The Study Of Magneto-Rayleigh-Taylor Instability In Magnetized Liner Inertial Fusion

Recently,the Z-pinch magnetized liner inertial fusion is an important way to drive the inertial fusion.The magneto-Rayleigh-Taylor(MRT)instability is emerged intensity at outer surface in the liner implosions.This instability is similar to the RT instability in the fluids,but the magnetic field play a role of a light fluid in the liner implosions.MRT instability is the key physical problems to determine the success or failure of MagLIF.In the studies of the MRT insta-bility in the liner implosions,most of the researchers are still using the classical two-region slab model.But the liner need to employ the three-region slab model including the vacuum region,the liner region and the fuel region.The thickness and magnetic field of the liner can affect the development of the MRT instability.It can be used to study the effect of the feedthrough in the inner surface.Firstly,the dispersion relation of the growth rate is given by using the three-region slab model and the magneto-hydrodynamic(MHD)equations in incom-pressible condition.It is obtained that the axial magnetic field BOz has a obvious effect on mitigating the MRT instability.The stronger the magnetic field is,the smaller the growth rate of the most dangerous MRT mode is.The pertur-bation of MRT instability is mainly sensitive to the short wavelength instabili-ty.It is found that the growth rate increases with the density increases.When BOz ? 0,the smaller the density is,the smaller the growth rate of MRT insta-bility.Furthermore,the effects of inner surface perturbation development from the MRT instability through using the three-region slab model is studied,where the feedthrough factor is that the ratio of the perturbation of inner surface and the perturbation of outer surface which is used to show the strength of the effect.When BOz = 0,the feedthrough factor is simply written as F = exp(-k?).The feedthrough is only relate to the perturbation wavelength and the liner thickness.For BOz?0,the effects of feedthrough is more complex.By using the condition of the liner implosions at Z facility in experiments,the time evolution of MRT instability is studied in MagLIF.Employing the zero-dimensional model to describe the liner implosions,the variations of the growth rate with the implosion time is given.It is shown the growth rate is increases with the time increases.In(x,y)plane,the azimuthal magnetic field can be increased to over 1000T completely mitigate the perturbations during liner implosions in(x,y)plane.In(x,z)plane,the axial magnetic field is several Tesla and also mitigate obviously the perturbations development.The acceleration progress of the liner will change through the the liner parameters,and then change the development of the MRT instability.It is shown that the case of high aspect ratio,the more rapid development of MRT instability.The feedthrough factor is much larger due to the liner thickness is small of the high aspect ratio.So the high aspect ratio should be avoided in MagLIF concept.But the case of very low aspect ratio should be also avoided due to low energy conversion efficiency in liner implosions.The dispersion relation and the MRT instability development is studied in compressible situation.It is shown that in the case of zero magnetic field the growth rate in compressible assumption is approximately same as that in incom-pressible assumption.However,the growth rate of MRT instability in compress-ible condition is generally lower than that in incompressible condition,because the magnetic field frozen in the plasma can provide stronger restoring force when the plasma is compressible.When the acoustic velocity cs is small,this effect is more remarkable.When the acoustic velocity is large,the growth rate will approach that in incompressible condition.The presence of magnetic field can remarkably reduce the growth rate specially for short wavelength perturbations.The last work is the study of the Richtmyer-Meshkov(RM)instability in MagLIF.Using the Richtmyer impulsive model,we give the variations of the perturbation displacement with the time in different axial magnetic fields B0z.The axial magnetic field B0z has a obviously mitigate for RM instability.The effects of the mitigation is similar to MRT instability.If B0z is enough large,the RM instability can be completely mitigated.It is given that the variations of the perturbation displacement with the perturbation wavelength.It is shown that the perturbation displacement monotonically decreases with the perturba-tion wavelength without the magnetic field.However,it will first increases and then decreases with perturbation wavelength.But the perturbation displacement is always lower in a magnetic field than B0z = 0.When B0z ? 0,the effects of mitigation of short wavelength perturbation is more stronger than long wave-length perturbation.