Variability of MHD Instabilities in Benign Termination of High-Current Runaway Electron Beams in the JET and DIII-D Tokamaks

TL;DR

The paper tackles the problem of reliably achieving benign termination of high-current runaway electron beams in tokamaks, a key disruption-mitigation challenge for reactors like ITER. It combines fast magnetic measurements, EFIT-based equilibria, and linear resistive MHD modeling with CASTOR3D to analyze ~40 JET and ~20 DIII-D discharges with hydrogenic injections. A central finding is that RE current peaking, captured by the internal inductance $l_i$, largely determines which MHD boundary is encountered, with benign terminations linked to less peaked profiles and larger cross-sections, while non-benign cases exhibit higher $j_{RE}$ and more peaked profiles; growth rates are similar across termination types, suggesting that Alfvén times alone do not explain deconfinement. The results indicate that the interplay of ideal and resistive dynamics, via kink-mode physics, governs termination, and they motivate standardized cross-machine classification and nonlinear resistive MHD modeling to extend these insights to reactor-relevant regimes.

Abstract

Benign termination, in which magnetohydrodynamic (MHD) instabilities deconfine runaway electrons (REs) following hydrogenic injections, is a promising strategy for mitigating dangerous RE loads after disruptions. Recent experiments on the Joint European Torus (JET) have explored this scenario at higher pre-disruptive plasma currents than are achievable on other devices, revealing challenges in obtaining benign terminations at $I_p \geq 2.5$ MA. This work analyzes the evolution of these high-current RE beams and their terminating MHD events using fast magnetic sensor measurements and EFIT equilibrium reconstructions for approximately $40$ JET and $20$ DIII-D tokamak discharges. On JET, unsuccessful non-benign terminations occur at low edge safety factor ($q_{\text{edge}} \approx 2$), and are preceded by intermittent, non-terminating MHD events at higher rational $q_{\text{edge}}$. Trends in the internal inductance $l_i$ indicate more peaked RE current profiles in the high-$I_p$ non-benign population, which may hinder successful recombination through re-ionization. In contrast, benign terminations on JET typically occur at higher $q_{\text{edge}} \geq 3$ and exhibit less peaked RE current profiles. DIII-D displays a range of terminating edge safety factors, correlated with the measured $l_i$ values. Across both tokamaks, the RE current peaking is therefore found to determine which MHD instability boundary is encountered, confirmed by linear resistive MHD modeling with the CASTOR3D code. Measured growth rates are similar for benign and non-benign cases, indicating that ideal MHD timescales at low density after hydrogenic injection do not alone explain efficient RE deconfinement. Instead, non-benign cases are characterized by their lower MHD perturbation amplitudes $δB$. These observations suggest that the interplay between ideal and resistive dynamics governs the termination process.

Figures (14)

• Figure 1: The studied database for DIII-D (l.h.s.) and JET (r.h.s.). Panel (a): Runaway current $I_{RE}$ immediately before the terminating MHD event versus the pre-disruptive plasma current $I_p$. Panel (b): Runaway current density $j_{RE}$ immediately before the terminating MHD event versus the pre-disruptive plasma current $I_p$. On JET, non-benign cases terminate from higher RE current densities. DIII-D does not show a separation of benign and non-benign cases by the RE current density at low pre-disruptive $I_p$, despite reaching similar RE current densities. Benign termination cases are marked with a green circle; non-benign cases with a red star.
• Figure 2: Typical benign termination on JET (#102617), marking the primary disruption (0), the hydrogenic injection (1), the RE plateau phase with plasma compression towards the center post (2), and the onset of the terminating MHD event (3).
• Figure 3: Typical non-benign termination on JET (#105794), marking the primary disruption (0), the hydrogenic injection (1), the RE shorter plateau phase with plasma compression towards the center post (2), and the onset of the termination (3), without significant magnetic activity.
• Figure 4: Magnetic analysis of the terminating MHD event in the JET discharge #102617. Panel (a) shows the time trace of $\dot{B}$ of the $n=1$ component reconstructed from the toroidal Mirnov coil array (solid line), with the shaded area indicating the integrated perturbation amplitude $\delta B$ over the time span shown in the plot. A fitted exponential growth is overlaid (dotted line) for comparison. Panel (b) displays $\dot{B}$ on a logarithmic scale (solid line) together with a linear fit (dotted line), from which the growth rate $\gamma$ is extracted.
• Figure 5: Trajectory of the RE beam center before the onset of the terminating MHD event in JET. Color coding is based on the plasma cross-section. The JET wall contour is shown in black. Shown are several trajectories for different discharges in the studied database.