[Paper Review] Modeling the complete prevention of disruption-generated runaway electron beam formation with a passive 3D coil in SPARC

R. A. Tinguely, V.A. Izzo+9 more|arXiv (Cornell University)|Oct 20, 2021

Magnetic confinement fusion researchPhysics and Astronomy41 references41 citations

TL;DR

This study demonstrates that a passive 3D conducting coil (RE Mitigation Coil, REMC) in the SPARC tokamak can completely prevent runaway electron (RE) beam formation during plasma disruptions. By inducing stochastic magnetic fields via inductive coupling during current quench, the REMC accelerates electron loss faster than RE beams can form, achieving full suppression in the worst-case disruption scenario.

ABSTRACT

The potential formation of multi-mega-ampere beams of relativistic "runaway" electrons (REs) during sudden terminations of tokamak plasmas poses a significant challenge to the tokamak's development as a fusion energy source. Here, we use state-of-the-art modeling of disruption magnetohydrodynamics coupled with a self-consistent evolution of RE generation and transport to show that a non-axisymmetric in-vessel coil will passively prevent RE beam formation during disruptions in the SPARC tokamak, a compact, high-field, high-current device capable of achieving a fusion gain Q > 2 in deuterium-tritium plasmas.

Motivation & Objective

• To address the critical challenge of runaway electron (RE) beam formation during tokamak disruptions, which can damage plasma-facing components.
• To evaluate a passive mitigation strategy using a non-axisymmetric, in-vessel 3D coil (REMC) that passively generates stochastic magnetic fields during disruption current quench.
• To demonstrate complete suppression of RE beam formation in the worst-case SPARC disruption scenario (deuterium-tritium, H-mode, Q > 2).
• To validate the effectiveness of the REMC through integrated modeling of 3D MHD, vacuum field perturbations, and RE transport dynamics.

Proposed method

• Model the vacuum magnetic perturbation of the REMC using 3D finite element analysis in COMSOL, simulating its inductive coupling to the disruption-induced current decay.
• Use the NIMROD 3D MHD code to simulate the current quench phase with time-dependent external magnetic fields derived from the REMC's induced current (Icoil = 590 kA peak).
• Apply time-varying n = 1–10 toroidal Fourier modes at the NIMROD boundary, scaled proportionally to the plasma current decay (Icoil(t) ∝ 1 − Ip(t)/Ip(0)).
• Simulate the thermal quench via an artificial, rapid loss of thermal energy (4 × 10⁴ m²/s) over 0.045 ms, followed by a reduced diffusivity to stabilize the cold plasma state.
• Compute radial RE transport coefficients (advection A and diffusion D) using the ASCOT5 orbit-following code in the 3D stochastic magnetic fields from NIMROD.
• Use the computed transport coefficients in a fluid-kinetic solver to model RE generation and evolution, focusing on beam formation suppression.

Experimental results

Research questions

• RQ1 Can a passive 3D coil prevent runaway electron beam formation during the most severe disruption scenario in the SPARC tokamak?
• RQ2 To what extent do inductive, self-driven magnetic perturbations from the REMC induce sufficient field stochasticity to suppress RE beam formation?
• RQ3 How do nonlinear MHD mode growth and flux surface destruction during the current quench influence RE transport and beam formation?
• RQ4 What is the role of non-axisymmetric magnetic perturbations in achieving complete RE suppression without active control or external field sources?

Key findings

• The REMC induces a peak current of 590 kA passively during the disruption, generating strong n = 1 and n = 2 magnetic perturbations that drive nonlinear MHD mode growth.
• Nonlinear MHD simulations show rapid excitation and saturation of n = 1–10 modes by t ≈ 0.65 ms, with m/n = 1/1, 2/1, and 3/2 modes prominent near the plasma core.
• Global magnetic field stochasticity develops by t ≈ 0.7 ms, with complete destruction of flux surfaces and the formation of a small, slowly growing core magnetic island (width ~cm).
• The induced stochastic fields cause electron transport coefficients (A and D) that exceed the threshold for RE beam formation, enabling electron loss rates faster than beam growth.
• The simulation shows no RE beam formation in the worst-case scenario, confirming complete suppression of runaway electrons via passive mitigation.
• The method is robust under conservative assumptions, including an artificial thermal quench and no collisional or electric field effects in transport modeling.