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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. The force-free field strength equation is
The helicity invariant is given by
where is related to through the vector potential as below
- ^ 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.
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- ^ Kholodenko, A. L. (2013). Applications of contact geometry and topology in physics. World Scientific.