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 $D_{mumu}=D(1-mu^2)$, 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.
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