Historical development of electron swarm physics based on the Boltzmann equation towards in-depth understanding of a low-temperature collisional plasma

Abstract Theoretical study of the electron kinetics (i.e. the velocity distribution and the transport parameter) in gases is generally conducted using the electron Boltzmann equation. The year 2022 marked 150 years since the formulation of the Boltzmann equation. Even in the last several decades, the historical progress has been made synchronously with the development of innovative technologies in gaseous electronics and in combination with the appearance of computers with sufficient speed and memory. Electron kinetic theory based on the Boltzmann equation has mostly been developed as the swarm physics in the hydrodynamic regime in the dc and radio frequency electric fields. In particular, the temporal characteristics are understood in terms of the collisional relaxation times between electron and gas molecule. There are two main theoretical approaches based on the Boltzmann equation for finding the velocity distribution. One is the traditional description of the electron kinetics, starting from the Boltzmann statistics in velocity space under a uniform density or a small density gradient of electrons. The other most recent approach is based on the phase-space tracking of the velocity distribution where the electron transport parameter is given by the moment of the electron density distribution in position space. In the present paper, we will explore the historical development of the electron Boltzmann equation with respect to three key items: collision term, solution method, and intrinsic electron transport in a hydrodynamic regime involved as the key elements in the low-temperature collisional plasma. The important topics listed in a table are briefly noted and discussed.