Linear analysis of magnetic and flow shear stabilization of Z-pinch instabilities

Abstract

Articles you may be interested inLinear and nonlinear development of m = 0 instability in a diffuse Bennett Z-pinch equilibrium with sheared axial flow Phys. Linear analysis of sheared flow stabilization of global magnetohydrodynamic instabilities based on the Hall fluid model Phys. Plasmas 9, 913 (2002);A global normal mode stability analysis on the effect of radially sheared azimuthal flow and radially sheared magnetic fields on magnetohydrodynamic ͑MHD͒ instabilities in Z-pinch plasmas is presented. A linearized set of ideal MHD equations allows the investigation of plasmas with both magnetic shear and flow shear included in the plasma equilibrium. The stabilizing effects of sheared azimuthal flow and sheared axial magnetic field are presented. Here we show that radial shear in the functional form of a vortex is particularly efficient at reducing instability growth rates.

Sheared Flow as a Stabilizing Mechanism in Astrophysical Jets

“…Analytical, experimental and numerical results show that sheared flow in z-pinch plasmas can reduce the growth of MHD instabilities (Arber and Howell, 1995;Bateman, 1978;DeSouzaMachado et al, 2000;Golingo et al, 2005;Shumlak and Hartman, 1995;Sotnikov et al, 2002Sotnikov et al, , 2004Ruden, 2002;Winterberg, 1985Winterberg, , 1999Wanex et al, 2004;Wanex, 2005a). Velocity shear stabilization is primarily a phase mixing process that disrupts the growth of unstable modes (DeSouzaMachado et al, 2000;Wanex et al, 2005b).…”

“…The use of fixed boundary conditions allows a global stability analysis of internal unstable modes (Arber and Howell, 1995;Appl et al, 2000). It has been shown that sheared azimuthal flow is effective at reducing the growth rate of the kink instability in z-pinch plasmas but has little effect on axisymmetric modes (see Wanex et al, 2005b for a detailed explanation). Sheared axial flow is effective for stabilizing the sausage mode (DeSouzaMachado et al, 2000).…”

“…The MHD equations are made dimensionless by normalizing the scales to the average radius of the jet in the asymptotic cylindrical region, the average thermal velocity of the jet plasma, the ambient pressure, and the ambient density. The linearized equations are solved numerically with a generic two-step predictor-corrector, second-order accurate space and time-centered advancement scheme (see Wanex et al, 2005b for details). The problem is treated by introducing perturbations into the plasma equilibrium state and following their linear development in time.…”

Experimental Design for the Laboratory Simulation of Magnetized Astrophysical Jets

“…If such instabilities develop indeed, they should eventually disrupt the jet collimation. On the other hand, axial magnetic fields or radial velocity shears could prevent the disruption (Hsu and Bellan, 2003;Wanex et al, 2005). Jets from young stellar objects are most likely threaded by axial magnetic field (Königl and Pudritz, 2000).…”

Heights integrated model as instrument for simulation of hydrodynamic, radiation transport, and heat conduction phenomena of laser-produced plasma in EUV applications.

“…The ideal MHD equation set (1.20) can be used to solve a limited physical problem such as a dense space plasma [10,14,15], to conduct theoretical investigations of instabilities [16][17][18] or to simplify real devices [19,20]. Key in modeling DPP or LPP devices, however, is representing the correct energy exchange and taking into account the main dissipative processes.…”