On the proper treatment of magnetic fluctuations in full-$f$ field-aligned turbulence codes

TL;DR

This paper addresses the inconsistency in full-$f$ plasma turbulence simulations caused by background magnetic components in magnetic fluctuations, proposing a dynamic filtering method to improve numerical accuracy in field-aligned codes.

Contribution

It introduces a novel dynamic filtering technique to accurately separate background magnetic fields from turbulent fluctuations in full-$f$ turbulence simulations.

Findings

The filtering method preserves turbulence fidelity in tokamak simulations.

It prevents spurious transport caused by improper background removal.

The approach is validated in both low and high confinement conditions.

Abstract

Plasma turbulence in the edge of magnetic confinement devices is customarily treated as full-$f$ due to large fluctuations. For computational efficiency, field-aligned coordinates are employed, separating the magnetic field into equilibrium $B_0$ and delta-f perturbations which are handled by the magnetic flutter operators. Evolving the full-$f$ pressure with delta-$f$ magnetic perturbations can cause inconsistency since the latter contain background components such as the Shafranov shift, which are actually parts of the equilibrium magnetic field. Such background components ($B_s$) contained in the magnetic perturbations undermine the field-aligned numerics when treated as flutter: errors arise if $B_s/B_0\ll l_\perp/h_\parallel$ is not satisfied, with the perpendicular turbulence scale $l_\perp$ and the parallel grid distance $h_\parallel$. We find that the commonly used removal of $B_s$ by subtracting the toroidal average of magnetic perturbations intervenes in the Alfv\'en dynamics, causing spurious $E\times B$ transport. Instead, we propose an improved method to dynamically filter out the evolving background from the turbulent magnetic fluctuations in the time domain. The filter is verified in both low and high confinement tokamak conditions, confirming its capability to preserve the turbulence fidelity, provided sufficient filter width.