Runaway electron production in DIII-D killer pellet experiments, calculated with the CQL3D/KPRAD model

Runaway electrons are calculated to be produced during the rapid plasma cooling resulting from “killer pellet” injection experiments, in general agreement with observations in the DIII-D [J. L. Luxon et al., Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159] tokamak. The time-dependent dynamics of the kinetic runaway distributions are obtained with the CQL3D [R. W. Harvey and M. G. McCoy, “The CQL3D Code,” in Proceedings of the IAEA Technical Committee Meeting on Numerical Modeling, Montreal, 1992 (International Atomic Energy Agency, Vienna, 1992), p. 489] collisional Fokker–Planck code, including the effect of small and large angle collisions and stochastic magnetic field transport losses. The background density, temperature, and $Z_{\mathrm{eff}}$ are evolved according to the KPRAD [D. G. Whyte and T. E. Evans et al., in Proceedings of the 24th European Conference on Controlled Fusion and Plasma Physics, Berchtesgaden, Germany (European Physical Society, Petit-Lancy, 1997), Vol. 21A, p. 1137] deposition and radiation model of pellet–plasma interactions. Three distinct runway mechanisms are apparent: (1) prompt “hot-tail runaways” due to the residual hot electron tail remaining from the pre-cooling phase, (2) “knock-on” runaways produced by large-angle Coulomb collisions on existing high energy electrons, and (3) Dreicer “drizzle” runaway electrons due to diffusion of electrons up to the critical velocity for electron runaway. For electron densities below ${\text{≈1×10}}^{15} {\mathrm{cm}}^{\mathrm{-3}},$ the hot-tail runaways dominate the early time evolution, and provide the seed population for late time knock-on runaway avalanche. For small enough stochastic magnetic field transport losses, the knock-on production of electrons balances the losses at late times. For losses due to radial magnetic field perturbations in excess of $\text{≈0.1\%}$ of the background field, i.e., ${\mathrm{\delta B}}_r\text{/B⩾0.001,}$ the losses prevent late-time electron runaway.