In plasma physics, a Taylor state is the minimum energy state of a plasma while the plasma is conserving magnetic flux. This was first proposed by John Bryan Taylor in 1974 and he backed up this claim using data from the ZETA machine. Taylor-States are critical to operating both the Dynomak and the reversed field pinch - both run in a Taylor State.

Examples

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. This process worked if the plasma: These claims were later checked by Marshall Rosenbluth in 1979. 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:

Derivation

Consider a closed, simply-connected, flux-conserving, perfectly conducting surface S surrounding a plasma with negligible thermal energy. Since on S. 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 S. 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 .