Aligning Thermal and Current Quenches with a High Density Low-Z Injection

TL;DR

The paper tackles disruption mitigation by aligning the thermal quench (TQ) with the current quench (CQ) through dilutional cooling using high-density, low-Z hydrogen injection in a tokamak. It employs 3D extended MHD simulations with the PIXIE3D code, incorporating Braginskii transport, Bremsstrahlung cooling, and a Bohm sheath boundary to model wall losses, under an ITER-like 15 MA equilibrium with a strong (n=1,m=1) kink drive that yields global magnetic stochasticity. Results across three density regimes reveal an optimal window (≈300×) where TQ is slowed to ~20 ms and aligns with CQ, while too low or too high densities either fail to slow TQ sufficiently or induce radiation-dominated TQ with potential runaway, respectively. The findings indicate a viable disruption-mitigation pathway that reduces wall loads and suppresses runaway growth, with future work needed on non-ideal wall effects and more realistic post-injection density profiles. E_c = $\frac{n_e e^3 \ln{\Lambda}}{4 \pi \epsilon_0^2 m_e c^2}$ is referenced as the runaway threshold criterion.

Abstract

The conventional approach for thermal quench mitigation in a tokamak disruption is through a high-Z impurity injection that radiates away the plasma's thermal energy before it reaches the wall. The downside is a robust Ohmic-to-runaway current conversion due to the radiatively clamped low post-thermal-quench electron temperature. An alternative approach is to deploy a low-Z (either deuterium or hydrogen) injection that aims to slow down the thermal quench, and ideally aligns it with the current quench. This approach has been investigated here via 3D MHD simulations using the PIXIE3D code. By boosting the hydrogen density, a fusion-grade plasma is dilutionally cooled at approximately the original pressure. Energy loss to the wall is controlled by a Bohm outflow condition at the boundary where the magnetic field intercepts a thin plasma sheath at the wall, in addition to Bremsstrahlung bulk losses. Robust MHD instabilities proceed as usual, while the collisionality of the plasma has been greatly increased and parallel transport is now in the Braginskii regime. The main conclusion of this study is that the decreased transport loss along open field lines due to a sufficient low-Z injection slows down the thermal quench rate to the order of 20 ms, aligned with the current quench timescale for a 15 MA ITER plasma.

Figures (17)

• Figure 1: Geometry of the PIXIE3D simulations. The geometry and grid are toroidally symmetric with uniformly spaced grid points in the toroidal direction. The grid has dimensions $128\times64\times64$. Poloidal grid points are in gray, the equilibrium's separatrix is in red, the numerical boundary is in blue, and the actual ITER boundary is shown in black. Boundary grid points where the critical grazing angle is met is shown in green (described in Section \ref{['sec22']}). The coordinate map for these grid points is described in the Appendix.
• Figure 2: Initial q-profile for the equilibrium used in the simulations. This normalized radius is along $\theta =0$ from the geometric axis to the separatrix. The q-profile is extrapolated beyond the separatrix to the boundary. The vertical line shows the location where $q=1$ is crossed, which is where the internal kink mode appears which drives the disruption.
• Figure 3: Poincare cross section plots of magnetic fields at various times throughout the $300\times$ simulation. The Alfvén time is $\tau_A = 3.2 \mu$s. The $(n=1, m=1)$ kink grows to large amplitude while higher m modes are also excited outside the $q=1$ surface all the way to the separatrix ($t=1332\tau_A$). Global stochasticity of the magnetic field lines is reached at $t=1883 \tau_A$. As the pressure drops, some core flux surfaces re-heal, but total plasma current and pressure continue to dissipate until they reach small values after approximately 23 ms, when the simulation is stopped.
• Figure 4: Temperature profiles at various times throughout the $300\times$ simulation, at $\phi=0$. The thermal energy has completely quenched after 23 ms.
• Figure 5: Radial profile for the temperature from the magnetic axis (r=0) to the wall (r=1) for the $300\times$ simulation. Sheath losses near the divertor (left) result in lower temperature there than on the outboard side (right), but the entire system has a net cooling. The normalization value is 68 eV.