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

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 $\mathit{\text{Letter}}$, 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.