Lifetime and universal distribution of seed runaway electrons
Adrian Fontanilla, B. N. Breǐzman · Physics of Plasmas · 2017
The lifetime of pre-existing runaway electrons determines how likely the runaways will undergo avalanche multiplication. We estimate the lifetime of runaway electrons via kinetic analysis. We show that the rate of runaway decay depends on the combination of parameters α≡(Z+1)/τ¯rad (where τ¯rad is the synchrotron timescale normalized to the collisional timescale and Z is the ion charge) compared to the electric field. We identify two cases where the decay rate is slow enough to enable a quasi-steady shape of the runaway distribution function. This distribution and its lifetime represent the eigenfunction and the lowest eigenvalue of the kinetic equation. In one case, α≪1: the field required to sustain the pre-existing runaways is barely larger than the Connor-Hastie critical value. In the same manner as by Aleynikov and Breizman [Phys. Rev. Lett. 114, 155001 (2015)], we solve the kinetic equation perturbatively but extend the work to demonstrate that the lifetime grows exponentially with the field at a rate that depends on α. In the second case, α≫1: the sustainment field is much greater than the Connor-Hastie value, and the largeness of the field in this case enables us to universalize the kinetic equation via the re-scaling procedure.