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Bootstrap current in quasi-symmetric stellarators

This study compares the bootstrap current in quasi-symmetric stellarators using two separate codes. The results show qualitative agreement and provide insights into the impact of the bootstrap current on rotational transform.

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Bootstrap current in quasi-symmetric stellarators

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  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

  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

  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)

  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).

  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 toMinor 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)]

  6. HSX LHD QPS NCSX W7X

  7. The Equilibrium Profiles • Two separate sets of profiles for Te, Ti, and n, have been studied. • Both use a broad density profile with pedestals in both n and T • Both assume ne = ni = n • r = (flux/fluxedge)1/2

  8. Broad density and peaked temperature profiles for ECH and ICH plasmas • ECH: Low density, hot electrons • ICH:High density, TeTi > ~ ECH ICH

  9. Both electrons and ions are fairly collisional for the ICH plasmas • Effective collisionality: * = R0/vth • Ions and electrons have * > 1 Ions Electrons

  10. Electrons have low collisionality for the ECH plasmas • Effective collisionality: * = R0/vth • Ions have * > 1, while electrons have * < 1 Ions Electrons

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

  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 <J·B> for the VMEC equilibrium with the <J·B> 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

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