Finite-Larmor-radius equations for coffisionless plasmas in general magnetic fields

Expressing the Vlasov equation in a local system of co-ordinates defined by the magnetic field, the distribution function is expanded in terms of a small parameter e (assumed < 1), the ratio of the ion Larmor radius to a characteristic length of change perpendicular to the magnetic field. Since the finite-Larmorradius (FLR) approximation restricts consideration to weakly unstable systems, the equations apply only to magnetic configurations in which the curvature of the lines of force is weak. In allowing for the effects of plasma pressure (β ∼ I) it is found that the FLR corrections to the stress tensor take their simplest form in the centre-of-mass frame, while the case of low β yields equations best expressed in the guiding-centre frame.