Geometrical Formulation of Hybrid Kinetic and Gyrokinetic Hamiltonian Field Theory for Astrophysical and Laboratory Plasmas

In the present work, a consistent Lagrangian model that encapsulates fully kinetic ions and gyrokinetic electrons for solar wind electromagnetic turbulence is formulated. Using a consistent method, where both electrons and ions are treated with the same mathematical formalism, we derive and implement a model in which high frequency waves and kinetic electrons effects are described in a computationally cost-efficient way. To that aim, higher order Lie-transform perturbation methods applied to Hamiltonian formulation of guiding center motion are used in order to describe the dynamics of particles and fields. Furthermore, the use of a Hamiltonian formulation allow us to introduce an abelian and gauge invariant electromagnetic field theory for the closure of the system. From a numerical perspective, we analyze a linearized version of the system through a dispersion relation solver, and compare our results with a fully kinetic and a fluid solvers. This work should allow us to investigate in more detail the nature of energy dissipation of weakly collisional plasmas both in space and laboratory plasmas, opening doors to a computationally feasible treatment of ion kinetic physics and its relationship to a cross-scale energy transfer.