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

Published online by Cambridge University Press:  03 July 2018

Alexander R. D. Close*
Department of Mathematics, University of Surrey, Guildford GU2 7XH, UK
Joshua W. Burby
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
Cesare Tronci
Department of Mathematics, University of Surrey, Guildford GU2 7XH, UK
Email address for correspondence:


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–Poincaré 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 and phase space particle trajectories reflects an intricate variational structure which can be approached by letting the four-dimensional guiding center trajectories evolve in the full six-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.

Research Article
© Cambridge University Press 2018 

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