Modeling the effect of MHD activity on runaway electron generation during SPARC disruptions

TL;DR

This work presents self-consistent 3-D MHD + runaway electron (RE) simulations for SPARC disruptions using the extended MHD code M3D-C1, incorporating an RE fluid model, impurity dynamics, and axisymmetric vertical displacement events. By comparing Ne-only, D2-only, and combined D2+Ne MGI scenarios, the study shows that MHD activity can initially boost RE generation via Dreicer, while impurity-driven stochasticity can cause RE losses; flux-surface re-healing can confine REs and form large RE plateaus for Ne-only injections, whereas combined D2+Ne injections slow RE growth and may trigger a cold VDE that terminates the RE beam. The results underscore the importance of self-consistent RE-MHD-impurity coupling for predicting RE behavior and mitigation in high-current tokamaks like SPARC, with Ne-only injections yielding large plateaus and D2+Ne injections offering significant RE reduction and potential termination pathways. Future work will extend to more realistic multi-injector MGI, non-axisymmetric VDEs, and coupling with REMC fields to further inform disruption mitigation strategies.

Abstract

Magnetohydrodynamic (MHD) instabilities and runaway electrons (REs) interact in several ways, making it important to self-consistently model these interactions for accurate predictions of RE generation and the design of mitigation strategies, such as massive gas injection (MGI). Using M3D-C1 - an extended MHD code with a RE fluid model - we investigate the effects of 3-D nonlinear MHD activity, material injection, and 2-D axisymmetric vertical displacement events (VDEs) on RE evolution during disruptions on SPARC - a high-field, high-current tokamak designed to achieve a fusion gain Q > 1. Several cases, comprising different combinations of neon (Ne) and deuterium ($\text{D}_2$) injection, are considered. Our results demonstrate key effects that arise from the self-consistent RE + MHD coupling, such as an initial increase in RE generation due to MHD instability growth, decreased saturation energies of the m/n = 1/1 mode driving sawteeth-like activity, RE losses in stochastic magnetic fields, and subsequent RE confinement and plateau formation due to re-healing of flux surfaces. Large RE plateaus (>5 MA) are obtained with Ne-only injection ($2-5 \times 10^{21}$ atoms), while combined $\text{D}_2$ + Ne injection ($2 \times 10^{21}$ Ne atoms; $1.8 \times 10^{22} \, \text{D}_2$ molecules) produces a lower RE current (<2 MA). With $\text{D}_2$ + Ne injection, a post thermal quench "cold" VDE terminates the RE beam, preventing a steady plateau. These simulations couple REs, 3-D MHD instabilities, MGI, and axisymmetric VDEs for the first time in SPARC disruption simulations and represent a crucial step in understanding RE generation and mitigation in high-current devices like SPARC.

Figures (11)

• Figure 1: Flux-averaged profiles of the (a) ion density $n_i$ (left) and electron temperature $T_e$ (right), and (b) toroidal current density $j_\phi$ (left) and safety factor $q$ (right) at $t = 0ms$. (c) M0 Simulation geometry and equilibrium distribution of the poloidal flux at $t = 0ms$. White contours show lines of constant flux. The simulation geometry comprises the plasma volume (major radius $R_0 = 1.85m$, minor radius $a = 0.57m$) with a perfectly conducting (simplified) first wall. (d) M1 Double-walled vacuum vessel geometry comprising the first wall, inner vessel, outer vessel, and an outer vacuum region. A perfectly conducting boundary is imposed on boundary of the simulation domain.
• Figure 2: Initial flux-averaged distributions of the main ion (D) and Ne densities. The solid black line shows $n_D$ for cases A-C and the gray solid line shows $n_D$ for case D (combined Ne + D$_2$ MGI). The dashed blue line shows $n_{Ne}$ for cases C-D, and the dotted blue line shows that for case B. There is no injected Ne in case A.
• Figure 3: (a) Evolution of plasma (blue, solid) and RE (orange, solid) currents in the 3-D nonlinear simulation of an idealized disruption without impurities (case A). The dashed lines represent the result from a 2-D axisymmetric simulation. (b) Kinetic energy as a function of toroidal mode number $n$. (c) Magnetic field line perturbation as a function of toroidal mode number $n$. (d-e) Magnified version of \ref{['fig:unmitigated_3d']}(a-b) showing the runaway electron current evolution and the mode kinetic energy during the first crash. The purple line shows the result for the 3-D simulation where the Dreicer term is turned off around $t = 0.9ms$. (f-g) RE current density at $t = 0.85m s$ and $t = 0.94m s$ at the $\phi = 0$ plane. (h) Temporal evolution of the square root of the normalized poloidal flux $\sqrt{\psi_N}$ at the $q=1$ surface, as a function of time. The red line shows the total kinetic energy of the $1\leq n \leq 3$ modes (right axis). We plot values between $2ms< t < 6ms$, during which the M3D-C1 results were output at a higher frequency.
• Figure 4: (a) Linear growth rate of the $m/n = 1/1$ mode as a function of the Lundquist number. Blue circles assume spatially-uniform resistivity, while the red star uses non-uniform Spitzer resistivity, and represents the actual conditions in the post-TQ plasma used for the nonlinear simulation shown in \ref{['fig:unmitigated_3d']}. (b) Linear Growth Rate of the $m/n = 1/1$ mode as a function of the RE current fraction. Here, $\gamma_0 \approx 1e-3\tau_A^{-1}$ is the growth rate for $j_r/j_p = 0$ RE fraction. (c) The perturbed poloidal flux $\delta\psi$ and obtained from a linear simulation of $n = 1$ modes in the post-TQ plasma. Here, the RE current is set to 0. Temperature-dependent Spitzer resistivity is used. The black contour represents the $q = 1$ flux surface.
• Figure 5: The flux-averaged post-TQ (a) electron $n_e$, deuterium $n_i$, and neon $n_Z$ densities, (b) electron and ion temperature, (c) effective ionization $Z_\text{eff}$, and (d) parallel electric field $E_\parallel$ at $t = 0.1ms$ in case B ($4.8e21$ Ne atoms). The red dashed line is $E_\parallel$ normalized by $E_C$.