Guiding-center theory for three-dimensional collisionless finite Larmor radius plasmas

The guiding-center theory appropriate for describing an arbitrary three-dimensional collisionless plasma system is developed. The generalization of the drift kinetic equation for the finite Larmor radius (FLR) case is derived by the Vlasov kinetic equation expansion in powers of inverse cyclotron frequency in terms of conventional magnetohydrodynamic (MHD) variables. It is shown that the first integrals of this equation analogous to energy and magnetic moment can also be found in the nonstationary case. It allows one to get a compact and physically clear form for the drift kinetic equation, including FLR corrections. The moment equations similar to MHD ones, but including the FLR corrections, are also derived. Some acceptable ways to truncate the moment equations series are considered. In particular the FLR generalization of Chew–Goldberger–Low equations is also developed. All results are given explicitly in invariant vector form. They can be used to extend the applicability and to optimize numerical codes as MHD as combined MHD kinetic ones, and should be considered rather as methodological ones.