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.
