Evolution equation and transport coefficients defined by arrival-time spectra of swarms

Abstract

Arrival-time spectra of the evolution of swarms in the hydrodynamic regime have been studied theoretically starting from the Boltzmann equation and its eigenvalue problem. In order to express the development of the number density of the one-dimensional pulse swarm, a new evolution equation with new transport parameters, which are obtained directly from the arrival-time spectra, is introduced. Relations between the longitudinal transport coefficients and the new parameters are also presented. By means of this theory, it is shown that the distribution functions for the different types of experiments (steady-state Townsend or pulsed Townsend) are distinguished from each other in non-conservative cases, and drift velocities defined by different principles have in general their own values even if the kind of gas and the value of E/N are the same.

Electron transport properties and collision cross sections in C2F4

“…6 The meanarrival-time drift velocity W m was introduced as appropriate for the drift velocity observed in a drift tube experiment. 4,5 Figure 4 shows the drift velocity W m determined in the present work as well as the measurements of the drift velocity as defined by Goyette et al 1 The latter lie somewhat below our mean arrival time measurements at higher values of E/N. For comparison, drift velocities in other gases are also plotted, although the definition of those velocities differs from that of the mean-arrival-time drift velocity.…”

“…The coefficients ␣ (0) and ␣ (1) correspond to the ionization coefficient and the inverse of the mean-arrival-time drift velocity W m , respectively. 5 The relationship between ␣ (2) and the longitudinal diffusion coefficient D L is given by 5…”

Time-of-flight observation of electron swarm in methane

“…The difference is up to about 16% at E / N = 500 Td. The relation between W r and W m is theoretically given 6 by…”

“…We call this approach to capture the swarm behavior the time-offlight ͑TOF͒ method hereafter. Contrary to this, Kondo and Tagashira 6 presented the arrival-time-spectra ͑ATS͒ method in which the swarm is observed at a certain location in the drift tube and the arrival-time distribution of electrons is treated to deduce macroscopic parameters emerging in another type of continuity equation. This continuity equation was obtained by interchanging time and space variables in the conventional continuity equation ͑see also Date et al 7 ͒, where the spatial derivative of electron number is expanded in a series of time derivatives with higher orders.…”

“…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.…”