High-order diamond differencing schemes for the Boltzmann Fokker–Planck equation in 1D and 2D Cartesian geometries

•High-order diamond differencing is proposed for the solution of the Boltzmann Fokker-Planck (BFP) equation.•The BFP equation is used to represent the transport of electrons.•A continuous slowing down termwith stopping power coefficient is introduced.•Soft and catastrophic energy domains are used for representing collisional and radiative scattering. This paper presents the implementation of high-order diamond differencing schemes, specifically the DD1 and DD2 schemes which are 4th- and 6th-order accurate respectively, to handle the spatial discretization of the Boltzmann Fokker–Planck equation in 1D and 2D Cartesian geometries. While being as computationally expensive as linear/quadratic discontinuous Galerkin schemes, the DD1/DD2 schemes are respectively an order more accurate. The energy deposition calculations presented in this work show that, besides providing correction to the oscillations and a reduced propensity to yield negative fluxes than the classical diamond difference closure relation, they tend to perform better than discontinuous Galerkin schemes, even in regions with abrupt variations of the solution due to rapid energy loss, to interface implying high-Z variations and to domain borders.