Collisionless fluid closure theory and the phase velocity transform

Fluid equations are derived that describe wave-particle resonances, which usually require kinetic theory. The phase velocity transform is introduced, which decomposes a function of space and time into a sum over components with constant phase velocity. This leads to a new technique to solve partial differential equations, similar but not identical to the Radon transform, and produces recursive solutions. This technique is applied to the collisionless drift kinetic equation, to give closure of the fluid moment hierarchy. The result is a new term in the highest moment equation that retains many nonlinear wave-particle effects not before described by fluid equations.