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

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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.