Simulation Procedure for Lifelong Flight Behavior of Electrons Consistent in Three Domains of Time t, Position x, and Energy ε

Abstract

Research on the flight behavior of electrons and ions in a gas under an electric field has recently moved in a direction of clarifying the mechanism of the spatiotemporal development of a swarm, but the symbolic unknown state function \(f(r,c,t)\) of the Boltzmann equation has not been obtained in an explicit form. However, a few papers on the spatiotemporal development of an electron swarm using the Monte Carlo simulation have been published. On the other hand, a new simulation procedure for obtaining the lifelong state function \(F_{\text{fT}}(t,x,\varepsilon )\) and local transport quantities \(J(t,x,\varepsilon )\) of electrons in the three domains of time t, one-dimensional position x, and energy e under arbitrary initial and boundary conditions has been developed by extending the flight-time-integral (FTI) methods previously reported and is named the 3D-FTI method. A preliminary calculation has shown that this method can extensively provide the flight behavior of individual electrons in a swarm and ...