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

2. 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  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

3. 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)  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)

4. 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).  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).

5. 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: = 0.33 m Magnetic field strength: = 1.0 T  Calculations of the bootstrap current were done using the vacuum magnetic configuration [only NCSX had plasma current (~110 kA)]  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: = 0.33 m Magnetic field strength: = 1.0 T  Calculations of the bootstrap current were done using the vacuum magnetic configuration [only NCSX had plasma current (~110 kA)]

6. HSXLHD NCSX W7X QPS

7. 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/flux edge ) 1/2  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/flux edge ) 1/2

8. Broad density and peaked temperature profiles for ECH and ICH plasmas  ECH: Low density, hot electrons  ICH: High density, T e T i  ECH: Low density, hot electrons  ICH: High density, T e T i ~ > ECHICH

9. Both electrons and ions are fairly collisional for the ICH plasmas  Effective collisionality: * = R 0 /  v th  Ions and electrons have * > 1  Effective collisionality: * = R 0 /  v th  Ions and electrons have * > 1 IonsElectrons

10. Electrons have low collisionality for the ECH plasmas  Effective collisionality: * = R 0 /  v th  Ions have * > 1, while electrons have * < 1  Effective collisionality: * = R 0 /  v th  Ions have * > 1, while electrons have * < 1 IonsElectrons

11. Radial electric fields have more configurational variation for ECH than ICH  Ambipolar radial electric field used in the PENTA code ECHICH

12. Predicted bootstrap currents agree reasonably well for the ICH Cases  Except for QPS and LHD, BOOTSJ predictions slightly higher than those from PENTA

13. Predicted bootstrap currents agree surprisingly well for the ECH Cases  BOOTSJ predictions are lower than those from PENTA, especially for the QPS case

14. 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 for the VMEC equilibrium with the from BOOTSJ  Compare the rotational transform profiles with and without the plasma current  Calculate new equilibria with plasma current proportional to the bootstrap current for that device  Match for the VMEC equilibrium with the from BOOTSJ  Compare the rotational transform profiles with and without the plasma current

15. Only a small increase in the rotational transform for W7-X  A slight increase in the rotational transform on axis

16. A larger increase in the rotational transform for QPS  The impact is similar for LHD

17. The bootstrap current decreases the rotational transform for HSX  Acts to “unwind” the rotational transform

18. 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  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