Monte Carlo simulation studies on the validity of the Gram-Charlier calculations of velocity distributions of Na+ swarm in neon gas

Abstract

The Gram-Charlier analytical/iterative approach tailor-designed to account for the skewness, kurtosis and correlation of mutually orthogonal velocity components of ion swarm velocity distributions is tested by intensive Monte Carlo simulation of the motion of Na+ ion swarm drifting in Ne gas. Comparisons are made of the longitudinal and transverse ion temperatures and the shape parameters of the velocity distribution functions obtained by the two approaches. More detailed comparisons of the velocity distribution functions show that the analytical/iterative method significantly underestimates the high-velocity tail of the velocity distribution function. While the Gram-Charlier method is an improvement over the standard three-temperature theory, it still suffers from the difficulty arising from the truncation of velocity expansion terms at high velocities.