Rayleigh - Taylor Instability Magnetic Field Effect And Quantum Effect

Rayleigh-Taylor instability (RTI) occurs when the light fluid supports the heavy fluid or the light fluid accelerates the denser one. It is critical for the success of inertial confinement fusion (ICF) and for the astrophysics. Therefore it is essential to understand and estimate the evolution of the RTI.The effects of magnetic field gradient (i.e. the magnetic field transition layer effects) on the Rayleigh-Taylor instability with continuous magnetic field and density profiles are investigated analytically in an incompressible plasma. The transition layers of magnetic field and density with two different typical profiles are studied and the analytic expressions of the linear growth rate of the RTI, are obtained. It is found that the magnetic field effects strongly reduce the linear growth rate of the RTI, especially when the perturbation wavelength is short. The linear growth rate of the RTI increases with the thickness of the magnetic field transition layer, especially for the case of small thickness of the magnetic field transition layer. The numerical results are compared with the analytic linear growth rates and they agree well with each other.It is suggested that hydrodynamic instabilities, in particular, the Rayleigh-Taylor instability, play a critical role in the evolution of supernova. Quantum and magnetic field effects on the RTI, in an ideal incompressible plasma, are studied. A second-order ordinary differential equation (ODE) for the RTI including the quantum corrections, with a continuous density profile, in an uniform external magnetic field, is obtained. The analytic expressions of the linear growth rate of the RTI, with magnetic field, quantum, and density gradient modifications are presented. Numerical approaches are preformed to solve the second-order ODE. The analytical model proposed here agrees with the numerical calculation. It is shown that the magnetic field has stabilizing effects on RTI and the RTI is affected significantly by quantum effects. Quantum effects tend to damp the linear growth rate of the RTI, especially for large Atwood number and small normalized density gradient scale length. The presence of external transverse magnetic field beside the quantum effects will bring about more stability on the RTI. The RTI can be completely quenched by the magnetic field and/or the quantum effects in proper circumstance. Effects of magnetic field and quantum on the RTI, for parameters closely related to inertial confinement fusion, white dwarf, are discussed in some details. It is found that the magnetic field effects always play a larger role than the quantum effects. Results are supposed to be useful for RTI treatment to analyze mixing in supernova and other RTI-driven objects.