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.
ABSTRACT
In this paper we make a parallel between the swarm method in physics of ionized gases and modeling of positrons in radiation therapy and diagnostics. The basic idea is to take advantage of the experience gained in the past with electron swarms and to use it in establishing procedures of modeling positron diagnostics and therapy based on the well-established experimental binary collision data. In doing so we discuss the application of Monte Carlo technique for positrons in the same manner as used previously for electron swarms, we discuss the role of complete cross section sets (complete in terms of number, momentum and energy balance and tested against measured swarm parameters), we discuss the role of benchmarks and how to choose benchmarks for electrons that may perhaps be a subject to experimental verification. Finally we show some samples of positron trajectories together with secondary electrons that were established solely on the basis of accurate binary cross sections and also how those may be used in modeling of both gas filled traps and living organisms.
