This paper is the first in a series of three papers to summarize the recent work of an European-wide collaborationwhich is ongoing since about one decade using Particle-in-Cell (PIC) methods in low temperature plasma physics. In the present first paper the main aspects of this computational technique will be presented. In the second paper, an overview of applications in low-temperature plasma modelling will be given, whereas the third part will put emphasis on the specific results of modelling ion thrusters. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The Particle-In-Cell Method

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

Optimization of PIC codes by improved memory management

A Monte-Carlo method for coulomb collisions in hybrid plasma models

We consider the development of Monte Carlo schemes for molecules with Coulomb interactions. We generalize the classic algorithms of Bird and Nanbu-Babovsky for rarefied gas dynamics to the Coulomb case thanks to the approximation introduced by Bobylev and Nanbu [A. V. Bobylev and K. Nanbu, Theory of collision algorithms for gases
and plasmas based on the Boltzmann equation and the Landau-Fokker-Planck equation, Physical Review E, vol. 61, no. 4, pp. 4576–4586, 2000.]. Thus, instead of considering the original Boltzmann collision operator, the schemes are constructed through the use of an approximated Boltzmann operator. With the above choice larger time steps are possible in simulations; moreover the expensive acceptance-rejection procedure for collisions is avoided and every particle collides. Error analysis and comparisons with the original Bobylev-Nanbu (BN) scheme are performed. The numerical results show agreement with the theoretical convergence rate of the approximated Boltzmann operator and the better performance of Bird-type schemes with respect to the original scheme.

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N Nakajima

Papers

Vector Implementation of Nonlinear Monte Carlo Coulomb Collisions