# A singular finite element technique for calculating continuum damping of Alfvén eigenmodes

## Abstract

Damping due to continuum resonances can be calculated using dissipation-less ideal magnetohydrodynamics provided that the poles due to these resonances are properly treated. We describe a singular finite element technique for calculating the continuum damping of Alfvén waves. A Frobenius expansion is used to determine appropriate finite element basis functions on an inner region surrounding a pole due to the continuum resonance. The location of the pole due to the continuum resonance and mode frequency is calculated iteratively using a Galerkin method. This method is used to find the complex frequency and mode structure of a toroidicity-induced Alfvén eigenmode in a large aspect ratio circular tokamak and is shown to agree closely with a complex contour technique.

- Authors:

- Research School of Physical Sciences and Engineering, Australian National University, Acton, ACT 0200 (Australia)

- Publication Date:

- OSTI Identifier:
- 22408069

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ALFVEN WAVES; ASPECT RATIO; DAMPING; EIGENVALUES; FINITE ELEMENT METHOD; ITERATIVE METHODS; MAGNETOHYDRODYNAMICS; RESONANCE; TOKAMAK DEVICES

### Citation Formats

```
Bowden, G. W., and Hole, M. J.
```*A singular finite element technique for calculating continuum damping of Alfvén eigenmodes*. United States: N. p., 2015.
Web. doi:10.1063/1.4907792.

```
Bowden, G. W., & Hole, M. J.
```*A singular finite element technique for calculating continuum damping of Alfvén eigenmodes*. United States. doi:10.1063/1.4907792.

```
Bowden, G. W., and Hole, M. J. Sun .
"A singular finite element technique for calculating continuum damping of Alfvén eigenmodes". United States.
doi:10.1063/1.4907792.
```

```
@article{osti_22408069,
```

title = {A singular finite element technique for calculating continuum damping of Alfvén eigenmodes},

author = {Bowden, G. W. and Hole, M. J.},

abstractNote = {Damping due to continuum resonances can be calculated using dissipation-less ideal magnetohydrodynamics provided that the poles due to these resonances are properly treated. We describe a singular finite element technique for calculating the continuum damping of Alfvén waves. A Frobenius expansion is used to determine appropriate finite element basis functions on an inner region surrounding a pole due to the continuum resonance. The location of the pole due to the continuum resonance and mode frequency is calculated iteratively using a Galerkin method. This method is used to find the complex frequency and mode structure of a toroidicity-induced Alfvén eigenmode in a large aspect ratio circular tokamak and is shown to agree closely with a complex contour technique.},

doi = {10.1063/1.4907792},

journal = {Physics of Plasmas},

number = 2,

volume = 22,

place = {United States},

year = {Sun Feb 15 00:00:00 EST 2015},

month = {Sun Feb 15 00:00:00 EST 2015}

}