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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 .
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