Direct derivation of Skullerudʹs Monte Carlo method for charged particle transport from the linear Boltzmann equation

The Test Particle Monte Carlo technique with null collisions as proposed by Skullerud is derived directly from the linear Boltzmann equation including electric and magnetic field effects. To this aim the formal solution is written as the average of a Poisson distribution of multiple time integrals. The statistical properties of the stochastic processes used in the Monte Carlo method follow as natural requirements for the calculation of this average.