Abstract
We derive third-order transport coefficients of skewness for a phase-space kinetic model that considers the processes of scattering collisions, trapping, detrapping and recombination losses. The resulting expression for the skewness tensor provides an extension to Fick’s law which is in turn applied to yield a corresponding generalised advection-diffusion-skewness equation. A physical interpretation of trap-induced skewness is presented and used to describe an observed negative skewness due to traps. A relationship between skewness, diffusion, mobility and temperature is formed by analogy with Einstein’s relation. Fractional transport is explored and its effects on the flux transport coefficients are also outlined.
Highlights
Very little data regarding third-order transport coefficients can be found in the literature
We are concerned with the form of the skewness tensor for charged-particle transport in the presence of trapped states
We have considered up to the third-order transport coefficient of skewness bfQ, which takes the form of a rank-3 tensor
Summary
By integrating the generalised Boltzmann equation [1] throughout all of velocity space, we find the equation of continuity for the number density n(t, r):. Where W is the drift velocity vector, D is the rank-2 diffusion tensor and Q is the rank-3 skewness tensor To determine these flux transport coefficients it is a matter of writing the solution of the generalised Boltzmann equation [1] itself as a density gradient expansion f (t, r, v). Substituting the density gradient expansion of f (t, r, v) into the Boltzmann equation [1] and equating coefficients of spatial gradients, as done in Sec. IV of ref., gives the following coefficients f (0) (s) νcollw (αcoll, s) + Rνtrapw νcoll.
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