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

The Original Article was published on 09 February 2018

## Correction

In the publication of this article , 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.

## Reference

1. 1.

Nagata, Sawada (2018) A supplemental device to return escaping particles to a magnetic mirror reactor. 5:1. https://doi.org/10.1140/epjti/s40485-018-0042-4

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## Author information

Authors

### Corresponding author

Correspondence to Mitsuaki Nagata.

## Additional information

The original article can be found online at https://doi.org/10.1140/epjti/s40485-018-0042-4

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