Regular conditional probability

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In plasma physics, a Taylor state is the minimum energy state of a plasma satisfying the constraint of conserving magnetic helicity.[1]


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 .

See also


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