ANALYTIC MODEL FOR THE RUNAWAY DISTRIBUTION FUNCTION IN THE PRESENCE OF SPATIAL DIFFUSION

A steady-state kinetic model for runaway electrons in the presence of radial diffusion in a stochastic magnetic field is adopted and solved for a constant magnetic diffusivity. The model is constructed to recov er the correct runaway production rate in the absence of spatial diffu sion. The parallel energetic electron distribution function f is found by matching the solutions from three regions in parallel velocity spa ce and is employed to form moments of f. Upper and lower bounds on the spatial diffusion are obtained by using these moments and the model e xhibits the strong sensitivity to collisionality needed to explain the difference between similar plasmas with little or no hard x-ray signa l and those with significant hard x-my signals.