Variational quadratic form for low-frequency electromagnetic perturbations. I. Formalism

A variational formalism is obtained in the limit of large perpendicular wavenumber which simultaneously includes electrostatic and electromagnetic perturbations, finite Larmor radius corrections, equilibrium plasma rotation, and arbitrary particle bounce effects. A tractable final expression is obtained and kinetic integrals are evaluated in special limits. The more accurate noneikonal expression is obtained from the asymptotic matching of the eikonal form to more restrictive noneikonal quadratic forms derived elsewhere.