Charged Particle Transport in Harmonically Varying Electric Fields: Foundations and Phenomenology

On the approximation of transport properties in structured materials using momentum-transfer theory

“…While the primary aim of MTT initially was to furnish relationships between measurable quantities (e.g. the Wannier energy relations, generalized Einstein (Nernst-Townsend) relations (GER), etc), more recently it has been demonstrated to provide transport properties in good qualitative and semi-quantitative agreement with more rigorous treatments, such as Boltzmann equation solutions and Monte Carlo simulations [11,15,18,[20][21][22][23][24][25][26].…”

Uniform Moment Theory for Charged Particle Motion in Gases

“…Accordingly, applications of such equations have been given by others for situations where reacting ion swarms are controlled by DC electric fields [48], harmonically varying AC electric fields [21], and crossed electric and magnetic fields [4,49]. We note, however, that our second approximation will be slightly different than obtained by other approximations for closing the moment equations, so further work will be required to determine the importance of such differences.…”

“…Similarly, the equation forGvv9involves the vectorGv 2 v9that is related to the heat flux vector [16]. Deciding how to truncate this sequence by means of some closure or other approximation [21,22] determines the type of "fluid equation" one has.…”

“…Equation (23) must be solved in order to determine Gv9 in terms of the experimental parameters and microscopic properties. Even in first approximation, however, this cannot yet be attempted, because the collision frequency is a function of T eff through Equations (20)(21)(22). Hence, we will need to develop a moment equation for the effective temperature in the next section.…”

“…If all three effective temperatures are the same, then ξ u (T eff, x , T eff, y , T eff, z ) becomes identical with ξ(T eff ) as defined by Equation (21). The multi-temperature moment equation for the effective temperature was given previously [23].…”