A second-order approximation is formulated and studied within the context of the quasi-particle description of magnetized plasmas. The general case of relativistic particles in non-uniform but stationary magnetic fields, and in additional force fields that are strongly non-uniform but slowly evolving in time compared with particle gyrations with the cyclotron frequency, is considered. In order to reveal the physical significance of the second-order approximation, the mean (reduced) particle velocity is calculated up to second order, when polarization particle drift as well as the renormalization of the lower-order result become equally significant. A general expression for the velocity of particle polarization drift is obtained in terms of quasi-particle properties, and with account taken of finite-Larmor-radius effects and non-uniformity of magnetic fields. A guiding-centre transformation is found that makes it possible to achieve equal mean velocities of particle, guiding centre and quasi-particle up to second order. Then polarization drifts enter the particle, guiding-centre and quasi-particle equations of motion.
Hall and finite Larmor radius effects on the dipolarization fronts associated with interchange instability
