Nonlocal transport in the reversed field pinch

Several heuristic models for nonlocal transport in plasmas have been developed, but they have had a limited possibility of detailed comparison with experimental data. Nonlocal aspects introduced by the existence of a known spectrum of relatively stable saturated tearing modes in a low current reversed field pinch (RFP) offers a unique possibility for such a study. A numerical modeling of the magnetic structure and associated particle transport is carried out for the RFP experiment at the Consorzio RFX, Padova, Italy. A reproduction of the tearing mode spectrum with a guiding center code (White and Chance 1984 Phys. Fluids 27 2455) reliably reproduces the observed soft x-ray tomography. Following particle trajectories in the stochastic magnetic field shows the transport across the unperturbed flux surfaces to be due to a spectrum of Levy flights, with the details of the spectrum position dependent. The resulting transport is subdiffusive, and cannot be described by Rechester-Rosenbluth diffusion, which depends on a random phase approximation. If one attempts to fit the local transport phenomenologically, the subdiffusion can be fit with a combination of diffusion and inward pinch (Spizzo et al 2007 Phys. Plasmas 14 102310). It is found that whereas passing particles explore the stochastic field and hence participate in Levy flights, the trapped particles experience normal neoclassical diffusion. A two fluid nonlocal Montroll equation is used to model this transport, with a Levy flight defined as the motion of an ion during the period that the pitch has one sign. The necessary input to the Montroll equation consists of a time distribution for the Levy flights, given by the pitch angle scattering operator, and a distribution of the flight distances, determined numerically using a guiding center code. Results are compared with the experiment. The relation of this formulation to fractional kinetics is also described.