Hot tail runaway electron generation in tokamak disruptions

Hot tail runaway electron generation in tokamak disruptions is caused by incomplete thermal-ization of the electron velocity distribution during the rapid plasma cooling. Electrons at high velocities in the initial Maxwellian, where the electron collision time is longer than the cooling time, are in a transient phase left as a hot tail of the distribution. The part of this tail above the runaway threshold energy can easily be converted to runaways by the rising electric field. Analytical estimates of the hot tail runaway generation have previously been found for a type of cooling history, in which the cooling rate d lnT/dt is proportional to the collision frequency of thermal electrons [1, 2]. In reality however, one can expect the cooling rate to de-crease with time rather than to be proportional to the rising collision frequency. This is because the cooling rate can be lower at temperatures closer to the ionization energies and because pro-cesses like Ohmic heating and collisions with ions become important at the low temperatures in the end of the thermal quench. In this work, we therefore study the exponential-like cooling history T = Tfinal + (T0 − Tfinal)e−t/t0. (1) The cooling is assumed to be caused by strongly radiating impurities, and the supra-thermal electrons are mainly slowed down by collisions with thermal electrons. This is modelled by the kinetic equation and the collision operato