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

## 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–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.

- Authors:

- Publication Date:

- Research Org.:
- New York Univ. (NYU), NY (United States); Oak Ridge Associated Univ., Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1538939

- DOE Contract Number:
- FG02-86ER53223; AC05-06OR23100

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Plasma Physics

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 4; Journal ID: ISSN 0022-3778

- Publisher:
- Cambridge University Press

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Physics

### Citation Formats

```
Close, Alexander R. D., Burby, Joshua W., and Tronci, Cesare.
```*A low-frequency variational model for energetic particle effects in the pressure-coupling scheme*. United States: N. p., 2018.
Web. doi:10.1017/s0022377818000697.

```
Close, Alexander R. D., Burby, Joshua W., & Tronci, Cesare.
```*A low-frequency variational model for energetic particle effects in the pressure-coupling scheme*. United States. doi:10.1017/s0022377818000697.

```
Close, Alexander R. D., Burby, Joshua W., and Tronci, Cesare. Tue .
"A low-frequency variational model for energetic particle effects in the pressure-coupling scheme". United States. doi:10.1017/s0022377818000697.
```

```
@article{osti_1538939,
```

title = {A low-frequency variational model for energetic particle effects in the pressure-coupling scheme},

author = {Close, Alexander R. D. and Burby, Joshua W. and Tronci, Cesare},

abstractNote = {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.},

doi = {10.1017/s0022377818000697},

journal = {Journal of Plasma Physics},

issn = {0022-3778},

number = 4,

volume = 84,

place = {United States},

year = {2018},

month = {7}

}