The Kadomtsev Pinch Revisited for Sheared-Flow-Stabilized Z-Pinch Modeling

The Kadomtsev pinch, namely, the Z-pinch profile marginally stable to interchange modes, is revisited in light of observations from axisymmetric magnetohydrodynamics (MHD) modeling of the fusion Z-pinch experiment (FuZE) sheared-flow-stabilized Z-pinch experiment. We show that Kadomtsev’s stability criterion, cleanly derived by the minimum energy principle but of opaque physical significance, has an intuitive interpretation in the specific entropy analogous to the Schwarzschild–Ledoux criterion for convective stability of adiabatic pressure distributions in the fields of astrophysics, meteorology, and oceanography. By analogy, the Kadomtsev profile may be described as magnetoadiabatic in the sense that plasma pressure is polytropically related to area-averaged current density from the ideal MHD stability condition on the specific entropy. Furthermore, the nonideal stability condition of the entropy modes is shown to relate the specific entropy gradient to the ideal interchange stability function. Hence, the combined activity of the ideal interchange and nonideal entropy modes drives both the specific entropy and specific magnetic flux gradients to zero in the marginally stable state. The physical properties of Kadomtsev’s pinch are reviewed in detail and following from this the localization of pinch confinement, i.e., pinch size and inductance, is quantified by the ratio of extensive magnetic and thermal energies. In addition, results and analysis of axisymmetric MHD modeling of the FuZE Z-pinch experiment are presented where pinch structure is found to consist of a near-marginal flowing core surrounded by a super-magnetoadiabatic low-beta sheared flow.