Analytic model for neutral penetration and plasma fueling

Neutral atoms recycled from wall interaction interact with confined plasma, thereby refueling it, most strongly in the region closest to the wall. This occurs near the X-point in diverted configurations, or else near the wall itself in limited configurations. A progression of analytic models are developed for neutral density in the vicinity of a planar or linear source in an ionizing domain. First-principles neutral transport simulations with DEGAS2 are used throughout to test the validity and limits of the model when using equivalent sources. The model is further generalized for strong plasma gradients or the inclusion of charge exchange. An important part of the problem of neutral fueling from recycling is thereby isolated and solved with a closed-form analytic model. A key finding is that charge exchange with the confined plasma can be significantly simplified with a reasonable sacrifice of accuracy by treating it as a loss. The several assumptions inherent to the model (and the simulations to which it is compared) can be adapted according to the particular behavior of neutrals in the divertor and the manner in which they cross the separatrix.

💡 Research Summary

The paper presents a systematic analytic treatment of neutral atom penetration and plasma fueling, focusing on the region where recycled neutrals from plasma‑facing components re‑enter the confined plasma. Starting from first‑principles kinetic theory, the authors derive closed‑form solutions for the neutral distribution function in several idealized geometries: a planar source in a uniform ionizing medium, a planar source with a spatially varying loss rate that mimics a pedestal, and a radially symmetric “X‑point” line source representing the localized recycling at the magnetic null.

For the simplest case, the kinetic equation v∂f/∂x + γf = S(v)δ(x) is solved analytically, giving f(x,v)=S(v)v exp(‑γx/v). Assuming an isotropic Maxwellian source S(v), the neutral density nₙ(x) requires integration over velocity. In the high‑loss limit (γ≫vₜₙ/x) the authors apply the saddle‑point (steepest‑descent) method, obtaining the asymptotic expression

nₙ(x)≈2S₀√3 vₜₙ (γx/2vₜₙ)^{‑1/3} exp