A low-frequency variational model for energetic particle effects in the pressure-coupling scheme

TL;DR

This paper introduces a new variational hybrid kinetic-fluid model for energetic particles in magnetic confinement fusion, ensuring correct energy conservation and revealing a cross-helicity invariant absent in previous models.

Contribution

It develops a conservative pressure-coupling hybrid model using the Euler-Poincaré variational approach with guiding center kinetics, improving energy balance and invariants.

Findings

The model conserves energy accurately.

It introduces a cross-helicity invariant.

The approach uses phase space Lagrangians.

Abstract

Energetic particle effects in magnetic confinement fusion devices are commonly studied by hybrid kinetic-fluid simulation codes whose underlying continuum evolution equations often lack the correct energy balance. While two different kinetic-fluid coupling options are available (current-coupling and pressure-coupling), this paper applies the Euler-Poincar\'e variational approach to formulate a new conservative hybrid model in the pressure-coupling scheme. In our case the kinetics of the energetic particles are described by guiding center theory. The interplay between the Lagrangian fluid paths with phase space particle trajectories reflects an intricate variational structure which can be approached by letting the 4-dimensional guiding center trajectories evolve in the full 6-dimensional phase space. Then, the redundant perpendicular velocity is integrated out to recover a four-dimensional description. A second equivalent variational approach is also reported, which involves the use of phase space Lagrangians. Not only do these variational structures confer on the new model a correct energy balance, but also they produce a cross-helicity invariant which is lost in the other pressure-coupling schemes reported in the literature.