Skip to main content

Advertisement

We’d like to understand how you use our websites in order to improve them. Register your interest.

Correction to: Grad–Shafranov reconstruction of magnetohydrostatic equilibria with nonisotropic plasma pressure: the theory

Correction to: Earth, Planets and Space (2018) 70:34 https://doi.org/10.1186/s40623-018-0802-z

After publication of this article (Teh 2018), the author has noticed some error with the statement in the abstract and discussion sections. In “Theory” section, \({\mathbf{F}} \cdot \nabla \alpha = 0\) is an assumption to get \(\nabla \cdot {\mathbf{F}} = 0\). This assumption leads to \({\mathbf{F}} \cdot \nabla p_{T} = 0\). Therefore, the statement in the abstract and discussion sections that three field-line invariants are found in the system is not correct.

A correct statement is that only one intrinsic field-line invariant \(F_{z} (A)\) exists in the system, while \(\alpha (A)\) and \(p_{T} (A)\) are assumed. Since the new GS-like equation, Eq. (8) remains unchanged; therefore, the reconstruction does not need auxiliary equations for integration of Eq. (8). It is noteworthy that if \(\alpha (A)\) is applied to the equation (A7) of Sonnerup et al. (2006) for magnetohydrostatic conditions, auxiliary equations are still needed for integration of that resulting equation. Moreover, since \(\alpha (A)\) and \(p_{T} (A)\) are assumed, the reconstruction should be implemented with caution that these two assumptions are reasonably satisfied when applied to the real event studied. The reconstruction results for benchmark case are not affected.

Reference

  1. Teh WL (2018) Grad–Shafranov reconstruction of magnetohydrostatic equilibria with nonisotropic plasma pressure: the theory. Earth Planets Space 70:34. https://doi.org/10.1186/s40623-018-0802-z

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Wai-Leong Teh.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Teh, W. Correction to: Grad–Shafranov reconstruction of magnetohydrostatic equilibria with nonisotropic plasma pressure: the theory. Earth Planets Space 70, 185 (2018). https://doi.org/10.1186/s40623-018-0953-y

Download citation