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A finite Larmor radius approximation is derived from the classical Vlasovequation, in the limit of large (and uniform) external magnetic field. We alsoprovide an heuristic derivation of the electroneutrality equation in the finiteLarmor radius setting. Existence and uniqueness of a solution is proven in thestationary frame for solutions depending only on the direction parallel to themagnetic field and factorizing in the velocity variables.

Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solutions