The Study On Magneto-Rayleigh-Taylor Instability Of Solid Liner Implosion Compression In Magneto-Inertial-Fusion

Magneto-Rayleigh-Taylor instability(MRTI),which is inherent in magneto-inertial fusion,is the critical mechanism to determine the performance of fusion plasmas and the final ignition,deserving detailed investigations.Based on two-dimensional ideal magnetohydrodynamic(MHD)equations,linear stability theory is adopted to study the linear growth rate of MRTI and a WENO finite difference scheme is employed to develop 2D MHD code to explore the nonlinear evolution of MRTI in this thesis.Main contents and conclusions will be briefly presented in three parts in the following.Firstly,the basic theory and equations of electromagnetics and plasma kinetics are introduced to derive the two-fluid model of plasmas,include particle number,momentum and energy conservation equations.And ideal MHD equations are then derived for the following linear analysis and two dimensional simulation.Secondly,linear stability theory is adopted to study the MRTI in linear stage.Method of normal mode is employed to ideal,compressible magnetohydrodynamic equations to obtain the eigenequations.By using the discrete difference method,the problem of eigenequations can be transformed into a simple problem of matrix eigenvalues and eigenvectors.Based on assumptions of uniform magnetic fields,the variation of the growth rate with plasma parameters is studied.It is shown that the growth rate is remarkably decreased with the increase of the magnetic field vertical to the acceleration direction.And there is a critical magnetic field,beyond which the MRTI over a critical wave number will be completely stabilized.However,in the case of magnetic field parallel to the direction of acceleration,the MRTI is just slightly affected by the magnetic field even its magnitude is large.Finally,A 2D numerical simulation code is developed for nonlinear evolution of magneto-Rayleigh-Taylor instability(MRTI).Based on ideal magnetohydrodynamic model,the 5th WENO scheme is employed to calculate the MHD equations and a projection scheme is used to clean spurious magnetic field divergence.The code is validated by comparison with the results of linear stability theory.It is shown that vertical magnetic field evidently suppresses MRTI in both linear and nonlinear stages,and parallel magnetic field has few effect on MRTI in the linear stage.In the nonlinear regime of MRTI,high order harmonic perturbations will occur in the evolution of single mode.It is shown that parallel magnetic field will evidently reduce the Kelvin-Helmholtz instability in nonlinear regime,which is caused by nonlinear development of MRT instability.Consequently,the overall instability will also be decreased by parallel magnetic field.And many other modes except for fundamental modes and harmonic will be generated in the evolution of double modes.Most importantly,inverse cascade is the dominant mechanism in the evolution of multi modes,which means that perturbations evolve from short wavelength to long wavelength in nonlinear evolution of MRTI.