A closed-form solution for the two-dimensional Fokker-Planck equation for electron transport in the range of Compton Effect

In this paper we solve the Fokker-Planck (FP) equation, an alternative approach for the Boltzmann transport equation for charged particles in a rectangular domain. To construct the solution we begin applying the PN approximation in the angular variable and the Laplace Transform in the x-variable, thus obtaining a first order linear differential equation in y-variable, which the solution is straightforward. The angular flux of electrons and the parameters of the medium are used for the calculation of the energy deposited by the secondary electrons generated by Compton Effect. The remaining effects will not be taken into account. The results will be presented under absorbed energy form in several points of interested. We present numerical simulations and comparisons with results obtained by using Geant4 (version 8) program which applies the Monte Carlo's technique to low energy libraries for a two-dimensional problem assuming the screened Rutherford differential scattering cross-section