# Presentation: 535289

## Bootstrap current in quasi-symmetric stellarators

- Andrew Ware
*University of Montana*
- Collaborators: D. A. Spong, L. A. Berry, S. P. Hirshman, J. F. Lyon, *ORNL*

## Overview

- Undertake a comparison of the bootstrap current in quasi-symmetric stellarators as calculated by two separate codes:
- A new moments method for calculating neoclassical transport
- A fast code that uses an asymptotically collisionless expression for the bootstrap current

## PENTA: A moments-based transport model

- Developed at ORNL as a powerful tool for calculating plasma flows for arbitrary geometry
- Uses results from the DKES code coupled with analytic formulations
- The bootstrap current is one of the quantities that can be determined from the transport model
- For more details on this model, see the poster by D. Spong at this meeting and
- D. A. Spong, Phys. Plasmas **12**, 056114 (2005)

## BOOTSJ: Rapid estimation of the bootstrap current

- BOOTSJ is a code that has been used extensively for predictions of bootstrap currents during stellarator optimization
- The speed of the code (a few seconds of CPU time per configuration) makes it ideal for use in a optimization routine
- The code uses an analytic representation of the bootstrap current in the collisionless limit
- K.C. Shaing,, et al., Phys. Fluids B1, 148 (1989).

## The Equilibrium Configurations

- We have examined bootstrap current in five optimized configurations:
- HSX, NCSX, QPS, an inward shifted LHD, W-7X
- All configurations have been scaled to     Minor radius: <*a*> = 0.33 m          Magnetic field strength: <*B*> = 1.0 T
- Calculations of the bootstrap current were done using the *vacuum* magnetic configuration [only NCSX had plasma current (~110 kA)]

## HSX

***HSX***

***LHD***

***NCSX***

***W7X***

***QPS***

## The Equilibrium Profiles

*The Equilibrium Profiles*

- Two separate sets of profiles for *T**e*, *T**i*, and *n*, have been studied.
- Both use a broad density profile with pedestals in both *n* and *T*
- Both assume *n**e* = *n**i* = *n*
-  *r* = (flux/fluxedge)1/2

## Broad density and peaked temperature profiles for ECH and ICH plasmas

- ECH: Low density, hot electrons
- ICH: High density, *T**e*    *T**i*

- ~

- >

- ECH

- ICH

## Both electrons and ions are fairly collisional for the ICH plasmas

- Effective collisionality:  *** = ** *R*0/***v*th
- Ions and electrons have *** > 1

- Ions

- Electrons

## Electrons have low collisionality for the ECH plasmas

- Effective collisionality:  *** = ** *R*0/***v*th
- Ions have *** > 1, while electrons have *** < 1

- Ions

- Electrons

## Radial electric fields have more configurational variation for ECH than ICH

- Ambipolar radial electric field used in the PENTA code

- ECH

- ICH

## Predicted bootstrap currents agree reasonably well for the ICH Cases

- Except for QPS and LHD, BOOTSJ predictions slightly higher than those from PENTA

## Predicted bootstrap currents agree surprisingly well for the ECH Cases

- BOOTSJ predictions are lower than those from PENTA, especially for the QPS case

## Testing the impact of the bootstrap current on rotational transform

- Calculate new equilibria with plasma current proportional to the bootstrap current for that device
- Match <**J·B**> for the VMEC equilibrium with the <**J·B**> from BOOTSJ
- Compare the rotational transform profiles with and without the plasma current

## Only a small increase in the rotational transform for W7-X

- A slight increase in the rotational transform on axis

## A larger increase in the rotational transform for QPS

- The impact is similar for LHD

## The bootstrap current decreases  the rotational transform for HSX

- Acts to “unwind” the rotational transform

## Conclusions

- The bootstrap current predictions from the PENTA transport model and the BOOTSJ code agree qualitatively
- Quantitative agreement is better for the ICH case for some configurations and better for the ECH case for other configurations
- The total bootstrap current is small for all of these cases
- Work on examing the impact for cases with self-consistent bootstrap current is underway