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 $T'$ to $\kappa_{\parallel 0}$. Furthermore, by employing the isotropic pitch-angle scattering model $D_{\mu\mu}=D(1-\mu^2)$, we find that $T'$ has the different sign as that of $T$. In this paper the spatial perpendicular diffusion coefficient $\kappa_\bot$ with the adiabatic focusing effect is also obtained.