the magnetic field confined to a volume , can be expressed as where is the current density. Unlike magnetic helicity, current helicity is not an ideal invariant (it is not conserved even when the electrical resistivity is zero). Topological interpretation The name "helicity" relies on the fact that the trajectory of a fluid particle in a fluid with velocity and vorticity forms a helix in regions where the kinetic helicity . When , the helix is right-handed and when it is left-handed. This behaviour is very similar to magnetic field lines. Regions where magnetic helicity is not zero can also contain other sorts of magnetic structures as helical magnetic field lines. Magnetic helicity is indeed a generalization of the topological concept of linking number to the differential quantities required to describe the magnetic field. The linking number describes how many magnetic field lines are interlinked (see for a mathematical proof of it). Through a simple experiment with paper and scissors, one can show that magnetic field lines which turn around each other can be considered as being interlinked (figure 5 in ). Thus, the presence of magnetic helicity can be interpreted as helical magnetic field lines, interlinked magnetic structures, but also magnetic field lines turning around each other. Magnetic field lines turning around each other can take several shapes. Let's consider for example a set of turning magnetic field lines in a close neighborhood, which forms a so-called "magnetic flux tube" (see figure for an illustration). "Twist" means that the flux tube rotates around its own axis (figures with Twist=). Topologically speaking, units of twist and of writhe (which means, the rotation of the flux tube axis itself — figures with Writhe=) can be transformed into each other. One can also show that knots are also equivalent to units of twist and/or writhe. As with many quantities in electromagnetism, magnetic helicity (which describes magnetic field lines) is closely related to fluid mechanical helicity (which describes fluid flow lines) and their dynamics are interlinked. Ideal quadratic invariance In the late 1950s, Lodewijk Woltjer and Walter M. Elsässer discovered independently the ideal invariance of magnetic helicity, that is, its conservation when resistivity is zero. Woltjer's proof, valid for a closed system, is repeated in the following: In ideal magnetohydrodynamics, the time evolution of a magnetic field and magnetic vector potential can be expressed using the induction equation as respectively, where is a