Anomalous, quasilinear, and percolative regimes for magnetic-field-line transport in axially symmetric turbulence

We studied a magnetic turbulence axisymmetric around the unperturbed magnetic field for cases having different ratios $l_{\Vert }{/l}_{\perp }.$ We find, in addition to the fact that a higher fluctuation level $\delta {B/B}_0$ makes the system more stochastic, that by increasing the ratio $l_{\Vert }{/l}_{\perp }$ at fixed $\delta {B/B}_0,$ the stochasticity increases. It appears that the different transport regimes can be organized in terms of the Kubo number $R=\left(\delta {B/B}_0{\left)\right(l}_{\Vert }{/l}_{\perp }\right).\mathrm{}$ The simulation results are compared with the two analytical limits, that is the percolative limit and the quasilinear limit. When $R\ll 1$ weak chaos, closed magnetic surfaces, and anomalous transport regimes are found. When $R\approx 1$ the diffusion regime is Gaussian, and the quasilinear scaling of the diffusion coefficient $D_{\perp }\sim (\delta {B/B}_0{)}^2$ is recovered. Finally, for $R\gg 1$ the percolation scaling of the diffusion coefficient $D_{\perp }\sim (\delta {B/B}_0{)}^{0.7}$ is obtained.