A Grid-Based Coulomb Collision Model for PIC Codes
01 Jan 1996-Journal of Computational Physics (Academic Press Professional, Inc.)-Vol. 123, Iss: 1, pp 169-181
TL;DR: In this article, a grid-based collision field is proposed to model the intermediate regime between collisionless and Coulomb collision dominated plasmas in particle-in-cell codes.
About: This article is published in Journal of Computational Physics.The article was published on 1996-01-01. It has received 134 citations till now. The article focuses on the topics: Coulomb collision & Langevin equation.
Citations
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TL;DR: Particle-in-cell (PIC) methods have a long history in the study of laser-plasma interactions as discussed by the authors, and they have been widely used in the literature.
Abstract: Particle-in-cell (PIC) methods have a long history in the study of laser-plasma interactions. Early electromagnetic codes used the Yee staggered grid for field variables combined with a leapfrog EM-field update and the Boris algorithm for particle pushing. The general properties of such schemes are well documented. Modern PIC codes tend to add to these high-order shape functions for particles, Poisson preserving field updates, collisions, ionisation, a hybrid scheme for solid density and high-field QED effects. In addition to these physics packages, the increase in computing power now allows simulations with real mass ratios, full 3D dynamics and multi-speckle interaction. This paper presents a review of the core algorithms used in current laser-plasma specific PIC codes. Also reported are estimates of self-heating rates, convergence of collisional routines and test of ionisation models which are not readily available elsewhere. Having reviewed the status of PIC algorithms we present a summary of recent applications of such codes in laser-plasma physics, concentrating on SRS, short-pulse laser-solid interactions, fast-electron transport, and QED effects.
1,203 citations
TL;DR: In this paper, the kinetic theory basis of the particle simulation method is first described and state-of-the-art probabilistic treatments of collisions are described for electron-molecule, ion-molescule, molecule-molcule, and Coulomb collisions.
Abstract: The use of high plasma density and low gas density, a recent trend in plasma-assisted materials processing, requires a particle simulation method for plasmas and gas flows. The kinetic theory basis of the particle simulation method is first described. Based on this theoretical viewpoint, state-of-the-art probabilistic treatments of collisions are described for electron-molecule, ion-molecule, molecule-molecule, and Coulomb collisions.
291 citations
Cites methods from "A Grid-Based Coulomb Collision Mode..."
...Jones et al. [ 53 ] presented a method to calculate the force acting on a particle from grid quantities in the PIC codes....
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TL;DR: In this article, a review of recent advances in relativistic beam-plasma instabilities is presented from both theoretical and numerical points of view, focusing on the potentially dominant waves propagating obliquely to the beam direction.
Abstract: The interest in relativistic beam-plasma instabilities has been greatly rejuvenated over the past two decades by novel concepts in laboratory and space plasmas. Recent advances in this long-standing field are here reviewed from both theoretical and numerical points of view. The primary focus is on the two-dimensional spectrum of unstable electromagnetic waves growing within relativistic, unmagnetized, and uniform electron beam-plasma systems. Although the goal is to provide a unified picture of all instability classes at play, emphasis is put on the potentially dominant waves propagating obliquely to the beam direction, which have received little attention over the years. First, the basic derivation of the general dielectric function of a kinetic relativistic plasma is recalled. Next, an overview of two-dimensional unstable spectra associated with various beam-plasma distribution functions is given. Both cold-fluid and kinetic linear theory results are reported, the latter being based on waterbag and Maxwell–Juttner model distributions. The main properties of the competing modes (developing parallel, transverse, and oblique to the beam) are given, and their respective region of dominance in the system parameter space is explained. Later sections address particle-in-cell numerical simulations and the nonlinear evolution of multidimensional beam-plasma systems. The elementary structures generated by the various instability classes are first discussed in the case of reduced-geometry systems. Validation of linear theory is then illustrated in detail for large-scale systems, as is the multistaged character of the nonlinear phase. Finally, a collection of closely related beam-plasma problems involving additional physical effects is presented, and worthwhile directions of future research are outlined.
255 citations
TL;DR: In this paper, a Coulomb collision algorithm for weighted particles is proposed, which is based on the cumulative property of Coulomb collisions in plasmas, and the law of scattering is given by the exponential cosine function.
131 citations
01 Jan 2003
TL;DR: Hybrid codes, in which the ions are treated kinetically and the electrons are assumed to be a massless fluid, have been widely used in space physics over the past two decades.
Abstract: Hybrid codes, in which the ions are treated kinetically and the electrons are assumed to be a massless fluid, have been widely used in space physics over the past two decades These codes are used to model phenomena on ion inertial and gyro-radius scales, which fall between longer scales obtained by magnetohydrodynamic simulations and shorter scales attainable by full particle simulations In this tutorial, the assump- tions and equations of the hybrid model are described along with some most commonly used numerical implementations Modifications to include finite electron mass are also briefly discussed Examples of results of two-dimensional hybrid simulations are used to illustrate the method, to indicate some of the tradeoffs that need to be addressed in a realistic calculation, and to demonstrate the utility of the technique for problems of contemporary interest Some speculation about the future direction of space physics research using hybrid codes is also provided
117 citations
Cites methods from "A Grid-Based Coulomb Collision Mode..."
...This can involve new types of collision models, such as collision-field methods in which the collision “force” is treated as a grid quantity [77][78]....
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References
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TL;DR: In this paper, a Taylor's series method was used to solve Lagrange's equations of motion for N-acetyl alanine amide and Nacetyl methionide amide under the influence of the ECEPP/2 potential energy function.
Abstract: A new algorithm is presented for performing molecular dynamics simulations of peptides with fixed geometry, with the aim of simulating conformational changes and of exploring conformational space. The principle of the method is to expand the potential energy as a Taylor's series in the coordinates around the current point, retaining the force and its first two derivatives, and obtain a series solution of the resulting differential equations using a method due to Lyapunov. By choosing the time step so that the second term in the series is small compared to the first, the true solution can in principle be approximated to any desired degree of accuracy. The algorithm has been used to solve numerically Lagrange's equations of motion for N-acetyl alanine amide and N-acetyl methionide amide, regarded as fixed at their C-termini, under the influence of the ECEPP/2 potential energy function, and time steps of 15–30 fsec have been achieved with little variation in the total energy. Possible directions for future development are discussed.
55 citations
TL;DR: In this article, a one-dimensional algorithm for fluid simulation of interpenetrating multi-component plasmas, developed earlier for the collisionless case, is extended to include collisions between species.
35 citations
TL;DR: In this paper, a time-implicit Monte Carlo collision algorithm was developed to allow particle-in-cell electron transport models to be applied to arbitrarily collisional systems, and the algorithm was formulated for electrons moving in response to electric and magnetic accelerations and subject to collisional drag and scattering due to a background plasma.
17 citations
01 Jan 1991
TL;DR: In this paper, the authors developed and incorporated one type of interparticle collision model into the hybrid version of the particle-in-cell code ISIS and used it to model high density plasmas.
Abstract: Particle-in-cell methods have long been used to model collisionless plasma phenomena. At the other extreme, fluid methods have been used to model highly collisional plasmas. Hybrid models in which ions are treated by the particle-in-cell method and electrons are treated as a massless fluid allow one to ignore phenomena on the electron plasma frequency time scale and thus have proven to be useful for modeling certain aspects high density plasmas. Until now particle collisions in PIC or hybrid models have been limited to scattering of the particles off a fixed background. The key ingredient in developing plasma simulation methods that allow one to study the transitional region between collisionless and collisional plasmas has been the development of an adequate interparticle collision model that takes into account the self-consistent reaction of the colliding species. We have developed and incorporated one type of interparticle collision model into the hybrid version of our particle-in-cell code ISIS. The method is highly efficient and ensures local conservation of momentum and energy.
1 citations
01 Jan 1989
TL;DR: In this article, the authors considered a hybrid model in which the Darwin approximation is not used and instead the full set of Maxwell's equations are solved, where high density plasma is next to vacuum.
Abstract: Hybrid simulation methods in which ions are treated by particle-in- cell and electrons are treated as a massless fluid have proven to be useful for modeling a variety of low frequency plasma phenomena. In addition to the massless electron approximation, usually the models assume quasineutrality and the Darwin approximation to Maxwell's equations. We have considered a hybrid model in which the Darwin approximation is not used. Rather the full set of Maxwell's equations are solved. This model appears to particularly suited to modeling situation in which the plasma has a finite extent i.e., where high density plasma is next to vacuum. This model allows electromagnetic waves to propagate in the vacuum and to be properly handled in the plasma. 5 refs., 1 fig.
1 citations