Hot-Tail Runaway Seed Landscape during the Thermal Quench in Tokamaks

Runaway electron populations seeded from the hot tail generated by the rapid cooling in plasma-terminating disruptions are a serious concern for next-step tokamak devices such as ITER. Here, we present a comprehensive treatment of the thermal quench, including the superthermal electron dynamics, heat and particle transport, atomic physics, and radial losses due to magnetic perturbations: processes that are strongly linked and essential for the evaluation of the runaway seed in disruptions mitigated by material injection. We identify limits on the injected impurity density and magnetic perturbation level for which the runaway seed current is acceptable without excessive thermal energy being lost to the wall via particle impact. The consistent modeling of generation and losses shows that runaway beams tend to form near the edge of the plasma, where they could be deconfined via external perturbations.

Figure 1

Maximum seed runaway current as a function of injected neon density and normalized magnetic perturbation $\delta B/B$. The injected deuterium density is $n_D={10}^{21}{\mathrm{m}}^{-3}$. Injected deuterium and neon profiles assumed to be (a),(b),(d) flat and (c) quadratic $n_{\mathrm{Ne}/\mathrm{D}}(r)=n_{\mathrm{Ne}/\mathrm{D}}[2/11+(18/11)(r/a{)}^2]$. Below the dashed lines, the transport losses are acceptably low, and left of the solid lines the hot-tail seed is acceptably small. The initial central temperature is $T_0=15\mathrm{keV}$ in (a),(b),(c).

Figure 2

Simulation of an ITER-like disruption with initial plasma current $I_p=15\mathrm{MA}$ and injected deuterium and neon densities $n_{\mathrm{D}}={10}^{21}{\text{m}}^{-3}$ and $n_{\mathrm{Ne}}=9\times {10}^{19}{\mathrm{m}}^{-3}$, respectively. Injected deuterium and neon profiles assumed to be flat and in (a),(b) $\delta B/B=0.16\%$. (a) Cold electron temperature as a function of time at five different radii. (b) Induced electric field at the same radial positions as in (a). (c),(d) Cold electron temperature as a function of radius at four different times. (e),(f) Hot (dashed) and runaway (solid) current density profiles at the same times as in (c),(d). (c),(e) $\delta B/B=0$. (d),(f) $\delta B/B=0.16\%$.

Figure 3

(a) Electron energy density and (b) current for $\delta B/B=0.04\%$ (blue), $\delta B/B=0.16\%$ (red), and $\delta B/B=0.4\%$ (yellow) and injected densities $n_{\mathrm{D}}={10}^{21}{\text{m}}^{-3}$, $n_{\mathrm{Ne}}=5\times {10}^{19}{\mathrm{m}}^{-3}$.