Flux pumping and bifurcated relaxations of helical core in 3D magnetohydrodynamic modelling of ASDEX Upgrade plasmas

TL;DR

This work uses a two-temperature, full-MHD model implemented in JOREK to study flux pumping in the ASDEX Upgrade (AUG) tokamak. It reproduces the experimentally observed clamped $q_0\approx 1$ and core current-density redistribution driven by a dynamo associated with the $m/n=1/1$ instability, validating the dynamo mechanism as essential for sustaining the flux-pumping state. Systematic parameter scans over Hartmann number $H$, magnetic Prandtl number $P$, and plasma beta reveal a bifurcation of core dynamics into four regimes—flux pumping, sawtooth, single-crash, and quasi-stationary magnetic island—with transitions governed by the balance between the nonlinear dynamo and external current drive, as well as mode spectrum. The study connects these regimes to experimental conditions, estimates a qualitative operating window in density and temperature, and outlines future extensions to include two-fluid/kinetic effects and a fast surrogate model to enable efficient evaluation of flux pumping for ITER-era devices.

Abstract

Flux pumping was achieved in recent hybrid scenario experiments in the ASDEX Upgrade (AUG) tokamak, which is characterized by a sawtooth-free helical quiescent state and the anomalous radial redistribution of toroidal current density and poloidal magnetic flux. In this article, the self-regulation mechanism of the AUG core plasma during flux pumping is investigated at realistic parameters using the JOREK code based on the two-temperature, nonlinear, full magnetohydrodynamic (MHD) model. A key milestone in AUG flux pumping modelling is achieved by quantitatively reproducing the clamped current density and safety factor profiles in the plasma core, demonstrating the effectiveness of the dynamo effect in sustaining the flux pumping state. The dynamo term, that is of particular interest, is primarily generated by the pressure-gradient driven m/n = 1/1 quasi-interchange-like MHD instability. The work systematically extrapolates the parameter regimes of flux pumping from the above AUG base case by scanning dissipation coefficients and plasma beta. The simulation results reveal bifurcated plasma behaviours at different Hartmann numbers, including distinct states such as flux pumping (helical core with a flat current density), sawteeth (periodic kink-cycling), single crash (without subsequent cycle), and quasi-stationary magnetic island (peaked current density). Transitions from marginal flux pumping state to sawteeth are observed in long-term simulations. The relationships between system dissipation, plasma beta, and different plasma states are carefully analyzed. For practical purposes, the potential operational window for flux pumping, as determined by plasma density and temperature, is estimated. The modelling efforts advance the understanding of flux pumping and facilitate the development of a fast surrogate model for efficient evaluation of flux pumping.

Figures (13)

• Figure 1: Reconstructed profiles of the flux pumping phase at 4.8s of the AUG discharge #36663: (a) experimental (blue, with IMSE data) and modelled (red, without IMSE data) current densities; (b) corresponding effective electric field deficit. Reprinted from Burckhart2023NF. © 2023 The Author(s). https://creativecommons.org/licenses/by/4.0/.
• Figure 2: The quasi-stationary magnetic flux tubes in the 3D simulation of the AUG flux pumping discharge. The colored slices indicate the mode structure of toroidal magnetic field.
• Figure 3: (a) $q$ and (b) current density profiles at the saturated stages of the 2D (solid line) and 3D (dashed line) simulations, as well as of the initial equilibrium (dash-dotted line). (c) The parallel dynamo electric field vs. time from the 3D simulation.
• Figure 4: Different plasma states obtained at different system dissipations: Base case with $H=7.9\times10^7$ (blue solid line); case (a) with $H=7.9\times10^6$ (orange dashed line); case (b) with $H=7.9\times10^5$ (green dash-dotted line); case (c) with $H=7.9\times10^4$ (red dotted line); and case (d) with $H=7.9\times10^3$ (purple solid line). $P$ is fixed at 1400 for all cases.
• Figure 5: Temporal evolutions of the radial profile of dynamo electric field normalized by $(H/H_\text{base}\cdot\sqrt{P_\text{base}}/v_A)^{-1}$, respectively for cases (a) $H=7.9\times10^6$, (b) $H=7.9\times10^5$, (c) $H=7.9\times10^4$, and (d) $H=7.9\times10^3$. $P$ is fixed at 1400 for all cases.