Weighted particle methods solving kinetic equations for dilute ionized gases

The numerical treatment of kinetic equations for ionized gases has to handle two additional problems. The first one, the different time scales for the electrons and the heavy particle, is solved by asymptotic methods. The second one arises from small ionization rates and is treated with a weighted particle method. The derivation of a weighted particle method for general kinetic systems, the choice of the weights and the convergence properties are discussed in the first part of the paper. The use of variable weights in a particle scheme leads to nonconservative particle schemes which results in purely numerical instabilities. The second part of the paper presents possible modifications of the weighted particle method which conserve mass, charge, momentum and energy on the discrete level of description and lead to stable and convergent numerical methods. Numerical results for a reduced plasma system show the advantages in comparison to equiweighted particle method with respect to accuracy, computational time and computer memory.