open access

https://hdl.handle.net/2115/11393

The spatio-temporal development of electron swarms in gases: moment equation analysis and Hermite polynomial expansion

英語

1998-02

Institute of Physics

Journal of Physics D: Applied Physics

31(3)

319-327

Spatio-temporal development of electron swarms in gases is simulated using a propagator method based on a series of one-dimensional spatial moment equations. When the moments up to a suecient order are calculated, the spatial distribution function of electrons, p(x), can be constructed by an expansion technique using Hermite polynomials and the weights of the Hermite components are represented in terms of the electron diausion coeecients. It is found that the higher order Hermite components tend to zero with time, that is, the normalized form of p(x) tends to a Gaussian distribution. A time constant of the relaxation is obtained as the ratio of the second- and third-order diausion coeecients, D2 3=D3L . The validity of an empirical approximation in time-of-cight experiments that treats p(x) as a Gaussian distribution is indicated theoretically. It is also found that the diausion coeecient is deaned as the derivative of a quantity called the cumulant which quantiaes the degree of deviation of a statistical distribution from a Gaussian distribution.

学術雑誌論文

Accepted Manuscript

Copyright © 1998 Institute of Physics

0022-3727

1361-6463