# Calculation of large-aspect-ratio tokamak and toroidally-averaged stellarator equilibria of high-beta reduced magnetohydrodynamics via simulated annealing

## Abstract

A simulated annealing (SA) relaxation method is used for the calculation of high-beta reduced magnetohydrodynamics (MHD) equilibria in toroidal geometry. The SA method, based on artificial dynamics derived from the MHD Hamiltonian structure, is used to calculate equilibria of large-aspect-ratio and circular-cross-section tokamaks as well as toroidally averaged stellarators. Tokamak equilibria including incompressible poloidal rotations are obtained and the Shafranov shift is seen to increase nearly quadratically in the rotation speed. A mapping procedure between non-rotating and poloidally rotating equilibria is shown to explain the quadratic dependence of equilibria shift on rotation. Calculated stellarator equilibria are seen to agree reasonably with previous results. The numerical results demonstrate the first successful application of the SA method to obtain toroidal equilibria.

- Authors:

- Tottori Univ., Tottori (Japan)
- Univ. of Texas at Austin, Austin, TX (United States)
- National Institute for Fusion Science, Toki (Japan); SOKENDAI, The Graduate Univ. for Advanced Studies, Toki (Japan)

- Publication Date:

- Research Org.:
- Univ. of Texas, Austin, TX (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1540226

- Alternate Identifier(s):
- OSTI ID: 1463054

- Grant/Contract Number:
- [FG05-80ET53088]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- [ Journal Volume: 25; Journal Issue: 8]; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Physics

### Citation Formats

```
Furukawa, M., Watanabe, Takahiro, Morrison, P. J., and Ichiguchi, K. Calculation of large-aspect-ratio tokamak and toroidally-averaged stellarator equilibria of high-beta reduced magnetohydrodynamics via simulated annealing. United States: N. p., 2018.
Web. doi:10.1063/1.5038043.
```

```
Furukawa, M., Watanabe, Takahiro, Morrison, P. J., & Ichiguchi, K. Calculation of large-aspect-ratio tokamak and toroidally-averaged stellarator equilibria of high-beta reduced magnetohydrodynamics via simulated annealing. United States. doi:10.1063/1.5038043.
```

```
Furukawa, M., Watanabe, Takahiro, Morrison, P. J., and Ichiguchi, K. Mon .
"Calculation of large-aspect-ratio tokamak and toroidally-averaged stellarator equilibria of high-beta reduced magnetohydrodynamics via simulated annealing". United States. doi:10.1063/1.5038043. https://www.osti.gov/servlets/purl/1540226.
```

```
@article{osti_1540226,
```

title = {Calculation of large-aspect-ratio tokamak and toroidally-averaged stellarator equilibria of high-beta reduced magnetohydrodynamics via simulated annealing},

author = {Furukawa, M. and Watanabe, Takahiro and Morrison, P. J. and Ichiguchi, K.},

abstractNote = {A simulated annealing (SA) relaxation method is used for the calculation of high-beta reduced magnetohydrodynamics (MHD) equilibria in toroidal geometry. The SA method, based on artificial dynamics derived from the MHD Hamiltonian structure, is used to calculate equilibria of large-aspect-ratio and circular-cross-section tokamaks as well as toroidally averaged stellarators. Tokamak equilibria including incompressible poloidal rotations are obtained and the Shafranov shift is seen to increase nearly quadratically in the rotation speed. A mapping procedure between non-rotating and poloidally rotating equilibria is shown to explain the quadratic dependence of equilibria shift on rotation. Calculated stellarator equilibria are seen to agree reasonably with previous results. The numerical results demonstrate the first successful application of the SA method to obtain toroidal equilibria.},

doi = {10.1063/1.5038043},

journal = {Physics of Plasmas},

number = [8],

volume = [25],

place = {United States},

year = {2018},

month = {8}

}

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