## Radial confinement of deeply trapped particles in a non-symmetric magnetohydrodynamic equilibrium

## Abstract

Quasisymmetry and omnigeneity of an equilibrium magnetic field are two distinct properties proposed to ensure radial localization of collisionless trapped particles in any stellarator. These constraints are incompletely explored, but have stringent restrictions on a magnetic geometry. This work employs an analytical approach to understand the implications of the constraints. The particles move in an intrinsically three dimensional equilibrium whose representation is given by the earlier work of Weitzner and its extension here. For deeply trapped particles, a local equilibrium expansion around a minimum of the magnetic field strength along a magnetic line suffices. This analytical non-symmetric equilibrium solution enables explicit representation of the constraints. The results show that it is far easier to satisfy the omnigeneity condition than the quasisymmetry requirement. Correspondingly, there exists a large class of equilibrium close to quasisymmetry that remains omnigeneous while allowing inclusion of error fields, which may destroy quasisymmetry.

- Authors:

- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA

- Publication Date:

- Research Org.:
- New York Univ. (NYU), NY (United States)

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

- OSTI Identifier:
- 1540145

- Alternate Identifier(s):
- OSTI ID: 1420213

- Grant/Contract Number:
- FG02-86ER53223

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 25; Journal Issue: 2; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Physics

### Citation Formats

```
Sengupta, Wrick, and Weitzner, Harold. Radial confinement of deeply trapped particles in a non-symmetric magnetohydrodynamic equilibrium. United States: N. p., 2018.
Web. doi:10.1063/1.5011760.
```

```
Sengupta, Wrick, & Weitzner, Harold. Radial confinement of deeply trapped particles in a non-symmetric magnetohydrodynamic equilibrium. United States. doi:10.1063/1.5011760.
```

```
Sengupta, Wrick, and Weitzner, Harold. Thu .
"Radial confinement of deeply trapped particles in a non-symmetric magnetohydrodynamic equilibrium". United States. doi:10.1063/1.5011760. https://www.osti.gov/servlets/purl/1540145.
```

```
@article{osti_1540145,
```

title = {Radial confinement of deeply trapped particles in a non-symmetric magnetohydrodynamic equilibrium},

author = {Sengupta, Wrick and Weitzner, Harold},

abstractNote = {Quasisymmetry and omnigeneity of an equilibrium magnetic field are two distinct properties proposed to ensure radial localization of collisionless trapped particles in any stellarator. These constraints are incompletely explored, but have stringent restrictions on a magnetic geometry. This work employs an analytical approach to understand the implications of the constraints. The particles move in an intrinsically three dimensional equilibrium whose representation is given by the earlier work of Weitzner and its extension here. For deeply trapped particles, a local equilibrium expansion around a minimum of the magnetic field strength along a magnetic line suffices. This analytical non-symmetric equilibrium solution enables explicit representation of the constraints. The results show that it is far easier to satisfy the omnigeneity condition than the quasisymmetry requirement. Correspondingly, there exists a large class of equilibrium close to quasisymmetry that remains omnigeneous while allowing inclusion of error fields, which may destroy quasisymmetry.},

doi = {10.1063/1.5011760},

journal = {Physics of Plasmas},

number = 2,

volume = 25,

place = {United States},

year = {2018},

month = {2}

}