Taylor state
In plasma physics, a Taylor state is the minimum energy state of a plasma satisfying the constraint of conserving magnetic helicity.Derivation
Consider a closed, simply-connected, flux-conserving, perfectly conducting surface surrounding a plasma with negligible thermal energy.
Since on. This implies that.
As discussed above, the plasma would relax towards a minimum energy state while conserving its magnetic helicity. Since the boundary is perfectly conducting, there cannot be any change in the associated flux. This implies and on.
We formulate a variational problem of minimizing the plasma energy while conserving magnetic helicity.
The variational problem is
After some algebra this leads to the following constraint for the minimum energy state
