A phase-shift-periodic parallel boundary condition for low-magnetic-shear scenarios

TL;DR

This paper introduces a generalized phase-shift-periodic boundary condition for plasma simulations with low magnetic shear, improving accuracy and computational efficiency by avoiding convective cells and enabling statistical analysis of physical observables.

Contribution

It formulates a new boundary condition incorporating a phase shift, extending the twist-and-shift method for low-magnetic-shear plasma simulations.

Findings

Non-zero phase shift reduces convective cells in simulations.

Sampling at pseudo-irrational flux surfaces enables statistical analysis.

Proposed method offers an alternative to traditional boundary conditions.

Abstract

We formulate a generalized periodic boundary condition as a limit of the standard twist-and-shift parallel boundary condition that is suitable for simulations of plasmas with low magnetic shear. This is done by applying a phase shift in the binormal direction when crossing the parallel boundary. While this phase shift can be set to zero without loss of generality in the local flux-tube limit when employing the twist-and-shift boundary condition, we show that this is not the most general case when employing periodic parallel boundaries, and may not even be the most desirable. A non-zero phase shift can be used to avoid the convective cells that plague simulations of the three-dimensional Hasegawa-Wakatani system, and is shown to have measurable effects in periodic low-magnetic-shear gyrokinetic simulations. We propose a numerical program where a sampling of periodic simulations at random pseudo-irrational flux surfaces are used to determine physical observables in a statistical sense. This approach can serve as an alternative to applying the twist-and-shift boundary condition to low-magnetic-shear scenarios which, while more straightforward, can be computationally demanding.