Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-05T15:31:46.777Z Has data issue: false hasContentIssue false

Bootstrap current and parallel ion velocity in imperfectly optimized stellarators Corrigendum

Published online by Cambridge University Press:  10 December 2020

Peter J. Catto*
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA02139, USA
Per Helander
Affiliation:
Max-Planck-Institut für Plasmaphysik, 17491Greifswald, Germany
*
Email address for correspondence: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Type
Corrigendum
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

Our recent paper (Catto & Helander Reference Catto and Helander2020) presents a careful and rather general evaluation of the parallel ion flow and parallel current in an imperfectly optimized stellarator. As the disagreement between our and earlier analytical results (Shaing et al. Reference Shaing, Carreras, Dominguez, Lynch and Tolliver1989; Helander, Geiger & Maaßberg Reference Helander, Geiger and Maaßberg2011; Landreman & Catto Reference Landreman and Catto2012; Helander, Parra & Newton Reference Helander, Parra and Newton2017) and simulations (Beidler et al. Reference Beidler, Allmaier, Isaev, Kasilov, Kernbichler, Leitold, Maaßberg, Mikkelsen, Murakami and Schmidt2011; Kernbichler et al. Reference Kernbichler, Kasilov, Kapper, Martitsch, Nemov, Albert and Heyn2016) remains, we speculated on a possible cause of some of the disagreement. However, this explanation in § 8 of how a specious current might arise when an approximate form of the tangential drift is employed in simulations is flawed. Dr C. Beidler has observed that our speculation is invalid as stellarator symmetry causes the spurious terms to vanish. Stellarator symmetry requires the magnitude of the magnetic field of a stellarator to be exactly the same when it is turned over. Consequently, our paper needs to be modified in the following ways.

(1) Abstract: remove ‘However, it is also shown … accurate drift kinetic equation is used’.

(2) Introduction: remove the entire second paragraph and the penultimate sentence of last paragraph.

(3) Section 2: between (2.7) and (2.8) remove the sentence ‘Although these approximations … lead to errors in the parallel flows’.

(4) Section 5: between (5.2) and (5.3) remove the sentence ‘However, it will be shown that …. considered in § 8’.

(5) Section 6: (a) replace the material a line above (6.8) by ‘When used in (6.5), it gives the correct constraint’; (b) replace the final right side (not equal to zero, $\ne 0$) of (6.8) by equal to zero (= 0); and (c) replace the remainder of the paragraph following (6.8) by ‘Stellarator symmetry requires ${\varDelta _p}$ to be symmetric, and $\partial {\varDelta _p}{\kern 1pt} /\partial \alpha$ to be anti-symmetric so all flux surface averages in (6.8) vanish’.

(6) Section 7: remove the very last paragraph.

(7) Section 8: remove all of § 8.

(8) Discussion: remove all of the penultimate paragraph.

(9) Appendix A: remove all of appendix A.

We thank Dr Beidler for bringing this oversight to our attention. The discrepancy between analytic and numerical results for the bootstrap current remains unexplained.

Acknowledgements

Work supported by the US Department of Energy grant DE-FG02-91ER-54109.

Editor Alex Schekochihin thanks the referees for their advice in evaluating this article.

Declaration of interests

The authors report no conflict of interest.

References

Beidler, C. D., Allmaier, K., Isaev, M. Y., Kasilov, S. V., Kernbichler, W., Leitold, G. O., Maaßberg, H., Mikkelsen, D. R., Murakami, S., Schmidt, M., et al. 2011 Benchmarking of the mono-energetic transport coefficients – results from the International Collaboration on Neoclassical Transport in Stellarators (ICNTS). Nucl. Fusion 51 (7), 076001.Google Scholar
Catto, P. J. & Helander, P. 2020 Bootstrap current and parallel ion velocity in imperfectly optimized stellarators. J. Plasma Phys. 86, 905860105.CrossRefGoogle Scholar
Helander, P., Geiger, J. & Maaßberg, H. 2011 On the bootstrap current in stellarators and tokamaks. Phys. Plasmas 18, 092505.CrossRefGoogle Scholar
Helander, P., Parra, F. I. & Newton, S. L. 2017 Stellarator bootstrap current and plasma flow velocity at low collisionality. J. Plasma Phys. 83, 905830206.Google Scholar
Kernbichler, W., Kasilov, S. V., Kapper, G., Martitsch, A. F., Nemov, V. V., Albert, C. & Heyn, M. F. 2016 Solution of drift kinetic equation in stellarators and tokamaks with broken symmetry using the code NEO-2. Plasma Phys. Control. Fusion 58, 104001.Google Scholar
Landreman, M. & Catto, P. J. 2012 Omnigenity as generalized quasisymmetry. Phys. Plasmas 19, 056103.Google Scholar
Shaing, K. C., Carreras, B. A., Dominguez, N., Lynch, V. E. & Tolliver, J. S. 1989 Bootstrap current control in stellarators. Phys. Fluids B 1, 16631670.CrossRefGoogle Scholar