Finite Larmor Radius Effects in Plasmadynamics—Magnetosonic Disturbance

A disturbance of finite amplitude propagating across an initially uniform axial magnetic field within an initially uniform plasma of infinite extent is considered. The Vlasov equation is solved explicitly to second order in the adiabatic smallness parameter ε = (ωT)−1 = (R/L), with symbols defined in the text. It is shown also that the hierarchy of moment equations resulting from the Vlasov equation may be ordered to yield directly an expansion in powers of ε. The two methods yield equivalent results to second order. The fluid dynamic equations for each plasma species along with Maxwell's equations form a complete set which can be terminated consistently in second order. As an illustration, the dispersion of linearized magnetosonic waves to second order in ε is obtained.