Chaos generated subdiffusion and related convection in toroidal confinement devices

Transport in toroidal devices is usually described as the sum of diffusion and convection, $\Gamma = - D \nabla n + v \cdot n$, and $v$ is interpreted as the spatial variation $\partial D/\partial r$ of $D$. When the magnetic field is chaotic and it is near the stochastic threshold (as it is the case for the reversed-field pinch, RFP), the assumption that particles moving along chaotic field lines diffuse in the system is not valid. Instead, in such a condition, a convective velocity term appears quite naturally due to the streaming motion of particles with velocity nearly parallel to the magnetic field (i.e., with pitch $\lambda = v_{\parallel}/v$ close to 1), while particles with small pitch diffuse collisionally through the magnetic field. The convective term is a consequence of the intrinsic, non-diffusive character of the transport. Diffusive motion is recovered when the configuration consists of closed nested flux surfaces, such as in the ideal single helicity (SH) condition \footnote{D. F. Escande \textit{et al.}, Phys. Rev. Lett. \textbf{85 (15)}, 3169 (2000).}. The study is carried on calculating magnetic field lines and particle orbits with the code \textsc{Orbit} for a typical multiple helicity (MH) chaotic field, provided by a 3D MHD numerical simulation (SpeCyl) of the RFP.