Radial runaway losses in tokamak disruptions

A simple zero-dimensional model for a tokamak disruption is used to evaluate the effect of radial runaway losses on the avalanche multiplication of a runaway primary seed during the current quench phase of a fast disruptive event as well as during its termination phase. Analytical expressions for the resulting runaway current, the energy of the runaway beam, and the runaway energy distribution function are obtained. It is found that the formation of the runaway current takes place under an effective critical electric field for runaway current generation due to the radial losses larger than the avalanche threshold associated with the energy losses only. As a result, the amount of runaway current generated by avalanche decreases due to the radial losses, but because of the lower amount of runaway current during the formation phase, the electric field increases, which can lead to a noticeable energy deposition on the runaway population, most of it ultimately deposited onto the plasma facing components, unless the radial losses are sufficiently large. The decay of the current after the formation phase follows a marginal stability scenario, during which the electric field remains close (but below) to the effective critical field for the runaway current, which, as the critical field is larger than the avalanche threshold due to the energy losses only, can result in a substantial conversion of magnetic into runaway kinetic energy during slow current terminations.