Within the context of ideal magnetohydrodynamics (MHD), helicity is a global quantity that is a constant. It is a measure of how helical or spiraled the magnetic field lines are, in other words, a measure of flux linkage. Another way to think about it is as a measure of field aligned current. A current produces a circular magnetic field that can be added to the original field line present to give a helical shape.

One of the constraints of ideal MHD with no plasma resistance the field lines are "frozen in", that is they can not pass through each other or break. 
 

The plasma is bound to the field lines.  This means that there would be no way to change the field line configuration or flux linkages within a plasma. Therefore, helicity cannot be added or dissipated.

If this were truly the case, there could be no such thing as helicity injection current drive. Ideal MHD neglects the resistivity of the plasma, however. Plasma resistivity is usually very small for hot plasmas, and neglecting it results in a simplified theory. Even though the resistivity value is small, it allows for interesting magnetic effects such as the tearing and reconnection of magnetic field lines. 
 

Consider a uniform sheet of plasma current going into the page. The magnetic field lines on either side point in opposite directions. Considering only ideal MHD, figure 1, the picture will stay as shown indefinitely. The current and magnetic fields will be trapped as they are, since there is nothing to cause dissipation. When resistivity is included it is possible for the field lines to break and reconnect as shown in figure 2. This has been shown to occur readily in experiments.

So what about helicity in the resistive case? Helicity is no longer conserved; it is dissipated on a resistive time scale. The resistive or L/R time is the time it takes for current to decay. However, on reconnection time scales (much shorter than the L/R time scales) helicity can again be considered constant. 
 

The time it takes for field lines to reconnect is approximately the geometric mean of the L/R time and the Alfven time. The Alfven time is the time it takes for a hydrodynamic wave to move through the plasma. It is similar to the vibration of a plucked guitar string. This time can be on the order of microseconds.

In certain geometry, magnetic reconnection obeys Taylor's minimum energy principle, where a MHD equilibrium relaxes to a minimum magnetic energy while maintaining constant total helicity. This energy is within the magnetic field lines and is determined by their shape. 

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