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In plasma physics, a Taylor state is the minimum energy state of a plasma while the plasma is conserving magnetic flux.[1] This was first proposed by John Bryan Taylor in 1974 and he backed up this claim using data from the ZETA machine.[2]
Taylor-States are critical to operating both the Dynomak and the reversed field pinch - both run in a Taylor State.
In 1974, Dr. John B Taylor proposed that a spheromak could be formed by inducing a magnetic flux into a loop plasma. The plasma would then relax naturally into a spheromak also known as a Taylor State.[3][4] This process worked if the plasma:
These claims were later checked by Marshall Rosenbluth in 1979.[5] In 1974, Dr. Taylor could only use results from the ZETA pinch device to back up these claims. But, since then, Taylor states have been formed in multiple machines including:
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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