On collisional diffusion in a stochastic magnetic field

The effect of particle collisions on the transport in a stochastic magnetic field in tokamaks is investigated. The model of resonant magnetic perturbations generated by external coils at the plasma edge is used for the stochastic magnetic field. The particle collisions are simulated by a random walk process along the magnetic field lines and the jumps across the field lines at the collision instants. The dependencies of the local diffusion coefficients on the mean free path λmfp, the diffusion coefficients of field lines DFL, and the collisional diffusion coefficients, χ⊥ are studied. Based on these numerical data and the heuristic arguments, the empirical formula, Dr=χ⊥+v||DFL/(1+Lc/λmfp), for the local diffusion coefficient is proposed, where Lc is the characteristic length of order of the connection length lc=πqR0, q is the safety factor, R0 is the major radius. The formula quite well describes the results of numerical simulations. In the limiting cases, the formula describes the Rechester-Rosenbluth and Laval scalings