Velocity distribution of electrons in time-varying low-temperature plasmas: progress in theoretical procedures over the past 70 years

A time-varying low-temperature plasma sustained by electrical powers with various kinds of fRequencies has played a key role in the historical development of new technologies, such as gas lasers, ozonizers, micro display panels, dry processing of materials, medical care, and so on, since World War II. Electrons in a time-modulated low-temperature plasma have a proper velocity spectrum, i.e. velocity distribution dependent on the microscopic quantum characteristics of the feed gas molecule and on the external field strength and the frequency. In order to solve and evaluate the time-varying velocity distribution, we have mostly two types of theoretical methods based on the classical and linear Boltzmann equations, namely, the expansion method using the orthogonal function and the procedure of non-expansional temporal evolution. Both methods have been developed discontinuously and progressively in synchronization with those technological developments. In this review, we will explore the historical development of the theoretical procedure to evaluate the electron velocity distribution in a time-varying low-temperature plasma over the past 70 years. (topical review)