Abstract
The effects of external magnetic field effects on the Rayleigh-Taylor instability in an inhomogeneous stratified quantum plasma rotating uniformly are investigated. The external magnetic field is considered in both horizontal and vertical direction. The linear growth rate is derived for the case where a plasma with exponential density distribution is confined between two rigid planes at z=0 and z=h, by solving the linear QMHD equations into normal mode. Some special cases are particularized to explain the roles that play the variables of the problem. The results show that, the presence of both external horizontal and vertical magnetic field beside the quantum effect will bring about more stability on the growth rate of unstable configuration. The maximum stability will happen in the case of wave number parallels to or in the same direction of external horizontal magnetic field.
Highlights
Do you think of the sun, lightning bolts or fluorescent lamps? Or do you think of nuclear fusion, micro processsor manufacture or lasers? while naturally occurring plasma is relatively unusual on earth it is playing a larger and increasingly important role in how we use and develop modern technology
The results show that, the presence of both external horizontal and vertical magnetic field beside the quantum effect will bring about more stability on the growth rate of unstable configuration
3) The critical point for stability and that happens in the presence of quantum term it is affected by the presence of both external horizontal and vertical magnetic field
Summary
Our starting point is the system of equations describing the hydrodynamic motion of quantum rotating plasma as a fluid of electrons and immobile ions, where the plasma action by a constant magnetic field along the y and z-axis (i.e. B B0yey B0zez ) (see Refs. [22,23,24,25,26,27,28,29,30]). Where Q1 given in the appendix (see Equation (40)) We appeal to the fact that, for many situations of interest in ICF (inertial-confinement fusion), unstable flow occurs at velocities much smaller than the local sound speed. This has the effect that accelerations in the flow are not strong enough to change the density of a fluid element significantly, so the fluid moves without compressing or expanding. To say that fluid elements move without changing density is to say that the Lagrangian total derivative of density is zero, that d dt (5) Comparing this equation to Equation (5), which we can rewrite in expanded form as. Where Qx1, Qy1 and Qz1 given in the appendix (see Equations (44)-(46)) Eliminating some variables from the system of Equations (14)-(19) we get a differential equation in uz
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