## Bernstein modes in a non-neutral plasma column

## Abstract

Our report presents theory and numerical calculations of electrostatic Bernstein modes in an inhomogeneous cylindrical plasma column. These modes rely on finite Larmor radius effects to propagate radially across the column until they are reflected when their frequency matches the upper hybrid frequency. This reflection sets up an internal normal mode on the column and also mode-couples to the electrostatic surface cyclotron wave (which allows the normal mode to be excited and observed using external electrodes). Numerical results predicting the mode spectra, using a novel linear Vlasov code on a cylindrical grid, are presented and compared to an analytical Wentzel Kramers Brillouin (WKB) theory. A prior version of the theory [D. H. E. Dubin, Phys. Plasmas 20(4), 042120 (2013)] expanded the plasma response in powers of 1/B, approximating the local upper hybrid frequency, and consequently, its frequency predictions are spuriously shifted with respect to the numerical results presented here. A new version of the WKB theory avoids this approximation using the exact cold fluid plasma response and does a better job of reproducing the numerical frequency spectrum. The effect of multiple ion species on the mode spectrum is also reported on, to make contact with experiments that observe cyclotron modesmore »

- Authors:

- Univ. of California, San Diego, CA (United States)

- Publication Date:

- Research Org.:
- Univ. of California, San Diego, CA (United States)

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

- OSTI Identifier:
- 1540201

- Alternate Identifier(s):
- OSTI ID: 1438511

- Grant/Contract Number:
- SC0018236

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 25; Journal Issue: 5; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Walsh, Daniel, and Dubin, Daniel H. E. Bernstein modes in a non-neutral plasma column. United States: N. p., 2018.
Web. doi:10.1063/1.5027848.
```

```
Walsh, Daniel, & Dubin, Daniel H. E. Bernstein modes in a non-neutral plasma column. United States. doi:10.1063/1.5027848.
```

```
Walsh, Daniel, and Dubin, Daniel H. E. Wed .
"Bernstein modes in a non-neutral plasma column". United States. doi:10.1063/1.5027848. https://www.osti.gov/servlets/purl/1540201.
```

```
@article{osti_1540201,
```

title = {Bernstein modes in a non-neutral plasma column},

author = {Walsh, Daniel and Dubin, Daniel H. E.},

abstractNote = {Our report presents theory and numerical calculations of electrostatic Bernstein modes in an inhomogeneous cylindrical plasma column. These modes rely on finite Larmor radius effects to propagate radially across the column until they are reflected when their frequency matches the upper hybrid frequency. This reflection sets up an internal normal mode on the column and also mode-couples to the electrostatic surface cyclotron wave (which allows the normal mode to be excited and observed using external electrodes). Numerical results predicting the mode spectra, using a novel linear Vlasov code on a cylindrical grid, are presented and compared to an analytical Wentzel Kramers Brillouin (WKB) theory. A prior version of the theory [D. H. E. Dubin, Phys. Plasmas 20(4), 042120 (2013)] expanded the plasma response in powers of 1/B, approximating the local upper hybrid frequency, and consequently, its frequency predictions are spuriously shifted with respect to the numerical results presented here. A new version of the WKB theory avoids this approximation using the exact cold fluid plasma response and does a better job of reproducing the numerical frequency spectrum. The effect of multiple ion species on the mode spectrum is also reported on, to make contact with experiments that observe cyclotron modes in a multi-species pure ion plasma [M. Affolter et al., Phys. Plasmas 22(5), 055701 (2015)].},

doi = {10.1063/1.5027848},

journal = {Physics of Plasmas},

number = 5,

volume = 25,

place = {United States},

year = {2018},

month = {5}

}