The Boltzmann-Vlasov equation in orthogonal curvilinear coordinate system and its application in non-uniform magnetic field

We have derived the simple form of Boltzmann-Vlasov equation in the orthogonal curvilinear coordinate system by use of the curvature and the torsion of the coordinate axes, tried to introduce a term of the effect of non-uniform magnetic field configuration and formulated it also in a simple magnetic mirror field configuration. Moreover we have derived a few of momentum equations from the Boltzmann-Vlasov equation derived above. it is shown that the derived momentum equations become to well-known fluid equations of plasma if fluid approximation is satisfied. In application, we have examined the axial distribution function of collision-free plasma particles in a idealized magnetic mirror field configuration by use of the Boltzmann-Vlasov equation in non-uniform magnetic field. (author)