2nd order differential operator for plasma dielectric to include all-order finite Larmor radius effects

It is well known that the dielectric response to the RF fields in hot plasma is non-local, and the Maxwell wave problem is an integro-differential equation. A differential form of dielectric operator, based on the small k⊥ρ expansion, typically includes up-to the second order terms, and thus the use of such an operator is limited to the waves that satisfy k⊥ρ < 1. We propose an alternative approach to construct a dielectric operator, which includes all-order finite Larmor radius effects without explicitly containing higher order derivatives. We use a rational approximation of the plasma dielectric tensor in the wave number space, in order to yield a differential operator acting on the dielectric current (J). To demonstrate this approach, we use the Petra-M framework and solve the 1D O-X-B mode-conversion of the electron Bernstein wave in the non-relativistic Maxwellian plasma. An agreement with analytic calculation and the conservation of wave energy carried by the Poynting flux and electron thermal motion (“sloshing”) is found. The connection between our construction method and superposition of Green’s function for these screened Poisson’s equations is presented. An approach to extend the operator in a multi-dimensional setting will also be discussed.