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Register a new userA spectral, quasi-cylindrical and dispersion-free Particle-In-Cell algorithm
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We propose a spectral Particle-In-Cell (PIC) algorithm that is based on the combination of a Hankel transform and a Fourier transform. For physical problems that have close-to-cylindrical symmetry, this algorithm can be much faster than full 3D PIC algorithms. In addition, unlike standard finite-difference PIC codes, the proposed algorithm is free of numerical dispersion. This algorithm is benchmarked in several situations that are of interest for laser-plasma interactions. These benchmarks show that it avoids a number of numerical artifacts, that would otherwise affect the physics in a standard PIC algorithm - including the zero-order numerical Cherenkov effect.
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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 then demonstrate how the timestep constraints of conventional electrostatic particle-in-cell methods are relaxed by the speed-limiting approach, thus enabling larger timesteps and faster simulations. These results indicate that the SLPIC method is a fast, accurate, and powerful technique for modeling plasmas wherein electron kinetic behavior is nontrivial (such that a fluid/Boltzmann representation for electrons is inadequate) but evolution is on ion timescales.
Particle dynamics are investigated in plasma turbulence, using self-consistent kinetic simulations, in two dimensions. In steady state, the trajectories of single protons and proton-pairs are studied, at different values of plasma beta (ratio between kinetic and magnetic pressure). For single-particle displacements, results are consistent with fluids and magnetic field line dynamics, where particles undergo normal diffusion for very long times, with higher beta being more diffusive. In an intermediate time range, with separations lying in the inertial range, particles experience an explosive dispersion in time, consistent with the Richardson prediction. These results, obtained for the first time with a self-consistent kinetic model, are relevant for astrophysical and laboratory plasmas, where turbulence is crucial for heating, mixing and acceleration processes.
The expansion of a magnetized high-pressure plasma into a low-pressure ambient medium is examined with particle-in-cell (PIC) simulations. The magnetic field points perpendicularly to the plasmas expansion direction and binary collisions between particles are absent. The expanding plasma steepens into a quasi-electrostatic shock that is sustained by the lower-hybrid (LH) wave. The ambipolar electric field points in the expansion direction and it induces together with the background magnetic field a fast E cross B drift of electrons. The drifting electrons modify the background magnetic field, resulting in its pile-up by the LH shock. The magnetic pressure gradient force accelerates the ambient ions ahead of the LH shock, reducing the relative velocity between the ambient plasma and the LH shock to about the phase speed of the shocked LH wave, transforming the LH shock into a nonlinear LH wave. The oscillations of the electrostatic potential have a larger amplitude and wavelength in the magnetized plasma than in an unmagnetized one with otherwise identical conditions. The energy loss to the drifting electrons leads to a noticable slowdown of the LH shock compared to that in an unmagnetized plasma.
Quasi-phase matched direct laser acceleration (DLA) of electrons can be realized with guided, radially polarized laser pulses in density-modulated plasma waveguides. A 3-D particle-in-cell model has been developed to describe the interactions among the laser field, injected electrons, and the background plasma in the DLA process. Simulations have been conducted to study the scheme in which seed electron bunches with moderate energies are injected into a plasma waveguide and the DLA is performed by use of relatively low-power (0.5-2 TW) laser pulses. Selected bunch injection delays with respect to the laser pulse, bunch lengths, and bunch transverse sizes have been studied in a series of simulations of DLA in a plasma waveguide. The results show that the injection delay is important for controlling the final transverse properties of short electron bunches, but it also affects the final energy gain. With a long injected bunch length, the enhanced ion-focusing force helps to collimate the electrons and a relatively small final emittance can be obtained. DLA efficiency is reduced when a bunch with a greater transverse size is injected; in addition, micro-bunching is clearly observed due to the focusing and defocusing of electrons by the radially directed Lorentz force. DLA should be performed with a moderate laser power to maintain favorable bunch transverse properties, while the waveguide length can be extended to obtain a higher maximum energy gain, with the commensurate increase of laser pulse duration and energy.
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.
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