# A method for embedding circular force-free flux ropes in potential magnetic fields

## Abstract

We propose a method for constructing approximate force-free equilibria in pre-eruptive configurations in which a thin force-free flux rope is embedded into a locally bipolar-type potential magnetic field. The flux rope is assumed to have a circular-arc axis, a circular cross-section, and electric current that is either concentrated in a thin layer at the boundary of the rope or smoothly distributed across it with a maximum of the current density at the center. The entire solution is described in terms of the magnetic vector potential in order to facilitate the implementation of the method in numerical magnetohydrodynamic (MHD) codes that evolve the vector potential rather than the magnetic field itself. The parameters of the flux rope can be chosen so that its subsequent MHD relaxation under photospheric line-tied boundary conditions leads to nearly exact numerical equilibria. To show the capabilities of our method, we apply it to several cases with different ambient magnetic fields and internal flux-rope structures. These examples demonstrate that the proposed method is a useful tool for initializing data-driven simulations of solar eruptions.

- Authors:

- Predictive Science Inc., 9990 Mesa Rim Road, Suite 170, San Diego, CA 92121 (United States)

- Publication Date:

- OSTI Identifier:
- 22365453

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astrophysical Journal; Journal Volume: 790; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; APPROXIMATIONS; BOUNDARY CONDITIONS; CONFIGURATION; CROSS SECTIONS; CURRENT DENSITY; EQUILIBRIUM; ERUPTION; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; MASS; MATHEMATICAL SOLUTIONS; RELAXATION; SIMULATION; SUN; THIN FILMS

### Citation Formats

```
Titov, V. S., Török, T., Mikic, Z., and Linker, J. A., E-mail: titovv@predsci.com.
```*A method for embedding circular force-free flux ropes in potential magnetic fields*. United States: N. p., 2014.
Web. doi:10.1088/0004-637X/790/2/163.

```
Titov, V. S., Török, T., Mikic, Z., & Linker, J. A., E-mail: titovv@predsci.com.
```*A method for embedding circular force-free flux ropes in potential magnetic fields*. United States. doi:10.1088/0004-637X/790/2/163.

```
Titov, V. S., Török, T., Mikic, Z., and Linker, J. A., E-mail: titovv@predsci.com. Fri .
"A method for embedding circular force-free flux ropes in potential magnetic fields". United States.
doi:10.1088/0004-637X/790/2/163.
```

```
@article{osti_22365453,
```

title = {A method for embedding circular force-free flux ropes in potential magnetic fields},

author = {Titov, V. S. and Török, T. and Mikic, Z. and Linker, J. A., E-mail: titovv@predsci.com},

abstractNote = {We propose a method for constructing approximate force-free equilibria in pre-eruptive configurations in which a thin force-free flux rope is embedded into a locally bipolar-type potential magnetic field. The flux rope is assumed to have a circular-arc axis, a circular cross-section, and electric current that is either concentrated in a thin layer at the boundary of the rope or smoothly distributed across it with a maximum of the current density at the center. The entire solution is described in terms of the magnetic vector potential in order to facilitate the implementation of the method in numerical magnetohydrodynamic (MHD) codes that evolve the vector potential rather than the magnetic field itself. The parameters of the flux rope can be chosen so that its subsequent MHD relaxation under photospheric line-tied boundary conditions leads to nearly exact numerical equilibria. To show the capabilities of our method, we apply it to several cases with different ambient magnetic fields and internal flux-rope structures. These examples demonstrate that the proposed method is a useful tool for initializing data-driven simulations of solar eruptions.},

doi = {10.1088/0004-637X/790/2/163},

journal = {Astrophysical Journal},

number = 2,

volume = 790,

place = {United States},

year = {Fri Aug 01 00:00:00 EDT 2014},

month = {Fri Aug 01 00:00:00 EDT 2014}

}