Theory of the Drift-Wave Instability at Arbitrary Collisionality

TL;DR

This paper introduces a numerically efficient spectral framework for analyzing drift-wave instabilities in magnetized plasmas, accurately capturing effects across all collisional regimes with implications for fusion device modeling.

Contribution

It develops a Hermite-Laguerre spectral method that incorporates the full Coulomb collision operator at arbitrary collisionalities, improving upon existing models.

Findings

The framework accurately reproduces known collisional and collisionless limits.

Deviations from simplified collision operators are significant at intermediate collisionalities.

Full Coulomb operator inclusion affects predicted instability growth rates and eigenmodes.

Abstract

A numerically efficient framework that takes into account the effect of the Coulomb collision operator at arbitrary collisionalities is introduced. Such model is based on the expansion of the distribution function on a Hermite-Laguerre polynomial basis, to study the effects of collisions on magnetized plasma instabilities at arbitrary mean-free path. Focusing on the drift-wave instability, we show that our framework allows retrieving established collisional and collisionless limits. At the intermediate collisionalities relevant for present and future magnetic nuclear fusion devices, deviations with respect to collision operators used in state-of-the-art turbulence simulation codes show the need for retaining the full Coulomb operator in order to obtain both the correct instability growth rate and eigenmode spectrum, which, for example, may significantly impact quantitative predictions of transport. The exponential convergence of the spectral representation that we propose makes the representation of the velocity space dependence, including the full collision operator, more efficient than standard finite difference methods.