Ion Current Screening Modeling of the Ion–Weibel Instability

Ion–Weibel instability (IWI) is an important mechanism of generating a magnetic field in supernova remnants; it plays a key role in the generation of high-energy cosmic rays. Computational efficiency has been a bottleneck in numerical exploration of the large-scale evolution of IWI. Here I report a new hybrid particle-in-cell (PIC) method that can quickly simulate IWI. The method is based on a new model that describes the relation of the ion current and its magnetic field under the electron screening. The new method’s computational efficiency is nearly two orders of magnitude higher than that of the PIC method. This method is suitable for the full-scale simulation of the IWI in laser-plasma experiments and supernova remnants.

A fast convergence fourth-order Vlasov model for Hall thruster ionization oscillation analyses

A 1D1V hybrid Vlasov-fluid model was developed for this study to elucidate ionization oscillations of Hall thrusters (HTs). The Vlasov equation for ions velocity distribution function (IVDF) with ionization source term is solved using a constrained interpolation profile conservative semi-Lagrangian (CIP-CSL) method. The fourth-order weighted essentially non-oscillatory (4th WENO) limiter is applied to the first derivative term to minimize numerical oscillation in the discharge oscillation analyses. The fourth-order spatial accuracy is verified through a 1D scalar test case. Nonoscillatory and high-resolution features of the Vlasov model are confirmed by simulating the test cases of the Vlasov–Poisson (VP) system and by comparing the results with a particle-in-cell (PIC) method. A 1D1V Hall thruster simulation is performed through the hybrid Vlasov-fluid model. The ionization oscillation is analysed. The macroscopic plasma properties are compared with those obtained from a hybrid PIC method. The comparison indicates that the hybrid Vlasov-fluid model yields noiseless results and that the steady-state waveform is calculable in a short time period.

Integrated study on the comprehensive magnetic-field configuration performance in the 150 kW superconducting magnetoplasmadynamic thruster

Higher magnetic fields are always favoured in the magnetoplasmadynamic thruster (MPDT) due to its superior control of the plasma profile and acceleration process. This paper introduces the world's first integrated study on the 150 kW level AF-MPDT equipped with a superconductive coil. A completely new way of using superconducting magnet technology to confine plasma with high energy and extremely high temperatures is proposed. Using the PIC method of microscopic particle simulation, the plasma magnetic nozzle effect and performance of the MPDT under different magnetic-field conditions were studied. The integrated experiment used demonstrated that, in conjunction with the superconducting coil, greater homogeneity and a stronger magnetic field not only caused more even cathode ablation and improved its lifespan but also improved the performance of the MPDT (maximum thrust was 4 N at 150 kW, 0.56 T). Maximum thrust efficiency reached 76.6% and the specific impulse reached 5714 s.

A scaled MP-PIC method for bubbling fluidization

Coarse-grained methods have been widely used in simulations of gas-solid fluidization. However, as a key parameter, the coarse-graining ratio, and its relevant scaling law is still far from reaching a consensus. In this work, a scaling law is developed based on a similarity analysis, and then it is used to scale the multi-phase particle-in-cell (MP-PIC) method, and validated in the simulation of two bubbling fluidized beds. The simulation result shows this scaled MP-PIC can reduce the errors of solids volume fraction and velocity distributions over a wide range of coarse-graining ratios. In future, we expect that a scaling law with consideration of the heterogeneity inside a parcel or numerical particle will further improve the performance of coarse-grained modeling in simulation of fluidized beds.

Geometric electrostatic particle-in-cell algorithm on unstructured meshes

We present a geometric particle-in-cell (PIC) algorithm on unstructured meshes for studying electrostatic perturbations with frequency lower than electron gyrofrequency in magnetized plasmas. In this method, ions are treated as fully kinetic particles and electrons are described by the adiabatic response. The PIC method is derived from a discrete variational principle on unstructured meshes. To preserve the geometric structure of the system, the discrete variational principle requires that the electric field is interpolated using Whitney 1-forms, the charge is deposited using Whitney 0-forms and the electric field is computed by discrete exterior calculus. The algorithm has been applied to study the ion Bernstein wave (IBW) in two-dimensional magnetized plasmas. The simulated dispersion relations of the IBW in a rectangular region agree well with theoretical results. In a two-dimensional circular region with fixed boundary condition, the spectrum and eigenmode structures of the IBW are obtained from simulations. We compare the energy conservation property of the geometric PIC algorithm derived from the discrete variational principle with that of previous PIC methods on unstructured meshes. The comparison shows that the new PIC algorithm significantly improves the energy conservation property.

PIC methods in astrophysics: simulations of relativistic jets and kinetic physics in astrophysical systems

The Particle-In-Cell (PIC) method has been developed by Oscar Buneman, Charles Birdsall, Roger W. Hockney, and John Dawson in the 1950s and, with the advances of computing power, has been further developed for several fields such as astrophysical, magnetospheric as well as solar plasmas and recently also for atmospheric and laser-plasma physics. Currently more than 15 semi-public PIC codes are available which we discuss in this review. Its applications have grown extensively with increasing computing power available on high performance computing facilities around the world. These systems allow the study of various topics of astrophysical plasmas, such as magnetic reconnection, pulsars and black hole magnetosphere, non-relativistic and relativistic shocks, relativistic jets, and laser-plasma physics. We review a plethora of astrophysical phenomena such as relativistic jets, instabilities, magnetic reconnection, pulsars, as well as PIC simulations of laser-plasma physics (until 2021) emphasizing the physics involved in the simulations. Finally, we give an outlook of the future simulations of jets associated to neutron stars, black holes and their merging and discuss the future of PIC simulations in the light of petascale and exascale computing.

A Phylogenetic Independent Contrast Method under the Ornstein-Uhlenbeck Model and its Applications in Correlated Evolution

Phylogenetic comparative methods are essential in studying the evolution of traits across a phylogeny. Felsenstein's phylogenetic independent contrast (PIC) method and the generalized least squares (GLS) regression were often utilized to study whether evolutionary changes between traits were correlated. However, a neutral Brownian model is assumed in the PIC method, which impacts the performance of the PIC method when the trait is subject to adaptation. In recent years, the Ornstein-Uhlenbeck (OU) model has attracted increasing attention in studying the evolution of traits with stabilizing selection. In this study, we extended Felsenstein's PIC method under the OU model, which we termed OU-PIC. We simulated trait evolution under the OU model on phylogenetic trees with 8, 10, and 55 species. Compared to the PIC method, the OU-PIC method with correct stabilizing selection parameters achieved an appropriate type I error rate, the highest test power, and the lowest mean squared error. We presented a concise proof of the intrinsic connection between the OU-PIC and the generalized least squares (GLS) regression method in evaluating correlated evolution under the OU model. The OU-PIC method has a broad range of applications when trait evolution could be sufficiently modeled by the OU process. Compared with other phylogenetic comparative methods, OU-PIC avoids the inverse of the covariance matrix and would facilitate the analysis of correlated evolution on large phylogenies.

Particle acceleration in 3D current sheets with magnetic islands: energy, density and pitch angle distributions

<div> <div> <div> <p>We will overview particle motion in 3D Harris-type RCSs without and with magnetic islands using particle-in-cell (PIC) method considering the plasma feedback to electromagnetic fields. We evaluate particle energy gains and pitch angle distributions (PADs) of accelerated particles of both changes in different locations inside current sheets as seen under the different directions by a virtual spacecraft passing through. The RCS parameters are considered comparable to heliosphere and solar wind conditions. </p> <p>The energy gains and the PADs of particles are shown to change depending on a topology of magnetic fields.  We report separation of electrons from ions at acceleeration in current sheets with strong guiding fields  and formation of transit and bounced beams from the particles of the same charge. The  transit particles are shown to form  bi-directional energetic electron beams (strahls), while bounced particles are mainly account from driopout fluxes in the heliosphere. In topologies with weak guding field strahls are mainly present inside the magneticislands and located closely above/below the X-nullpoints in the inflow regions. As the guiding field becomes larger, the regions with bi-directional strahls are compressed towards small areas in the exhausts of current sheets. Mono-directional strahls with PADS along 0 or 180 degrees are found quasi-parallel to the magnetic field lines near the X-nullpoint due to the dominant Fermi-type magnetic curvature drift acceleration. Meanwhile, high-energy electrons confined inside magnetic islands create PADs about 90◦. </p> </div> </div> </div>

Simulation of Velocity Evolution of a Cold Collision-less Non-Magnetised Plasma by Particle-in-Cell Method

This work presents simple numerical simulation algorithm to analyse the velocity evolution of high density non-magnetized glow discharge (cold) collision-less plasma using Particle-in-Cell (PIC) method. In the place of millions of physical electrons and background ions, fewer particles called super particles are used for simulation to capture the plasma properties such as particle velocity, particle energy and electrical field of the plasma system. The plasma system which is of interest in this work is weakly coupled plasma having quasi-neutrality nature. Simulation results showed symmetric velocity distribution about zero with slight left skewness, indicating static system. The order of directional velocity of individual particle seems to agree with the input electron temperature of the considered plasma system. The particle and field energy evolution were observed having fluctuations about zero which indicates that the system is equilibrating. This work marks the preliminary work to study the transport of plasma species in plasma column of gliding arc discharge.

Electron dynamics in plasmons

The Particle-in-Cell (PIC) method for plasmons provides a mechanical, single-particle picture of plasmon resonances by tracking in time the movement of all the individual conduction electrons.