Pseudochaotic poloidal transport in the laminar regime of the resistive ballooning instabilities

TL;DR

This paper investigates the superdiffusive poloidal transport in resistive ballooning instabilities within the laminar regime, using fractional models to describe the complex, topologically rich iso-surfaces affecting particle advection.

Contribution

It introduces a fractional periodic model for poloidal transport and validates it with numerical simulations, revealing superdiffusive behavior with index 1.

Findings

Poloidal transport is superdiffusive with index 1.

Fractional models accurately describe poloidal transport.

Iso-surface topology significantly influences transport dynamics.

Abstract

In toroidal geometry, and prior to the establishment of a fully developed turbulent state, the so-called topological instability of the pressure-gradient-driven turbulence is observed. In this intermediate state, a narrow spectral band of modes dominates the dynamics, giving rise to the formation of iso-surfaces of electric potential with a complicated topology. Since E x B advection of tracer particles takes place along these iso-surfaces, their topological complexity affects the characteristic features of radial and poloidal transport dramatically. In particular, they both become strongly non-diffusive and non-Gaussian. Since radial transport determines the system confinement properties and poloidal transport controls the equilibration dynamics (on any magnetic surface), the development of non-diffusive models in both directions is thus of physical interest. In previous work, a fractional model to describe radial transport was constructed by the authors. In this contribution, recent results on periodic fractional models are exploited for the construction of an effective model of poloidal transport. Numerical computations using a three-dimensional reduced magnetohydrodynamic set of equations are compared with analytical solutions of the fractional periodic model. It is shown that the aforementioned analytical solutions accurately describe poloidal transport, which turns out to be superdiffusive with index $\alpha=1$.