# Stellarator bootstrap current and plasma flow velocity at low collisionality

## TL;DR

This paper provides a comprehensive analysis of bootstrap current and plasma flow velocity in low-collisionality stellarators, highlighting the limitations of conventional formulas and proposing necessary modifications across different collisionality regimes.

## Contribution

It offers a unified calculation method for bootstrap current and flow velocity in all low-collisionality regimes in stellarators, extending beyond the traditional $1/
u$-regime.

## Key findings

- Conventional formulas are accurate only in the $1/
u$-regime.
- Modifications are needed in the $\sqrt{
u}$-regime.
- Finite collisionality correction scales as $
u^{2/5}$.

## Abstract

The bootstrap current and flow velocity of a low-collisionality stellarator plasma are calculated. As far as possible, the analysis is carried out in a uniform way across all low-collisionality regimes in general stellarator geometry, assuming only that the confinement is good enough that the plasma is approximately in local thermodynamic equilibrium. It is found that conventional expressions for the ion flow speed and bootstrap current in the low-collisionality limit are accurate only in the $1/\nu$-collisionality regime and need to be modified in the $\sqrt{\nu}$-regime. The correction due to finite collisionality is also discussed and is found to scale as $\nu^{2/5}$.