A 3D Fokker-Planck code for studying transport along the magnetic field lines

There are numerous situations in tokamak plasmas which are in an intermediate collisional regime, where the mean-free path is comparable to plasma parameter scale-lengths along the magnetic field lines. To study this class of problems the authors are developing a new code CQLperpendicular starting from the Fokker-Planck code CQL3D, which solves the Fokker-Planck equations with two velocity coordinates (u, momentum per rest mass, and θ, pitch-angle) and the radial spatial coordinate. In CQLperpendicular, the spatial coordinate is now along the magnetic field lines B/B. The diverse features of CQL3D are kept: multi-species, nonlinear, relativistic, toroidal geometry, non-circular flux surfaces. In addition, they shall also allow for arbitrary magnetic field variation and extend the code to non-up/down symmetric plasma cross-section. The equation is coupled to Poisson's equation in order to calculate the electric field iteratively in a consistent way. Finite differences and an alternating direction implicit method (ADI) are used to solve the equation. The model is presented together with the different boundary and geometrical conditions, as well as the different source terms which can be included. Some of the possible immediate applications are in divertor physics: sheath problem with a consistent electric field couple to non-Maxwellian distribution functions, presheath transport, coupling between presheath and sheath, new neoclassical effects of parallel gradients in an inhomogeneous magnetic field, and parallel transport of impurities. Different source terms can be included simulating, for example, the flow of neutrals from the divertor with ionization and charge-exchange processes, the entrainment of impurities by plasma flow to the divertor plate (source added at mid-plane of cross-section), the premature loss of ions due to their finite Larmor orbits when the angle of incidence of the field with the plate is very small