Theoretical Research On Richtmyer-Meshkov Instability In Magnetized Plasmas

The Richtmyer-Meshkov(RM) instability arises when an incident shock wave impacts a corrugated interface of a stratified fluid or a stratified system is impulsively accelerated.The RM instability plays an important role in applications ranging from the supernova in astrophysics to combustion in inertial confinement fusion(ICF).It is believed that the RM instability occurs when the outward propagating shock wave generated by the collapsing core of a dying star travels through the helium-hydrogen interface. In ICF,the shock inducing growth of the defects will destroy the symmetry of the shell which encapsulates the deuterium-tritium fuel and be a major obstacle to achieve required conditions for the fuel ignition at the end of the implosion.There have existed several theories to investigated RM instability,including the Richtmyer's impulsive model,linear compressible theory,nonlinear theory and ablative RM theory etc.. In this dissertation,we discuss the RM instability in magnetized plasmas.The main content are as follows.First,the effects of transverse magnetic field and shear flow on the RM instability is investigated.An explicit expression describing the behavior of the interface perturbation and criterion of the stability is analytically obtained by solving the linearized magnetohydrodynamics equations.It is shown that the perturbation develops exponentially with time rather when(1-A_t²)δ_u²ï¼ž4v_a²,where A_t is Atwood number,v_a is the mean Alfv(?)n velocity andδ_u the relative shear velocity,respectively.The growth rate of the instability increases with the growth of the shear velocity and decreases with the growth of the strength of magnetic field.Thus,RM instability is suppressed by the transverse magnetic field and reinforce by the presence of shear flow.When both the transverse magnetic field and shear flow are present,there exists a competition between the effects of magnetic field and shear flow.Whether the system is stable or not is determined by the dominating one of the stabilizing mechanism of magnetic field and the destabilizing mechanism of shear flow.Second,we have investigated the behavior of an obliquely impulsively-accelerated interface which separates two semi-infinite uniform viscous fluids.The fluids are immersed in magnetic fields which are parallel to the interface.We analytically obtained the expression of the interface amplitude and the criterion of the instability.It turns out that the presence of the magnetic field will elevate the threshold of the RM instability. When the magnetic field is strong enough thatΔv＜2v_a,the interface amplitude will damp and the instability will not arise.Thus the transverse magnetic field can suppress the RM instability.It is also shown that criterion is independent on the viscosity, which means the RM instability will always occur no matter how big the coefficient of kinematic viscosity is whenΔv＞2v_a.However,the presence of the viscosity will slow down the growth speed.Therefore,viscosity can somehow suppress but cannot eliminate the RM instability when the interface is obliquely accelerated.Finally,we have investigated the behaviors of the interfaces of an N-layer stratified fluid,which is impulsively accelerated.The whole system is immersed in an ambient homogeneous transverse magnetic field.By analytically solving the initial value problem and the second-order linear differential equation describing the perturbed velocities, we can get the growth rates and initial conditions.Hence,we can get the expressions of the interface amplitudes.Thus we can treat an arbitrary density distribution problem with a transverse magnetic field in presence by stratifying the fluid into an N-layer discrete discontinuous fluid.As examples,we considered two special cases N=2 and N=3. It is shown when a transverse magnetic field is present,the interfaces will develop as oscillation rather than linearly or exponentially growth.We focused ourselves a lot on the "layer-cake" model(ρ₁=ρ₃=ρ＜ρ₂).Results show when the system is embedded by a transverse magnetic field,the interfaces oscillate with a high fr(?)quency and the oscillations repeat themselves periodically with a low frequency.We also discussed the influence of the thickness of the middle layer on the evolution of the interfaces.It is illustrated that thickness greatly affects the evolution when the thickness is comparable to or smaller than the perturbed wave length(kt＜1 or kt～1).However,when the middle layer is thick enough(kt＞＞1),the two interfaces will develop independently.