Numerical Solution of the Spencer-Lewis Equation for Kilovolt Electron Transport in Plane Slabs

We have developed a computer program BOLT for the numerical solution of the Spencer-Lewis equation for kilovolt electron transport in finite slabs. The method of solution used is a discrete ordinates method utilizing Gauss-quadrature angles equivalent to a 20th order Legendre polynomical expansion of the electron flux distribution function. The ultimate goal of the program is to compute x-ray photoelectron emission from thin targets and energy and charge deposition profiles near solid-vacuum boundaries and at interfaces between materials of differing atomic number. In this paper results are presented for a uniformly distributed monoenergetic electron source function, anisotropic in angle with form (1 + ß cos θ). The values for the charge and energy flow and deposition profiles agree within a few percent with analytic solutions characteristic of an infinite medium and with Monte Carlo transport calculations using simulated electron trajectories. The equilibrium value for the net flow or "Compton current" for 30 kilovolt electrons is found to be about 7 percent higher than the analytic value while all other quantities are believed to be accurate to within 2 percent. The principal source of error appears to be in the evaluation of the collision integral involving the exceedingly narrow deflections characteristic of kilovolt electron scattering. The discretization error due to finite grid sizes in the discrete ordinates scheme used was found to be very small.