestep. SLPIC thus offers more feasible, fully kinetic simulation in regimes that historically have required fluid approaches, such as magnetohydrodynamic (MHD), two-fluid, or Boltzmann electron treatments. In particular, SLPIC allows an explicit time advance with steps much larger than the inverse plasma frequency, avoiding the instability explicit PIC faces wi…
Particle-In-Cell (PIC) methods are frequently used for kinetic, high-fidelity simulations of plasmas. Implicit formulations of PIC algorithms feature strong conservation properties, up to numerical round-off errors, and are not subject to time-step limitations which make them an attractive candidate to use in simulations fusion plasmas. Currently they remain prohibitively expensive for high-fidelity simulation of macroscopic plasmas. We investigate how amortized solvers can be incorporated with PIC methods for simulations of plasmas. Incorporated into the amortized solver, a neural network pre…
Studies on the interaction of plasma generated at atmospheric pressure and at room temperature (low temperature plasma or just cold plasma) with biological cells and tissues have revealed that cold plasma has therapeutic effects that form the basis for new medical therapies. Cold plasma exhibits bactericidal properties and at low doses can modulate cell functions, including proliferation, attachment, and migration. Research in the last two decades has shown that cold plasma can be used for wound healing and can kill cancer cells in a selective manner. This paper describes the fundamental scien…
Particle-In-Cell (PIC) simulations of relativistic flowing plasmas are of key interest to several fields of physics (including e.g. laser-wakefield acceleration, when viewed in a Lorentz-boosted frame), but remain sometimes infeasible due to the well-known numerical Cherenkov instability (NCI). In this article, we show that, for a plasma drifting at a uniform relativistic velocity, the NCI can be eliminated by simply integrating the PIC equations in Galilean coordinates that follow the plasma (also sometimes known as comoving coordinates) within a spectral analytical framework. The elimination…
A lot of plasma physics problems are not amenable to exact solutions due to many reasons. It is worth mentioning among them, for example, nonlinearity of the motion equations, variable coefficients or non lineal conditions on known or unknown borders. To solve these problems, different types of approximations which are combinations of analytical and numerical simulation methods are put into practice. The problem of plasma behavior in numerous varieties of a minimum-B magnetic trap where the plasma is heated under electron cyclotron resonance (ECR) conditions is the subject of numerical simulat…
Energy conserving particle-in-cell schemes are constructed for a class of reduced relativistic Vlasov--Maxwell equations of laser-plasma interaction. Discrete Poisson equation is also satisfied by the numerical solution. Specifically, distribution function is discretized using particle-in-cell method, discretization of electromagnetic fields is done using compatible finite element method in the framework of finite element of exterior calculus, and time discretization used is based on discrete gradient method combined with Poisson splitting. Numerical experiments of parametric instability are d…
We derive the kinetic theory of fluctuations in physically and numerically stable particle-in-cell (PIC) simulations of electrostatic plasmas. The starting point is the single-time correlations at the simulation start between the statistical fluctuations of weighted densities of macroparticle centers in the plasma particle phase-space. The single-time correlations at all time steps and in each spatial grid cell are then determined from the Laplace-Fourier transforms of the discretized Klimontovich-like equation for the macroparticles and Maxwell's equations for the fields as computed by modern…
We present the results of numerical studies of laser pulse propagating in a 3.5 cm Rb vapor cell in the linear dispersion regime by using a 1D model and a 2D code that has been modified for our special case. The 2D simulation finally aimed at finding laser beam parameters suitable to make the Rb vapor fully ionized to obtain a uniform, 10 m-long, at least 1 mm in radius plasma in the next step for the AWAKE experiment.
We analyze here in some detail, the derivation of the Particle and Monte Carlo methods of plasma simulation, such as Particle in Cell (PIC), Monte Carlo (MC) and Particle in Cell / Monte Carlo (PIC/MC) from formal manipulation of transport equations.
The thermal motion of a dust particle levitated in a plasma chamber is similar to that described by Brownian motion in many ways. The primary differences between a dust particle in a plasma system and a free Brownian particle is that in addition to the random collisions between the dust particle and the neutral gas atoms, there are electric field fluctuations, dust charge fluctuations, and correlated motions from the unwanted continuous signals originating within the plasma system itself. This last contribution does not include random motion and is therefore separable from the random motion in…
Ion-scale magnetospheres have been observed around comets, weakly-magnetized asteroids, and localized regions on the Moon, and provide a unique environment to study kinetic-scale plasma physics, in particular in the collisionless regime. In this work, we present the results of particle-in-cell simulations that replicate recent experiments on the Large Plasma Device at the University of California, Los Angeles. Using high-repetition rate lasers, ion-scale magnetospheres were created to drive a plasma flow into a dipolar magnetic field embedded in a uniform background magnetic field. The simulat…
An implicit, conservative and asymptotic-preserving electrostatic particle-in-cell algorithm for arbitrarily magnetized plasmas in uniform magnetic fields
One dimensional Particle-in-cell simulations using OSIRIS-4.0 has been conducted to study the interaction of a laser electromagnetic pulse with an overdense magnetized plasma target. The external magnetic field has been chosen to be directed along the laser propagation direction. This geometry supports the propagation of right (R) and left (L) circularly polarised electromagnetic waves in the plasma. The laser pulse is allowed to propagate inside the plasma when its frequency falls in the pass band of the dispersion curves of L and/or R waves. The strength of the applied external magnetic fiel…
The characteristics of the surface waves along the interface between a plasma and a dielectric material have been investigated using kinetic Particle-In-Cell (PIC) simulations. A microwave source of GHz frequency has been used to trigger the surface wave in the system. The outcome indicates that the surface wave gets excited along the interface of plasma and the dielectric tube and appears as light and dark patterns in the electric field profiles. The dependency of radiation pressure on the dielectric permittivity and supplied input frequency has been investigated. Further, we assessed the cap…
We describe Pegasus, a new hybrid-kinetic particle-in-cell code tailored for the study of astrophysical plasma dynamics. The code incorporates an energy-conserving particle integrator into a stable, second-order--accurate, three-stage predictor-predictor-corrector integration algorithm. The constrained transport method is used to enforce the divergence-free constraint on the magnetic field. A delta-f scheme is included to facilitate a reduced-noise study of systems in which only small departures from an initial distribution function are anticipated. The effects of rotation and shear are implem…
Here we present the mathematical and numerical details of a general hybrid model for plasmas. All grid quantities are stored at cell centers on the grid. The most common discretization of the fields in PIC solvers is to have the electric and magnetic fields staggered, introduced by Yee. This automatically ensures that div(B)=0, down to round-off errors. Here we instead present a cell centered discretization of the magnetic field. That the standard cell centered second order stencil for rot(E) in Faraday's law will preserve div(B)=0 was noted by Toth. The advantage of a cell centered discretiza…
We describe a new electrostatic Particle-In-Cell (PIC) code in curvilinear geometry called Curvilinear PIC (CPIC). The code models the microscopic (kinetic) evolution of a plasma with the PIC method, coupled with an adaptive computational grid that can conform to arbitrarily shaped domains. CPIC is particularly suited for multiscale problems associated with the interaction of complex objects with plasmas. A map is introduced between the physical space and the logical space, where the grid is uniform and Cartesian. In CPIC, most operations are performed in logical space. CPIC was designed follo…
Following some recent unexpected hints of neutron production in setups like high-voltage atmospheric discharges and plasma discharges in electrolytic cells, we present a measurement of the neutron flux in a configuration similar to the latter. We use two different types of neutron detectors, poly-allyl-diglicol-carbonate (PADC, aka CR-39) tracers and Indium disks. At 95% C.L. we provide an upper limit of 1.5 neutrons cm^-2 s^-1 for the thermal neutron flux at ~5 cm from the center of the cell. Allowing for a higher energy neutron component the largest allowed flux is 64 neutrons cm^-2 s^-1. Th…
Superconducting Radio Frequency (SRF) cavities performance preservation is crucial, from vertical test to accelerator operation. Field Emission (FE) is still one of the performance limiting factors to overcome and plasma cleaning has been proven successful by the Spallation Neutron Source (SNS), in cleaning field emitters and increasing the work function of Nb. A collaboration has been established between Fermi National Accelerator Laboratory (FNAL), SLAC National Accelerator Laboratory and Oak Ridge National Laboratory (ORNL) with the purpose of applying plasma processing to the Linac Coheren…
