DIII-D experiments on rapid shutdown runaway electron (RE) beams have improved the understanding of the processes involved in RE beam control and dissipation. Improvements in RE beam feedback control have enabled stable confinement of RE beams out to the volt-second limit of the ohmic coil, as well as enabling a ramp down to zero current. Spectroscopic studies of the RE beam have shown that neutrals tend to be excluded from the RE beam centre. Measurements of the RE energy distribution function indicate a broad distribution with mean energy of order several MeV and peak energies of order 30–40 MeV. The distribution function appears more skewed towards low energies than expected from avalanche theory. The RE pitch angle appears fairly directed (θ ∼ 0.2) at high energies and more isotropic at lower energies (ε < 100 keV). Collisional dissipation of RE beam current has been studied by massive gas injection of different impurities into RE beams; the equilibrium assimilation of these injected impurities appears to be reasonably well described by radial pressure balance between neutrals and ions. RE current dissipation following massive impurity injection is shown to be more rapid than expected from avalanche theory—this anomalous dissipation may be linked to enhanced radial diffusion caused by the significant quantity of high-Z impurities (typically argon) in the plasma. The final loss of RE beams to the wall has been studied: it was found that conversion of magnetic to kinetic energy is small for RE loss times smaller than the background plasma ohmic decay time of order 1–2 ms.
MHD simulations of rapid shutdown scenarios by massive particle injection in DIII-D, Alcator C-Mod and ITER are performed in order to study runaway electron transport during mitigated disruptions. The simulations include a runaway electron (RE) confinement model using drift-orbit calculations for test particles. A comparison of limited and diverted plasma shapes is studied in DIII-D simulations, and improved confinement in the limited shape is found due to both spatial localization and reduced toroidal spectrum in the nonlinear MHD activity. C-Mod simulations compare shutdown scenarios in which impurity (Ar) fueling is concentrated in the edge versus the core, and find the confinement of REs in the core is maintained until the onset of the m = 1 n = 1 mode, which is delayed in the case of edge deposition, relative to core deposition. But, the overall RE loss fraction is 100% regardless of Ar fueling profile. A comparison of simulations across the three devices points to a trend of increased RE confinement with increasing device size, wherein all REs are lost in C-Mod, all are confined in ITER, and a partial loss is observed in DIII-D. This trend is related to a reduction in the fluctuating field amplitude near the plasma edge during the thermal-quench-induced MHD activity. The result bodes poorly for RE mitigation strategies in ITER that rely on MHD deconfinement of runaway electrons.
Disruption mitigation experiments using massive gas injection (MGI) on Alcator C-Mod [Hutchinson et al., Phys. Plasmas 1, 1511 (1994)] and DIII-D [Luxon and Davis, Fusion Technol. 8, 441 (1985)] have shown that magnetohydrodynamics (MHD) plays an important role. The three-dimensional MHD code NIMROD [Sovinec et al., J. Comput. Phys. 195, 355 (2004)] has been extended to include atomic physics taken from the KPRAD code to perform simulations of MGI. Considerable benchmarking of the code has been done against Alcator C-Mod for neon and helium gas jet experiments. The code successfully captures the qualitative sequence of events observed in MGI experiments up to the end of the thermal quench. Neon jet simulations also show quantitative agreement with the experimental thermal quench onset time. For helium gas jets, we show that a small percent boron density can significantly alter the results even in the presence of a helium jet with three orders of magnitude higher density. The thermal quench onset time is considerably overpredicted unless boron radiation is included. A DIII-D helium jet simulation shows a faster rise time for total radiated power than the experiment, but comparable amplitude. Similar to the important role of boron in C-Mod, carbon radiation is a significant factor in DIII-D helium jet simulations and experiments.
The growth of avalanche runaway electrons, a potentially serious issue for disruptions in high-current tokamaks, was recently studied by Monte-Carlo and numerical solutions of the relativistic Fokker-Planck equation. Here a new analytical formulation based on the analysis of the particle trajectories of the knocked out secondary electrons offers insight and yields an analytical expression for the growth rate over the entire parameter range of interest. The growth rates are compared with the numerical simulations and analytical solutions of the Fokker-Planck equation in various limits [M.N. Rosenbluth and S.V. Putvinski, Nucl. Fusion 37, 1355 (1997)], and are found to be in good agreement.
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