Collisional transport of impurities with flux-surface varying density in stellarators

Abstract

High-Z impurities in magnetic confinement devices are prone to develop density variations on the flux-surface, which can significantly affect their transport. In this paper, we generalize earlier analytic stellarator calculations of the neoclassical radial impurity flux in the mixed-collisionality regime (collisional impurities and low-collisionality bulk ions) to include the effect of such flux-surface variations. We find that only in the homogeneous density case is the transport of highly collisional impurities (in the Pfirsch-Schlüter regime) independent of the radial electric field. We study these effects for a Wendelstein 7-X (W7-X) vacuum field, with simple analytic models for the potential perturbation, under the assumption that the impurity density is given by a Boltzmann response to a perturbed potential. In the W7-X case studied, we find that larger amplitude potential perturbations cause the radial electric field to dominate the transport of the impurities. In addition, we find that classical impurity transport can be larger than the neoclassical transport in W7-X. † Email address for correspondence: bstefan@chalmers.se

The importance of the classical channel in the impurity transport of optimized stellarators

“…This can be shown using the expression for neoclassical transport derived by Braun & Helander (2010) together with the expression for classical transport in, for example, Buller et al. (2018). For stellarators optimized for low (such as W7-X), the (2.1) ratio will be large and classical transport will thus dominate at high collisionality.…”

“…Before performing a detailed analysis, it is useful to consider a simple (but experimentally relevant) limit, where the importance of classical transport in a stellarator is apparent. For this purpose, we summarize results from earlier work (Buller et al 2018;Braun & Helander 2010;Helander et al 2017).…”

“…Equation 2.1 also enters into the ratio of classical and neoclassical transport at yet higher collisionalities: in the Pfirsch-Schlüter regime, where both bulk and impurity ions are collisional. This can be shown using the expression for neoclassical transport derived by Braun & Helander (2010) together with the expression for classical transport in, for example in Buller et al (2018). For stellarators optimized for low j /j ⊥ (such as W7-X), the (2.1) ratio will be large and classical transport will thus dominate at high collisionality.…”

“…Effects ofΦ and the radial electric field are not included in this demonstration (they are zero in the simulations), as this would make the drift-kinetic equation nonlinear, and add the complexity of finding the ambipolar electric field at each step. These effects are not expected to strongly affect the classical transport, which is independent of the radial electric field, and typically not as sensitive toΦ as the neoclassical transport (Buller et al 2018). The neoclassical transport can be both enhanced or reduced by these effects, which thus would affect the relative importance of classical transport.…”

“…Unlike analytical calculations of the neoclassical transport (Buller et al. 2018; Calvo et al. 2018), this procedure is not limited to a specific collisionality regime, which will let us assess the importance of classical transport for any collisionality.…”