# Woltjer's theorem

In plasma physics, **Woltjer's theorem** states that force-free magnetic fields, for a closed system with constant
, have the minimum magnetic energy and the magnetic helicity is invariant under this condition, named after Lodewijk Woltjer who derived in 1958[1][2][3][4][5][6]. The force-free field strength
equation is

The helicity invariant is given by

where is related to through the vector potential as below

- .

## See also

## References

- Woltjer, L. (1958). A theorem on force-free magnetic fields. Proceedings of the National Academy of Sciences, 44(6), 489-491.
- Chiuderi, C., & Velli, M. (2016). Basics of Plasma Astrophysics. Springer.
- Moffatt, H. K. (1978). Field generation in electrically conducting fluids. Cambridge University Press, Cambridge, London, New York, Melbourne.
- Sturrock, P. A. (1994). Plasma Physics: an introduction to the theory of astrophysical, geophysical and laboratory plasmas. Cambridge University Press.
- Solov'ev, A. A. (1985). Woltjer's theorem and the force-free magnetic field stability problem. Byulletin Solnechnye Dannye Akademie Nauk SSSR, 1985, 55-62.
- Kholodenko, A. L. (2013). Applications of contact geometry and topology in physics. World Scientific.

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