Gyrointegrated kinetic theory for arbitrary gradient scale lengths, Larmor radii and distribution functions

We present a 5D electromagnetic gyrointegrated kinetic theory (GI) valid for non-Maxwellian distribution functions in magnetized plasmas with arbitrary gradient scale lengths, Larmor radii and 3D magnetic geometry. GI theory describes collective full-orbit effects and yet differs fundamentally from gyrokinetic (GK) theory in the mathematical approach to the treatment of the kinetic physics. The fundamental difference in GI is the introduction of a new "gyrointegration" that is operated on the perpendicular velocity direction of all particles at the same 5D phase-space coordinate. This gyrointegration leads to the local definition of slower 5D macro-particles without requiring any ordering on gradient scale lengths or Larmor radii. Basis sets for complete representation of the distribution function with respect to the instantaneous gyroangle are chosen to allow for the exact analytic computation of gyrointegrals of the Boltzmann equation. We then show how GI can be applied to non-Maxwellians and include arbitrary 3D magnetic geometry, and discuss how GI avoids many of the GK challenges such as the cancellation problem and the evaluation of the Ampère's law. Evaluation of conservation laws, Hamiltonian structure, and dispersion relations are discussed within the GI theory.