# Equilibrium poloidal field distributions in reversed-field-pinch toroidal discharges

## Abstract

A comparison between the analytic formulae of Shafranov for equilibrium in axisymmetric toroidal reversed field pinch (RFP) systems and fully toroidal numerical solutions of the Grad-Shafranov equation is presented as a function of poloidal beta, internal plasma inductance, and aspect ratio. The Shafranov formula for the equilibrium poloidal field distribution is accurate to within 5% for aspect ratios greater than 2, poloidal betas less than 50%, and for plasma current channels that exceed one-third of the minor toroidal radius. The analytic description for the center shift of the innermost flux surface that encloses the plasma current (the Shafranov shift) is accurate to within 15% for aspect ratios greater than 2 and poloidal betas below 50%, provided the shift does not exceed one-tenth of the minor conducting boundary radius. The behavior of the magnetic axis shift as a function of plasma parameters is included. The Shafranov formulae provide a convenient method for describing the equilibrium behavior of an RFP discharge. Examples illustrating the application of the analytic formulae to the Los Alamos ZT-40M RFP experiment are given.

- Authors:

- Publication Date:

- Research Org.:
- Los Alamos National Lab., NM (USA)

- OSTI Identifier:
- 5223263

- Report Number(s):
- LA-9162-MS

ON: DE82014130; TRN: 82-017444

- DOE Contract Number:
- W-7405-ENG-36

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: Portions of document are illegible

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; REVERSE-FIELD PINCH; MAGNETIC FIELD CONFIGURATIONS; ANALYTICAL SOLUTION; NUMERICAL SOLUTION; PRESSURE VESSELS; ZT-40 DEVICES; CONTAINERS; PINCH EFFECT; 700202* - Fusion Power Plant Technology- Magnet Coils & Fields

### Citation Formats

```
Baker, D A, Mann, L W, and Schoenberg, K F.
```*Equilibrium poloidal field distributions in reversed-field-pinch toroidal discharges*. United States: N. p., 1982.
Web. doi:10.2172/5223263.

```
Baker, D A, Mann, L W, & Schoenberg, K F.
```*Equilibrium poloidal field distributions in reversed-field-pinch toroidal discharges*. United States. doi:10.2172/5223263.

```
Baker, D A, Mann, L W, and Schoenberg, K F. Thu .
"Equilibrium poloidal field distributions in reversed-field-pinch toroidal discharges". United States. doi:10.2172/5223263. https://www.osti.gov/servlets/purl/5223263.
```

```
@article{osti_5223263,
```

title = {Equilibrium poloidal field distributions in reversed-field-pinch toroidal discharges},

author = {Baker, D A and Mann, L W and Schoenberg, K F},

abstractNote = {A comparison between the analytic formulae of Shafranov for equilibrium in axisymmetric toroidal reversed field pinch (RFP) systems and fully toroidal numerical solutions of the Grad-Shafranov equation is presented as a function of poloidal beta, internal plasma inductance, and aspect ratio. The Shafranov formula for the equilibrium poloidal field distribution is accurate to within 5% for aspect ratios greater than 2, poloidal betas less than 50%, and for plasma current channels that exceed one-third of the minor toroidal radius. The analytic description for the center shift of the innermost flux surface that encloses the plasma current (the Shafranov shift) is accurate to within 15% for aspect ratios greater than 2 and poloidal betas below 50%, provided the shift does not exceed one-tenth of the minor conducting boundary radius. The behavior of the magnetic axis shift as a function of plasma parameters is included. The Shafranov formulae provide a convenient method for describing the equilibrium behavior of an RFP discharge. Examples illustrating the application of the analytic formulae to the Los Alamos ZT-40M RFP experiment are given.},

doi = {10.2172/5223263},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1982},

month = {4}

}