# Computation of stationary 3D halo currents in fusion devices with accuracy control

## Abstract

This paper addresses the calculation of the resistive distribution of halo currents in three-dimensional structures of large magnetic confinement fusion machines. A Neumann electrokinetic problem is solved on a geometry so complicated that complementarity is used to monitor the discretization error. An irrotational electric field is obtained by a geometric formulation based on the electric scalar potential, whereas three geometric formulations are compared to obtain a solenoidal current density: a formulation based on the electric vector potential and two geometric formulations inspired from mixed and mixed-hybrid Finite Elements. The electric vector potential formulation is usually considered impractical since an enormous computing power is wasted by the topological pre-processing it requires. To solve this challenging problem, we present novel algorithms based on lazy cohomology generators that enable to save orders of magnitude computational time with respect to all other state-of-the-art solutions proposed in literature. Believing that our results are useful in other fields of scientific computing, the proposed algorithm is presented as a detailed pseudocode in such a way that it can be easily implemented.

- Authors:

- Università degli Studi di Padova, Dipartimento di Ingegneria Industriale (DII), Via Gradenigo 6/A, 35131 Padova (Italy)
- (Italy)
- Università degli Studi di Udine, Dipartimento di Ingegneria Elettrica, Gestionale e Meccanica (DIEGM), Via delle Scienze 206, I-33100 Udine (Italy)

- Publication Date:

- OSTI Identifier:
- 22382103

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 273; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ALGORITHMS; BOUNDARY-VALUE PROBLEMS; CALCULATION METHODS; COMPARATIVE EVALUATIONS; CURRENT DENSITY; ELECTRIC CURRENTS; ELECTRIC FIELDS; ELECTRIC POTENTIAL; MAGNETIC CONFINEMENT; MONITORS; PARTIAL DIFFERENTIAL EQUATIONS; THERMONUCLEAR DEVICES; THREE-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Bettini, Paolo, E-mail: paolo.bettini@unipd.it, Consorzio RFX, C.so Stati Uniti 4, 35127 Padova, and Specogna, Ruben, E-mail: ruben.specogna@uniud.it.
```*Computation of stationary 3D halo currents in fusion devices with accuracy control*. United States: N. p., 2014.
Web. doi:10.1016/J.JCP.2014.04.060.

```
Bettini, Paolo, E-mail: paolo.bettini@unipd.it, Consorzio RFX, C.so Stati Uniti 4, 35127 Padova, & Specogna, Ruben, E-mail: ruben.specogna@uniud.it.
```*Computation of stationary 3D halo currents in fusion devices with accuracy control*. United States. doi:10.1016/J.JCP.2014.04.060.

```
Bettini, Paolo, E-mail: paolo.bettini@unipd.it, Consorzio RFX, C.so Stati Uniti 4, 35127 Padova, and Specogna, Ruben, E-mail: ruben.specogna@uniud.it. Mon .
"Computation of stationary 3D halo currents in fusion devices with accuracy control". United States. doi:10.1016/J.JCP.2014.04.060.
```

```
@article{osti_22382103,
```

title = {Computation of stationary 3D halo currents in fusion devices with accuracy control},

author = {Bettini, Paolo, E-mail: paolo.bettini@unipd.it and Consorzio RFX, C.so Stati Uniti 4, 35127 Padova and Specogna, Ruben, E-mail: ruben.specogna@uniud.it},

abstractNote = {This paper addresses the calculation of the resistive distribution of halo currents in three-dimensional structures of large magnetic confinement fusion machines. A Neumann electrokinetic problem is solved on a geometry so complicated that complementarity is used to monitor the discretization error. An irrotational electric field is obtained by a geometric formulation based on the electric scalar potential, whereas three geometric formulations are compared to obtain a solenoidal current density: a formulation based on the electric vector potential and two geometric formulations inspired from mixed and mixed-hybrid Finite Elements. The electric vector potential formulation is usually considered impractical since an enormous computing power is wasted by the topological pre-processing it requires. To solve this challenging problem, we present novel algorithms based on lazy cohomology generators that enable to save orders of magnitude computational time with respect to all other state-of-the-art solutions proposed in literature. Believing that our results are useful in other fields of scientific computing, the proposed algorithm is presented as a detailed pseudocode in such a way that it can be easily implemented.},

doi = {10.1016/J.JCP.2014.04.060},

journal = {Journal of Computational Physics},

issn = {0021-9991},

number = ,

volume = 273,

place = {United States},

year = {2014},

month = {9}

}