The integrals of drift particles motion with finite Larmor radius

A large number of cosmic and laboratory plasma objects is often described with help of collisionless magnetized plasma approximation. The object considered is assumed to vary its state with time and spatial scales which are more great than cyclotron period (∼1/Ω mc/eB) and Larmor radius (∼vT/Ω) but less than path and time between collisions. The particle motion consists of fast cyclotron rotation, drift across magnetic field lines and longitudinal moving. The dynamics of slow drift and longitudinal motions of particle ensemble could be described by Rudakov-Sagdeev drift-kinetic equation (DKE) derived from collisionless Vlasov equation by cyclotron rotation averaging. The importance of finite Larmor radius (FLR) effects for plasma equilibrium and stability problems has stimulated the various attempts to modify DKE for non zero value of 1/Ω. Contrary to previous papers concerned to 2D-geometry there was obtained the generalization of DKE, including entirely the all FLR-corrections at first order of 1/Ω for arbitrary 3D-case. Using this equation the problem of particle motion integral existence is here investigated taking into account a macroscopic plasma flow and FLR-corrections to drift motion. (author) 8 refs