Collisional passing alpha energy transport in nearly quasisymmetric stellarators

TL;DR

This work investigates collisional transport of fusion-born alpha particles in nearly quasisymmetric stellarators, focusing on resonant energy losses near rational surfaces where departures from quasisymmetry couple streaming and tangential drift. The authors develop a drift-kinetic, quasilinear model that resolves collisional boundary layers in pitch angle and yields a resonant plateau transport mechanism for passing alphas, with the energy flux computed via a Su–Oberman-type solution and an inhomogeneous Airy problem. The resulting energy diffusivity $D$ scales with perturbation harmonics and amplitudes, and can produce measurable losses (up to ~10%) for perturbations of order $\delta B \sim 10^{-3}$ T at $q\approx m/n$, while highlighting limits of the linearized, quasilinear approach near resonances. The findings have important implications for stellarator design, indicating that controlling error-field structure and magnitude is crucial to minimize alpha energy losses and sustain effective alpha heating in reactor-relevant regimes.

Abstract

Recent advances in stellarator optimization have found nearly precise quasisymmetric configurations. These are expected to reduce the non-turbulent background plasma transport to acceptable neoclassical levels while removing nearly all collisionless direct orbit losses of alpha particles. Yet, alpha particles under resonant conditions can be very sensitive to collisions, causing concerning energy losses and damaging plasma facing components. For the passing alphas such resonances can happen near rational surfaces in the presence of helical error field departures from quasisymmetry that change the magnetic field direction and magnitude. The cancellation between streaming motion and tangential drift of the alphas enhances the effective collision frequency, allowing the formation of a collisional boundary layer and giving rise to a perturbed distribution function. We develop an analytical model to illustrate and evaluate the resonant plateau transport this mechanism causes by formulating a drift kinetic treatment. The results indicate the associated energy losses can become significant in the vicinity of rational surfaces at values of q=m/n when error fields with poloidal and toroidal numbers m and n are present. In addition, we investigate the validity of the quasilinear approximation to the energy flux to show that it imposes a restriction on the error field amplitude that can be considered.

Figures (8)

• Figure 1: Resonance condition (left) and schematic of the collisional boundary layer perturbed solution around the resonance (right) as we move away from the rational surface.
• Figure 2: Transport results for the mode $m=n=3$ versus safety factor $q$. (a) Transport levels for different perturbation amplitudes. (b) Maximum perturbation allowed by the linearization condition. (c) Transport for the maximum allowable perturbations. (d) Resonant pitch angle.
• Figure 3: Sensitivity analysis of transport for $\delta B = 10^{-3}\,\mathrm{T}$. In (a) we vary $\bar{B}_0$. In (b), we change the radial location $r$ and the minor radius $r_0$. In (c), we scan different values of $Z_{\mathrm{eff}}$. In (d), we explore how losses change if $v_0$ could be decreased.
• Figure 4: Sensitivity analysis of transport for $\delta B = 10^{-3}\,\mathrm{T}$. In (a), we vary the poloidal and toroidal numbers of the QS background $M$ and $N$, and of the perturbation $m$ and $n$. In (b), we present the overlapping transport from different perturbation harmonics. In (c), we show the effect of the $B_\perp$ and $B_\parallel$ pieces of a $(m,n)=(10,9)$ error field for different $\bar{B}_0$ values.
• Figure 5: Sensitivity analysis of transport for $\delta B = 10^{-3}\,\mathrm{T}$. In (a) and (b) we change the density and temperature, respectively. In (c), we vary the shear. In (d), we compare the transport in a bigger stellarator similar to our baseline case, and a smaller stellarator.