Reduction of neoclassical bulk-ion transport to avoid helium-ash retention in stellarator reactors

Abstract

The reduction of neoclassical energy transport in stellarators has traditionally focussed on optimizing magnetic fields for small values of ‘effective helical ripple’ — $\epsilon_\mathrm{eff}$ , the geometric factor associated with electron $1/\nu$ transport—and relying on the radial electric field, $E_\mathrm{r}$ , needed to maintain ambipolarity in the plasma, to simultaneously diminish ion energy losses to a tolerable level. As one must generally expect $E_\mathrm{r} \lt 0$ , such a strategy has a drawback for reactor operation, however, as negative values of $E_\mathrm{r}$ tend to hinder the exhaust of helium ash, and this will become intolerable if it results in excessive fuel dilution. Theoretically, one can show that the neoclassical transport of low- Z impurities depends critically on the ratio $L_{11}^e/L_{11}^i$ , where the $L_{11}^\sigma$ are the neoclassical particle diffusion coefficients of the bulk-plasma electrons ( $\sigma = e$ ) and ions ( $\sigma = i$ ). Increasing the value of this ratio is shown here to counteract impurity retention, but maintaining good confinement of the bulk species requires this to be achieved by decreasing $L_{11}^i$ rather than increasing $L_{11}^e$ , implying the need for more than just minimization of $\epsilon_\mathrm{eff}$ in reactor design. To assess the prospects of such an endeavor, a predictive 1-D transport code is used here to determine the range of $L_{11}^e/L_{11}^i$ values which arises in simulations of conventionally optimized reactor candidates. This range is found to be considerable, and includes examples with $L_{11}^e/L_{11}^i$ values large enough to provide neoclassical temperature screening of the helium ash and even to flip the sign of the neoclassical convective velocity from inward- to outward-directed. More intriguingly, the strong reduction of $L_{11}^i$ in such cases can also lead to the appearance of $E_\mathrm{r} \gt 0$ (a so-called ‘electron root’) within the core of plasmas having central densities as large as $2\times 10^{20}$ m ^−3 . Having $E_\mathrm{r} \gt 0$ in the plasma core produces the ideal situation in which all thermodynamic forces aid in the exhaust of helium ash, although this benefit is tempered by the small values of $L_{11}^z$ which accompany an electron root (where $\sigma = z$ denotes helium ash). Means are discussed for improving the results presented here, so that avoiding helium-ash retention can be explicitly targeted in future reactor optimizations.

Keywords

• stellarator impurity transport
• stellarator reactor optimization
• neoclassical helium-ash retention