A new hybrid: kinetic ions with parallel-kinetic-perpendicular-moment (pkpm) electrons

The hybrid kinetic formalism, wherein one retains the complete Vlasov dynamics for some number of ion species while reducing the electron dynamics to a fluid model, is a workhorse simulation model for the plasma community, especially in applications to collisionless shocks. However, a known deficiency of this approach for collisionless shock applications is one must prescribe the ultimate temperature partition of the shock downstream between electrons and ions. Such a partition is fraught with difficulties due to the complex non-equilibrium dynamics of the shock, with the electrons typically undergoing significant non-adiabatic heating through their kinetic response to, for example, parallel electric fields which develop in the shock-wave. 

In this presentation, we discuss a recently developed formalism which extends the capabilities of the hybrid-kinetic approach by decomposing the electron dynamics into a kinetic response parallel to the magnetic field and a hierarchy of fluid equations which govern their perpendicular motion. This approach, known as a parallel-kinetic-perpendicular-moment (pkpm) model, has natural connections to high magnetization asymptotic models such as drift-kinetics, but with the added flexibility that the model can be derived independently for each plasma species, thus avoiding the challenges of trying to reduce the electron dynamics while leaving the ion dynamics unordered. We demonstrate the utility of this novel hybrid approach for a collisionless shock in which significant non-adiabatic heating of the electrons occurs.