Parallel and perpendicular diffusion coefficients of energetic charged particles with adiabatic focusing

It is very important to understand stochastic diffusion of energetic charged particles in non-uniform background magnetic field in plasmas of astrophysics and fusion devices. Using different methods considering along-field adiabatic focusing effect, various authors derived parallel diffusion coefficient ${\kappa }_{\parallel }$ and its correction $T$ to ${\kappa }_{\parallel 0}$, where ${\kappa }_{\parallel 0}$ is the parallel diffusion coefficient without adiabatic focusing effect. In this paper, using the improved perturbation method developed by He & Schlickeiser and iteration process, we obtain a new correction $T^{\mathrm{\prime }}$ to ${\kappa }_{\parallel 0}$. Furthermore, by employing the isotropic pitch-angle scattering model $D_{\mu \mu }=D(1-{\mu }^2)$, we find that $T^{\mathrm{\prime }}$ has the different sign as that of $T$. In this paper the spatial perpendicular diffusion coefficient ${\kappa }_{\mathrm{\perp }}$ with the adiabatic focusing effect is also obtained.