Improved stability condition for rotating plasmas

It is shown that the conservation of flow circulation along magnetic field lines can be used to improve on the δW stability criterion for rotating plasmas by adding to the energy integral a positive definite term. The improvement is most effective for ballooning modes in systems with a closed-line magnetic field. Such systems are investigated, both when the flow is sheared and when it is unsheared. In the unsheared case, instabilities grow exponentially in time, while, if the flow is sheared, an instability eventually saturates. The time-asymptotic behavior of such solutions is obtained and is different from the asymptotic behavior when the magnetic field is sheared.