Impurity Parallel Velocity Gradient instability

TL;DR

This paper investigates how impurities influence the Parallel Velocity Gradient (PVG) instability in magnetized plasmas, revealing a new impurity-modified PVG instability through linear analysis.

Contribution

It extends PVG theory to include impurity effects, deriving a generalized model that predicts impurity-modified PVG instability in a simplified plasma system.

Findings

Impurities can stabilize or destabilize PVG depending on parameters.

A new impurity-modified PVG instability is identified.

Maximum growth rate depends on impurity properties and flow shear.

Abstract

In magnetized plasmas, a radial gradient of parallel velocity, where parallel refers to the direction of magnetic field, can destabilise an electrostatic mode called Parallel Velocity Gradient (PVG). The theory of PVG has been mainly developed assuming a single species of ions. Here, the role of impurities is investigated based on a linear, local analysis, in a homogeneous, constant magnetic field. To further simplify the analysis, the plasma is assumed to contain only two ion species - main ions and one impurity species - while our methodology can be straightforwardly extended to more species. In the cold-ion limit, retaining polarization drift for both main ions and impurity ions, and assuming Boltzmann electrons, the system is described by 4 fluid equations closed by quasi-neutrality. The linearized equations can be reduced to 2 coupled equations: one for the electric potential, and one for the effective parallel velocity fluctuations, which is a linear combination of main ion and impurity parallel velocity fluctuations. This reduced system can be understood as a generalisation of the Hasegawa-Mima model. With finite radial gradient of impurity parallel flow, the linear dispersion relation then describes a new instability: the impurity-modified PVG (i-PVG). Instability condition is described in terms of either the main ion flow shear, or equivalently, an effective flow shear, which combines main ion and impurity flow shears. Impurities can have a stabilising or destabilising role, depending on the parameters, and in particular the direction of main flow shear against impurity flow shear. Assuming a reasonable value of perpendicular wavenumber, the maximum growth rate is estimated, depending on impurity mass, charge, and concentration.