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

Energetic particle effects in magnetic confinement fusion dev ices are commonly studied by hybrid kinetic-fluid simulation codes whose unde rlying continuum evolu- tion equations often lack the correct energy balance. While two different kinetic-fluid coupling options are available (current-coupling and pres sure-coupling), this paper applies the Euler-Poincar ́e variational approach to formu late a new conservative hybrid model in the pressure-coupling scheme. In our case th e kinetics of the en- ergetic particles are described by guiding center theory. T he interplay between the Lagrangian fluid paths with phase space particle trajectori es reflects an intricate variational structure which can be approached by letting th e 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 st ructures confer on the new model a correct energy balance, but also they produce a cr oss-helicity invariant which is lost in the other pressure-coupling schemes report ed in the literature