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  • Correction
  • Open Access

Correction to: A supplemental device to return escaping particles to a magnetic mirror reactor

EPJ Techniques and Instrumentation20185:8

  • Received: 12 February 2018
  • Accepted: 8 May 2018
  • Published:

The original article was published in EPJ Techniques and Instrumentation 2018 5:1


In the publication of this article [1], contained the following errors. In this Correction, the affected parts of the article are shown. The list of references is available in the original article. We omit pointing out obvious errata with respect to unnecessary periods and wrong symbols.

*In Eq.(2) \( \left\{\ \frac{m_e}{{\left(1-\frac{{\boldsymbol{\upsilon}}_0^2\ }{c^2}\right)}^{\frac{1}{2}}}+{\int}_{t_0}^t\frac{-q\mathbf{E}(t)\cdot \boldsymbol{\upsilon}\ \left(\boldsymbol{t},{\boldsymbol{t}}_{\mathbf{0}}\right)\ }{c^2} dt\right\}\frac{\partial \boldsymbol{\upsilon}\ \left(\boldsymbol{t},{\boldsymbol{t}}_{\mathbf{0}}\right)}{\partial t}+\boldsymbol{\upsilon}\ \left(\boldsymbol{t},{\boldsymbol{t}}_{\mathbf{0}}\right)\ \left(\frac{-q\mathbf{E}(t)\cdot \boldsymbol{\upsilon}\ \left(\boldsymbol{t},{\boldsymbol{t}}_{\mathbf{0}}\right)\ }{c^2}\right)=-q\mathbf{E}(t)- q\upsilon \left(\boldsymbol{t},{\boldsymbol{t}}_{\mathbf{0}}\right)\times \mathbf{B} \)

* In Eq.(6) \( \frac{m_e}{\sqrt{1-\frac{{\boldsymbol{\upsilon}}_0^2\ }{c^2}}}\equiv m,\kern0.5em \frac{qB}{m_e}\sqrt{1-\left(\frac{\upsilon_0^2}{c^2}\right)}=\frac{qB}{m}\equiv {\omega}_c,\left({c}^{{\prime\prime} }={c}^2\right) \)

* In Eq.(9), c(z0C)

\( \widehat{z}\left({\upsilon}_x^{\hbox{'}}B\right) \)

* In Eq.(15) \( \frac{qE}{m}\ \frac{-{\omega}_c}{\omega_c^2-{\omega}^2} \)

* In Eq.(17) \( -\frac{1}{4}\frac{qE}{m{\omega}_c}\frac{z_0^2}{c^{{\prime\prime} }}\left({\omega}_c^2{t}^2+3{S}^2\right)C \)

* In Eq.(21) \( \frac{-{\omega}_c}{\omega_c^2-{\omega}^2}\left(\frac{-1}{4}\right) \)

\( \frac{\mathit{\sin}\left(2{\omega}_c-\omega \right)t}{2{\omega}_c-\omega }-\frac{2 sin\omega t}{\omega } \)

* In Fig.9; n=1670

* Reference (14): J Plasma Phys. 44:47

This has now been included in this correction.



Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, 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.

Authors’ Affiliations

Nippon Electronic Engineering College, Noboribetsu-shi, Hokkaido, Japan
Soft Creator Company, Shinmachi, Nakagyo-ku, Kyoto, Japan


  1. Nagata, Sawada (2018) A supplemental device to return escaping particles to a magnetic mirror reactor. 5:1.


© The Author(s); licensee Springer on behalf of EPJ. 2018