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.

/pdf/contemporary-particle-in-cell-approach-to-laser-plasma-1hb69lir4e.pdf

Contemporary particle-in-cell approach to laser-plasma modelling

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.

Probability theory of electron-molecule, ion-molecule, molecule-molecule, and Coulomb collisions for particle modeling of materials processing plasmas and cases

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.

/pdf/multidimensional-electron-beam-plasma-instabilities-in-the-4rrb6d2ux6.pdf

Multidimensional electron beam-plasma instabilities in the relativistic regime

A Grid-Based Coulomb Collision Model for PIC Codes

Weighted Particles in Coulomb Collision Simulations Based on the Theory of a Cumulative Scattering Angle

We show how PISCES-like semiconductor models can be joined non-invasively to finite difference time domain models for the calculation of coupled external electromagnetics. The method involves "tricking" the standard current boundary condition for the device model into accepting an effective parallel external capacitance. For nearly steady state device conditions we show the results for a transmission line-coupled PISCES diode agree well with those for an ideal diode. >

Coupling of the PISCES device modeler to a 3-D Maxwell FDTD solver

The effects of diode geometry and externally applied magnetic fields on electron beam production and transport for KrF laser pumping has been studied using two and three dimensional particle-in-cell models. The efficiency with which electrons may be transported through the foil support structure depends critically on the size of the openings in the structure as well as the magnitude of the applied magnetic fields. As the electron diodes become larger the current which can be produced becomes limited by the self-magnetic field of the beam. Simulations show the diode current is limited to slightly more than the usual critical current.'' However this electron flow is found to be unstable. The application of strong guide fields not only increases the current from the diode but tends to stabilize the electron beam. 4 refs., 5 figs.

Three-dimensional particle-in-cell modeling of relativistic electron beam production and transport for KrF laser pumping

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.

A fully electromagnetic hybrid model for high density plasma simulations

Summary form only given. Extending the FDTD (finite-difference time-domain) method of Taflove (1990), the authors have constructed a 3D electromagnetic model for the simulation of fast photoconductive switches excited by ultrashort optical pulses. These are coupled to pulse forming networks for the optimized control of the pulse width. The switches consist of microstrip metal transmission lines laid down on a GaAs substrate. A 5 to 50 /spl mu/m wide gap divides a piece of the line that is charged to a few volts from a continuation of the line that is grounded. A 0.1 to 0.3 ps, 1 pJ, 0.6 /spl mu/m laser pulse generates the order of 10/sup 17/ cm/sup -3/ electron/hole densities in the substrate material to close gap, thereby launching a 1 to 3 ps pulse. Electromagnetic coupling to the networks truncates the pulse on comparable time scales. Maxwell's equations with drift diffusion have been solved, and the effects of alternative numerical treatments of the boundary conditions, electromagnetics, and transport have been explored.

http://ieeexplore.ieee.org/iel2/4487/12731/00593534.pdf

V.A. Thomas

Papers

A Grid-Based Coulomb Collision Model for PIC Codes

Coupling of the PISCES device modeler to a 3-D Maxwell FDTD solver

Three-dimensional particle-in-cell modeling of relativistic electron beam production and transport for KrF laser pumping

A fully electromagnetic hybrid model for high density plasma simulations

3D FDTD simulation of photoconducting switches