Relaxed magnetohydrodynamics with cross-field flow
This work addresses the challenge of modeling cross-field flow in plasma physics for applications like fusion energy, representing an incremental advancement by extending an existing framework to characterize steady-state solutions.
The paper tackles the problem of incorporating cross-field flow into relaxed magnetohydrodynamics equilibria while maintaining ideal force balance, resulting in the identification of a solvability condition that couples flow to geometry and the construction of equilibria in various geometries, with cross-field flow shown to strongly correlate with magnetic-island structure in toroidal geometry, such as modifying Fourier harmonics and driving transitions between island types.
The phase-space Lagrangian model of Dewar et al. (Phys. Plasmas 27, 062507, 2020) provides a framework for incorporating cross-field flow into relaxed equilibria while retaining ideal magnetohydrodynamics force balance. Here, we characterize the steady-state solution space and identify a solvability condition that couples the prescribed constrained flow to the geometry through the metric tensor. Using this condition, we construct equilibria in slab, cylindrical, and toroidal geometries. In toroidal geometry, the cross-field flow strongly correlates with magnetic-island structure: varying the rotation frequency modifies the dominant Fourier harmonic of the radial component of the magnetic field and can drive a transition from a primary (m = 1) island to secondary (m = 2) islands. In slab and cylindrical geometries, flow parameters weakly affect island width but strongly modify equilibrium profiles.