A scaling law of the neutral opacity and Balmer-$\alpha$ wing shape in high-temperature plasmas

TL;DR

This paper derives a scaling law for neutral opacity and Balmer-alpha wing shape in high-temperature plasmas, linking spectroscopic features to neutral atom velocity distributions and particle sources.

Contribution

It provides an analytical approximation for neutral transport and opacity in plasmas, validated by simulations and observations, enabling direct measurement of neutral particle sources.

Findings

Power-law decay in Balmer-alpha line wings predicted.

Analytical representation of neutral opacity derived.

Validation through Monte-Carlo simulation and spectroscopic data.

Abstract

Hydrogen atoms penetrating deep inside high-temperature magnetically confined plasmas by repetitive charge-exchange collisions result in a particle source, which affects the plasma performance significantly. In this \textit{Letter}, we present an approximate solution of the fluid equations for neutral transport and the analytical representation of the neutral opacity, in a simplified plasma geometry. This analysis predicts a power-law decay in the Balmer-$\alpha$ line wings which reflects the velocity distribution of the neutral atoms, with the power-law index analytically represented as well. These scaling laws are validated by the comparison with a simple Monte-Carlo simulation and spectroscopic observations of Large Helical Device plasmas. Since the Balmer-$\alpha$ line wings are experimentally accessible, our formulation opens the door to directly observe the neutral opacity and thus the particle source distribution in the plasma.