Non-diffusive nature of collisionless alfa-particle transport: Dependence on toroidal symmetry in stellarator geometries

Abstract

An adequate confinement of 𝛼-particles is fundamental for the operation of future fusion powered reactors. An even more critical situation arises for stellarator devices, whose complex magnetic geometry can substantially increase 𝛼-particle losses. A traditional approach to transport evaluation is based on a diffusive paradigm; however, a growing body of literature presents a considerable amount of examples and arguments toward the validity of non-diffusive transport models for fusion plasmas, particularly in cases of turbulent driven transport [R. Sánchez and D. E. Newman, Plasma Phys. Controlled Fusion 57, 123002 (2015)]. Likewise, a recent study of collisionless 𝛼-particle transport in quasi-toroidally symmetric stellarators [A. Gogoleva et al., Nucl. Fusion 60, 056009 (2020)] puts the diffusive framework into question. In search of a better transport model, we numerically characterized and quantified the underlying nature of transport of the resulting 𝛼-particle trajectories by employing a whole set of tools, imported from the fractional transport theory. The study was carried out for a set of five configurations to establish the relation between the level of the magnetic field toroidal symmetry and the fractional transport coefficients, i.e., the Hurst H, the spatial α, and the temporal β exponents, each being a merit of non-diffusive transport. The results indicate that the 𝛼-particle ripple-enhanced transport is non-Gaussian and non-Markovian. Moreover, as the degree of quasi-toroidal symmetry increases, it becomes strongly subdiffusive, although the validity of the fractional model itself becomes doubtful in the limiting high and low symmetry cases