a fully helical magnetic field, which means that it saturates the realizability condition: and . Assuming that all the energy and magnetic helicity transfers are done to another wavevector , the conservation of magnetic helicity on the one hand and of the total energy (the sum of (m)agnetic and (k)inetic energy) on the other hand gives: The second equality for the energy comes from the fact that we consider an initial state with no kinetic energy. Then we have necessarily . Indeed, if we would have , then: which would break the realizability condition. This means that . In particular, for , the magnetic helicity is transferred to a smaller wavevector, which means to larger scales. Gauge considerations Magnetic helicity is a gauge-dependent quantity, because can be redefined by adding a gradient to it (gauge choosing). However, for perfectly conducting boundaries or periodic systems without a net magnetic flux, the magnetic helicity contained in the whole domain is gauge invariant, that is, independent of the gauge choice. A gauge-invariant relative helicity has been defined for volumes with non-zero magnetic flux on their boundary surfaces. See also Woltjer's theorem References External links A. A. Pevtsov's Helicity Page Mitch Berger's Publications Page Physical quantities Plasma physics Astrophysics