Short-time and -distance relaxation of swarms in gases

Abstract

The establishment of the hydrodynamic regime is analysed, introducing equations with time-dependent as well as space-dependent transport coefficients and deriving the relations between the two sets of coefficients. Based upon the Fourier transformation technique, the short-time behaviour of swarms in idealized free space is investigated, starting from the Boltzmann equation by means of analysis of its eigenvalue problem. The relaxation times of time-dependent transport coefficients for the establishment of the hydrodynamic regime and the corresponding relaxation distances of space-dependent coefficients, which are defined from the position dependence of the arrival-time spectra and its time moments, have been formulated. By using the theoretical results, which were rewritten in matrix form using the Burnett basis function, the relaxation times of ionization growth, drift and diffusion have been calculated for electrons in krypton gas as functions of the reduced electric field and the mean energy of the initial Gaussian velocity distribution. The relaxation distances d0 in the measurement of the Townsend first ionization coefficient in krypton have been calculated.

Monte Carlo studies of electron transport in crossed electric and magnetic fields in CF4

“…In other words, direction of velocity is randomized owing to elastic collisions. Similar effects were observed by Shizgal and McMahon [75] in electron thermalization at low E/N and by Kondo et al [76,77] in rare gases.…”

Time-of-flight observation of electron swarm in methane

“…The relation described later is known to correspond to the lowest eigenvalue, which is given in the hydrodynamic regime. 15,18 Besides the transformation above, the solution f͑z , v ជ , t͒ for Eq. ͑2͒ can be expressed in a multiterm formula by the density gradient expansion method ͑e.g., Kumar et al 1 …”

“…It has been asserted, resorting to the simulation, that in the condition with ionization process, the macroscopic swarm parameters, such as the drift velocity and the diffusion coefficient, of an isolated electron swarm are affected quantitatively depending on their definitions. [5][6][7][14][15][16][17] A typical example is rendered by that the mean drift velocity of electrons in an isolated swarm is different from the center- of-mass drift velocity of electrons "in general" when ionization and/or attachment processes occur. 5 The knowledge of this effect may be of great importance in treating the behavior of charged particles with production and annihilation processes by external electric and/or magnetic fields.…”

Diffusion Cooling of Electrons in an A.C. Field

“…Over thirty years ago Parker (1965) identified the thermal diffusion coefficient in terms of the limit of an eigenvalue of a certain differential equation, for the particular case of electron transport in a finite medium, but it is only fairly recently that the eigenvalue nature of swarm transport properties in general has been recognised (see the reviews by Kumar 1991 andRobson 1991a) and calculations made accordingly (Date et al 1992(Date et al , 1993Kondo and Tagashira 1993). The generalised eigenvalue theory enables us to:…”

“…In what follows, the earlier analyses of the 1970s are put in the context of general eigenvalue theory given at this workshop (Robson 1991a;Kondo and Tagashira 1993) and the effect of an applied a.c. field is discussed, with calculations for two simple models.…”