Figure 1

The field line diffusion coefficient $K={\kappa }_{\perp }/l_{\parallel }$ versus the strength of the turbulent magnetic field with respect to the mean field $B=\delta B/B_0$ for $L=l_{\parallel }/l_{\perp }=1$ corresponding to isotropic turbulence. Shown is the nonlinear result obtained by solving Eq. (17) numerically (solid line) and the analytical result (dotted line) obtained by employing SQLT $\left(B,K\to 0\right)$. The analytical result for this limit is given by Eqs. (22, 23). The weak turbulence result without the quasilinear approximation is also shown (dashed line). Also shown is the value $R=1$ for the Kubo number, which separates the linear and nonlinear regimes within the WTA.Reuse & Permissions

Figure 2

The field line diffusion coefficient $K={\kappa }_{\perp }/l_{\parallel }$ versus the ratio of the turbulence correlation lengths $L=l_{\parallel }/l_{\perp }$ for weak turbulence $B=\delta B/B_0=0.1$. Shown is the nonlinear result obtained by solving Eq. (17) numerically (solid line) and the analytical result (dotted line) obtained by employing SQLT $\left(B,K\to 0\right)$. The analytical result for this limit is given by Eqs. (22, 23). The weak turbulence result without the quasilinear approximation is also shown (dashed line) but is in perfect coincidence with the solid line. Also shown is the value $R=1$ for the Kubo number, which separates the linear and nonlinear regimes within the WTA.Reuse & Permissions

Figure 3

The field line diffusion coefficient $K={\kappa }_{\perp }/l_{\parallel }$ versus the ratio of the turbulence correlation lengths $L=l_{\parallel }/l_{\perp }$ for intermediate turbulence $B=\delta B/B_0=1$. Shown is the nonlinear result obtained by solving Eq. (17) numerically (solid line) and the analytical result (dotted line) obtained by employing SQLT $\left(B,K\to 0\right)$. The analytical result for this limit is given by Eqs. (22, 23). The weak turbulence result without the quasilinear approximation is also shown (dashed line). Also shown is the value $R=1$ for the Kubo number which separates the linear and nonlinear regimes within the WTA.Reuse & Permissions

Figure 4

The field line diffusion coefficient $K={\kappa }_{\perp }/l_{\parallel }$ versus the ratio of the turbulence correlation lengths $L=l_{\parallel }/l_{\perp }$ for strong turbulence $B=\delta B/B_0=10$. Shown is the nonlinear result obtained by solving Eq. (17) numerically (solid line) and the analytical result (dotted line) obtained by employing SQLT $\left(B,K\to 0\right)$. The analytical result for this limit is given by Eqs. (22, 23). The weak turbulence result without the quasilinear approximation is also shown (dashed line). Also shown is the value $R=1$ for the Kubo number, which separates the linear and nonlinear regimes within the WTA.Reuse & Permissions

Figure 5

The parameter $\gamma$ which is defined as the exponent in the field line diffusion coefficient $K=\alpha B^{\beta }{L}^{\gamma }$ versus the parameter $L$. We have considered weak turbulence with $B=0.1$ (dotted line), intermediate turbulence with $B=1$ (dashed line), and strong turbulence with $B=10$ (solid line). Also shown are the standard quasilinear result with $\gamma =0$ and the percolative scaling with $\gamma =-1.3$.Reuse & Permissions