It is very important to understand stochastic diffusion of energetic charged particles in nonuniform 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 κ and its correction T to κ 0 , where κ 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 κ 0 . Furthermore, by employing the isotropic pitch-angle scattering model D µµ = D(1−µ 2 ), we find that T ′ has the different sign as that of T . In this paper the spatial perpendicular diffusion coefficient κ ⊥ with the adiabatic focusing effect is also obtained.

The equation κ zz = dσ 2 /(2dt) (hereafter DCDV) is a well-known formula of energetic particles describing the relation of parallel diffusion coefficient κ zz with the parallel displacement variance σ 2 . In this study, we find that DCDV is only applicable to two kinds of transport equations of isotropic distribution function, one is without cross terms, the other is without convection term. Here, by employing the more general transport equation, i.e., the variable coefficient differential equation derived from the Fokker-Planck equation, a new equation of κ zz as a function of σ 2 is obtained. We find that DCDV is the special case of the new equation. In addition, another equation of κ zz as a function of σ 2 corresponding to the telegraph equation is also investigated preliminarily.

The momentum diffusion of charged energetic particles is an important mechanism of the transport process in astrophysics, the physics of fusion devices, and laboratory plasmas. In addition to the momentum diffusion term for a uniform field, we obtain an additional momentum diffusion term due to the focusing effect of the large-scale magnetic field. After evaluating the coefficient of the additional momentum diffusion term, we find that it is determined by the sign of the focusing characteristic length and the cross helicity of the turbulent magnetic field. Furthermore, by deriving the mean momentum change rate contributed from the additional momentum diffusion term, we identify that the focused field provides an additional momentum loss or gain process.

The spatial parallel diffusion coefficient (SPDC) is one of the important quantities describing energetic charged particle transport. There are three different definitions for the SPDC: the displacement variance definition , the Fick’s law definition with , and the Taylor–Green–Kubo (TGK) formula definition . For a constant mean magnetic field, the three different definitions of the SPDC give the same result. However, for a focusing field, it is demonstrated that the results of the different definitions are not the same. In this paper, from the Fokker–Planck equation, we find that different methods, e.g., the general Fourier expansion and iteration method, can give different equations of the isotropic distribution function (EIDFs). But it is shown that one EIDF can be transformed into another by some derivative iterative operations (DIOs). If one definition of the SPDC is invariant for the DIOs, it is clear that the definition is also invariant for different EIDFs; therefore, it is an invariant quantity for the different derivation methods of the EIDF. For the focusing field, we suggest that the TGK definition is only an approximate formula, and the Fick’s law definition is not invariant to some DIOs. However, at least for the special condition, in this paper we show that the definition is an invariant quantity to the DIOs. Therefore, for a spatially varying field, the displacement variance definition , rather than the Fick’s law definition and TGK formula definition , is the most appropriate definition of the SPDCs.

In recent years, the development of electric vehicles has made remarkable achievements. Its popularization and application can alleviate the problem of energy shortage and environmental pollution to some extent. In the process of discharging, the battery will generate heat. If the heat cannot be transferred to the external environment in time, the normal operation of the battery will be affected. In this paper, a BTM system based on PCM/micro-channel cooling is designed, and its cooling effect on battery module is studied by numerical simulation. The electrochemical-thermal coupling model is established to study the heat production and temperature changes of the battery during discharging. The cooling effect of the flow rate at the inlet of the cooling plate and the thickness of PCM on the battery module is studied. The results show that the BTM system can not only reduce the maximum temperature of the battery module, but also effectively improve the temperature inhomogeneity among the batteries.