Sheared Flow Stabilization of them=1Kink Mode inZPinches

Abstract

The effect of a sheared axial How on the m = 1 kink instability in Z pinches is studied numerically by reducing the linearized magnetohydrodynamic equations to a one-dimensional displacement equation.An equilibrium is used that is made marginally stable against the m = 0 sausage mode by tailoring its pressure profile. The principal result reveals that a sheared axial flow stabilizes the kink mode when the shear exceeds a threshold that is dependent on the location of the conducting wall. For the equilibria studied here the maximum threshold shear (v, '/kVq) was about 0.1. PACS numbers: 52.55.Ez, 52.35.Py, 52.65.KjThe m = 1 kink instability is well known, both theoretically and experimentally, to plague Z-pinch plasmas [1,2].(In this paper we refer to a Z pinch as having only axial plasma current. ) Certain notable exceptions occur, mainly in Z pinches with a flow velocity, where the flow state is observed to be stable [3,4]. We have been led to reexamine the effects of flow on stability because of the profound implications a stable, high-density Z pinch would have for magnetic confinement thermonuclear fusion [5].By tailoring the pressure profile of a static Z-pinch equilibrium the m = 0 sausage mode can be stabilized, but the equilibrium remains unstable to the internal kink mode [6,7]. The introduction of an axial magnetic field

High energy density Z-pinch plasmas using flow stabilization

“…Theoretical analysis suggests that a sufficiently radially-sheared axial flow can stabilize the modes in a pure Z-pinch provided dv z / dr ≥ 0.1kV A . [9] Similar results exist for wire-array and annular gas puff Z-pinches. [10] The experimental apparatuses include ZaP, which is the original device that demonstrated sheared flow stabilization, and ZaP-HD, which is a new device that investigates scaling to HEDP conditions.…”

“…Flow-stabilization theory of a Z-pinch based on the MHD model [9] shows no additional limitations as the plasma is scaled to different parameters. If the experimental results continue to hold, then the flow Z-pinch can be scaled from ZaP conditions to HEDP conditions.…”

Evidence of Branching Phenomena in Current-Driven Ionization Waves

“…The magnetic pressure gradients produced as a consequence of such waves have been shown to have an essential role in the generation of astrophysical jets [1][2][3][4]. These waves also underpin the formation and acceleration of spheromak and compact toroid plasmas [5][6][7][8][9][10], as well as the recent advances in plasma-jet driven magnetized target fusion and shear-flow-stabilized Z pinch schemes [11][12][13]. Due to increasing interest in these plasma phenomena, there is a critical need for a reliable model that accurately predicts the behavior of plasmas formed and sustained by MHD ionization waves.…”

The physics of fast Z pinches

“…This stabilization mechanism for equilibrium Z pinches was discussed by Shumlak and Hartman (1995). Their conclusion was that, if the initial profile is not very far from the marginally stable "Kadomtsev profile," then even a weak velocity shear can produce considerable stabilization.…”

“…Nonlinear evolution of the sausage instability for an incompressible fluid was studied by Book et al (1 976). Stabilizing effects produced by the axial shear flow have recently been discussed, with somewhat inconclusive results (Arber et al, 1995;Shumlak and Hartman, 1995). It should be remembered that the plasma column after the self-impact can be so hot that the MHD approximation breaks down and numerous non-MHD effects, in particular the ones caused by the large ion orbits, may become important.…”