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It is very important to understand stochastic diffusion of energetic chargedparticles in non-uniform background magnetic field in plasmas of astrophysicsand fusion devices. Using different methods considering along-field adiabaticfocusing 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 adiabaticfocusing effect. In this paper, using the improved perturbation methoddeveloped by He \& Schlickeiser and iteration process, we obtain a newcorrection $T'$ to $\kappa_{\parallel 0}$. Furthermore, by employing theisotropic 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 spatialperpendicular diffusion coefficient $\kappa_\bot$ with the adiabatic focusingeffect is also obtained.

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