[Paper Review] Effect of plasma elongation on current dynamics during tokamak disruptions

Tünde Fülöp, P. Helander+7 more|arXiv (Cornell University)|Sep 30, 2019

Magnetic confinement fusion research33 references21 citations

TL;DR

This paper investigates how plasma elongation (κ) reduces runaway electron current during tokamak disruptions by lowering the induced electric field and suppressing avalanche multiplication. Using a 1D resistive diffusion model with elliptical flux surfaces, it shows that elongation reduces the maximum electric field by a factor of ~1/κ and the avalanche gain by a factor of 2/(κ + κ⁻¹), leading to significantly lower runaway currents in high-current devices like ITER when Dreicer generation dominates.

ABSTRACT

Plasma terminating disruptions in tokamaks may result in relativistic runaway electron beams with potentially serious consequences for future devices with large plasma currents. In this paper we investigate the effect of plasma elongation on the coupled dynamics of runaway generation and resistive diffusion of the electric field. We find that elongated plasmas are less likely to produce large runaway currents, partly due to the lower induced electric fields associated with larger plasmas, and partly due to direct shaping effects, which mainly lead to a reduction in the runaway avalanche gain.

Motivation & Objective

• To understand how plasma elongation affects runaway electron current dynamics during tokamak disruptions.
• To quantify the impact of elongation on the induced electric field and resistive diffusion of the toroidal electric field.
• To assess how shaping influences runaway avalanche multiplication and primary generation (Dreicer vs. tritium decay).
• To evaluate the role of elongation in mitigating runaway current growth in future devices like ITER and SPARC.
• To isolate shaping effects from MHD stability and transport effects by using idealized, pre-described temperature evolution.

Proposed method

• Derives a general equation for toroidal electric field evolution in axisymmetric tokamaks with elliptical flux surfaces using flux-surface-averaged MHD and resistive diffusion theory.
• Applies the large aspect ratio approximation to simplify the current density evolution equation, yielding ∂j∥/∂t ∝ (1 + κ⁻²)/r ∂/∂r (r ∂E/∂r).
• Uses the go code to simulate runaway current dynamics, incorporating Dreicer and tritium decay seed generation with neural network-trained runaway growth rates.
• Performs idealized simulations of thermal quench with exponentially decaying temperature profiles, comparing circular (κ=1) and elongated (κ=1.45) plasmas.
• Analyzes the effect of elongation on electric field evolution, runaway current growth, and current conversion (IRE/Itot) under varying quench times and final temperatures.
• Tests robustness by varying the temperature profile (e.g., flat final profile) and finds consistent trends in the effect of elongation.

Experimental results

Research questions

• RQ1 How does plasma elongation affect the maximum induced electric field during a tokamak disruption?
• RQ2 To what extent does elongation reduce the runaway avalanche multiplication gain?
• RQ3 Does the reduction in runaway current depend on the dominant runaway generation mechanism (Dreicer vs. tritium decay)?
• RQ4 How does elongation influence the final runaway current in high-current devices like ITER and SPARC?
• RQ5 Is the effect of elongation on runaway current robust under different temperature evolution profiles?

Key findings

• Plasma elongation reduces the maximum induced electric field by a factor of approximately 1/κ, due to the inverse dependence of current density on elongation.
• The runaway avalanche gain is reduced by a factor of 2/(κ + κ⁻¹), which for κ = 1.45 reduces the gain by ~25% compared to circular plasmas.
• In simulated ITER disruptions, where Dreicer generation dominates, the final runaway current is significantly reduced in elongated plasmas due to the combined effects of lower electric field and reduced avalanche gain.
• For SPARC, where Dreicer generation is dominant, the reduction in final runaway current is also substantial, though the trend is consistent across different quench times and final temperatures.
• When tritium decay dominates primary generation, the final runaway current is only marginally reduced by elongation, as the tritium seed increases slightly with κ but the avalanche suppression is insufficient to offset this.
• The effect of elongation on runaway current is robust even when the radial temperature profile is kept constant, indicating that the result is primarily due to geometric and resistive diffusion effects rather than temperature profile dynamics.