# SSPX simulation model

## Abstract

An analytical approximation to an R-L-C circuit representing SSPX is shown to reproduce the observed capacitor bank efficiency and gun optimization data. As in the SPICE code, the spheromak gun is represented by a fixed resistance chosen to balance energy transfer to the gun. A revised estimate of the magnetic decay time in SSPX Shot 1822 then brings our estimate of the gun efficiency itself in line with the observed spheromak magnetic field for this shot. Prompted by these successes, we present a turbulence-based theoretical model for the spheromak resistance that can be implemented in the SPICE code, of the form: R{sub s} = {kappa}I (1-I{sub 0}/I){sup 2} where I is the gun current, I{sub 0} = ({Lambda}{sub 0}/{mu}{sub 0}){Phi} with bias flux and Taylor eigenvalue {lambda}{sub 0}, and {kappa} is a coefficient based on the magnetic turbulence model employed in Dan Hua's spheromak simulation code. The value of {kappa} giving a good energy balance (around 0.1 m{Omega}/KA) implies substantial turbulence levels. Implementing our model in SPICE would provide a calibration for theoretical calculations of the turbulence. Our analytic approximation to the SPICE code provides guidance to optimize future performance in SSPX, the greatest benefit appearing to come from reducingmore »

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab., CA (US)

- Sponsoring Org.:
- USDOE Office of Energy Research (ER) (US)

- OSTI Identifier:
- 13082

- Report Number(s):
- UCRL-ID-135797; AT5015020

AT5015020; TRN: US0110728

- DOE Contract Number:
- W-7405-ENG-48

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 20 Sep 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; SSPX DEVICE; COMPUTERIZED SIMULATION; MATHEMATICAL MODELS; S CODES; CAPACITORS; ENERGY EFFICIENCY; RESISTORS

### Citation Formats

```
Fowler, T K.
```*SSPX simulation model*. United States: N. p., 1999.
Web. doi:10.2172/13082.

```
Fowler, T K.
```*SSPX simulation model*. United States. doi:10.2172/13082.

```
Fowler, T K. Mon .
"SSPX simulation model". United States. doi:10.2172/13082. https://www.osti.gov/servlets/purl/13082.
```

```
@article{osti_13082,
```

title = {SSPX simulation model},

author = {Fowler, T K},

abstractNote = {An analytical approximation to an R-L-C circuit representing SSPX is shown to reproduce the observed capacitor bank efficiency and gun optimization data. As in the SPICE code, the spheromak gun is represented by a fixed resistance chosen to balance energy transfer to the gun. A revised estimate of the magnetic decay time in SSPX Shot 1822 then brings our estimate of the gun efficiency itself in line with the observed spheromak magnetic field for this shot. Prompted by these successes, we present a turbulence-based theoretical model for the spheromak resistance that can be implemented in the SPICE code, of the form: R{sub s} = {kappa}I (1-I{sub 0}/I){sup 2} where I is the gun current, I{sub 0} = ({Lambda}{sub 0}/{mu}{sub 0}){Phi} with bias flux and Taylor eigenvalue {lambda}{sub 0}, and {kappa} is a coefficient based on the magnetic turbulence model employed in Dan Hua's spheromak simulation code. The value of {kappa} giving a good energy balance (around 0.1 m{Omega}/KA) implies substantial turbulence levels. Implementing our model in SPICE would provide a calibration for theoretical calculations of the turbulence. Our analytic approximation to the SPICE code provides guidance to optimize future performance in SSPX, the greatest benefit appearing to come from reducing or eliminating the protective resistor to increase bank efficiency. Eliminating the resistor altogether doubles the bank efficiency and the spheromak magnetic energy.},

doi = {10.2172/13082},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1999},

month = {9}

}