Search

A Monte Carlo method for angle scattering of electrons in air that accommodates the small-angle multiple scattering and larger-angle single scattering limits is introduced. The algorithm is designed for use in a particle-in-cell simulation of electron transport and electromagnetic wave effects in air. The method is illustrated in example calculations. [ABSTRACT FROM AUTHOR]

Abstract: The extension of Langevin-equation Monte-Carlo algorithms for Coulomb collisions from the conventional Euler–Maruyama time integration to the next higher order of accuracy, the Milstein scheme, has been developed, implemented, and tested. This extension proceeds via a formulation of the angular scattering directly as stochastic differential equations in the fixed-frame spherical-coordinate velocity variables. Results from the numerical implementation show the expected improvement [ vs. ] in the strong convergence rate both for the speed and angular components of the scattering. An important result is that this improved convergence is achieved for the angular component of the scattering if and only if the “area-integral” terms in the Milstein scheme are included. The resulting Milstein scheme is of value as a step towards algorithms with both improved accuracy and efficiency. These include both algorithms with improved convergence in the averages (weak convergence) and multi-time-level schemes. The latter have been shown to give a greatly reduced cost for a given overall error level when compared with conventional Monte-Carlo schemes, and their performance is improved considerably when the Milstein algorithm is used for the underlying time advance versus the Euler–Maruyama algorithm. A new method for sampling the area integrals is given which is a simplification of an earlier direct method and which retains high accuracy. This method, while being useful in its own right because of its relative simplicity, is also expected to considerably reduce the computational requirements for the direct conditional sampling of the area integrals that is needed for adaptive strong integration. [Copyright &y& Elsevier]

Abstract: A new framework is introduced for kinetic simulation of laser–plasma interactions in an inhomogeneous plasma motivated by the goal of performing integrated kinetic simulations of fast-ignition laser fusion. The algorithm addresses the propagation and absorption of an intense electromagnetic wave in an ionized plasma leading to the generation and transport of an energetic electron component. The energetic electrons propagate farther into the plasma to much higher densities where Coulomb collisions become important. The high-density plasma supports an energetic electron current, return currents, self-consistent electric fields associated with maintaining quasi-neutrality, and self-consistent magnetic fields due to the currents. Collisions of the electrons and ions are calculated accurately to track the energetic electrons and model their interactions with the background plasma. Up to a density well above critical density, where the laser electromagnetic field is evanescent, Maxwell’s equations are solved with a conventional particle-based, finite-difference scheme. In the higher-density plasma, Maxwell’s equations are solved using an Ohm’s law neglecting the inertia of the background electrons with the option of omitting the displacement current in Ampere’s law. Particle equations of motion with binary collisions are solved for all electrons and ions throughout the system using weighted particles to resolve the density gradient efficiently. The algorithm is analyzed and demonstrated in simulation examples. The simulation scheme introduced here achieves significantly improved efficiencies. [Copyright &y& Elsevier]