| In inertia]confinement fusion(ICF)implosion,there are non-uniform perturbations in the drive source and the target.The growth and evolution of these perturbations lead to the asymmetric compression of DT fuel,which destroy the formation of the high-temperature hot-spot in the main fuel.The results of the physical experiments and the numerical simulations show that the evolution of the drive asymmetry and the interface perturbation seriously affect the deformation of the hot-spot,and the large deformation of the hot-spot is one of the main reasons for the failure of ICF ignition.Therefore,the physical evolution mechanism of the drive asymmetry and interface perturbation is a fundamental research in ICF implosion.It is clear that the real ICF implosion is a three-dimensional spherical structure.It is found that the deformation of the hot-spot can be expanded by the spherical harmonic Ylm(?,?),which the perturbations along the spherical meridian and latitude show the Legendre polynomial Pl(cos ?)and the Fourier mode cos(m?),respectively.In order to understand the deformation process of the hot-spot,the spherical implosion is decomposed into four cases,including the perturbations in two-dimensional planar geometry,the Fourier perturbations in two-dimensional cylindrical geometry,the Legendre perturbations in two-dimensional spherical geometry,and the spherical harmonic perturbations in three-dimensional spherical geometry.In this paper,we adopt the thin shell model to investigate the physical mechanism of the interface perturbation and the driven asymmetry in planar,cylindrical and spherical geometries,respectively.Some new research results and physical understandings are obtained as follows:(1)A revised thin layer model for incompressible Rayleigh-Taylor(RT)instability has been de-veloped to describe the deformation and nonlinear evolution of the arbitrary Atwood num-bers and the initial multi-mode perturbations.On the basis of the thin layer approximation[E.Ott,Phys.Rev.Lett.29,1429(1972)]in two-dimensional planar geometry,the differ-ential equations for motion are obtained by analyzing the forces(the gravity and pressure difference)of fluid elements(i.e.,Newton's second law).Firstly,the numerical solutions for the vacuum on both sides of the layer are obtained by the revised thin layer model.It is found that the positions of the upper and lower interfaces obtained from the revised thin layer model with that initiated by only the lower interface perturbation agree with the weak-ly nonlinear(WN)model of a finite-thicknoss fluid layer[L.F.Wang et al.,Phys.Plasmas 21,122710(2014)].Secondly,the revised thin layer model is proposed to describe the de-formation and the nonlinear evolution of the classical RT instability.It is found that the bubble-spike amplitude obtained from the revised thin layer model agrees well with that the WN model[L.F.Wang et al.,Phys.Plasmas 17,052305(2010)]and the expanded Layzer's theory[V.N.Goncharov,Phys.Rev.Lett.88,134502(2002)]in the early nonlinear growth regime.And the evolution of the perturbed interface obtained from the revised thin layer model is consistent with that from the numerical simulation.A series of tests on the revised thin layer model show that the revised thin layer model is accurate and credible.Based on the force analysis of the revised thin layer model,the model can also describe the nonlinear evolution of the layer initiated by the large amplitude and the multi-mode perturbations.[More detailed results in Phys.Plasmas 25.032708(2018)and Acta Phys.Sin.67,094701(2018)](2)A thin shell model generalizes the thin layer model in planar geometry to the case of the two-dimensional cylindrical geometry.The present model describes the evolution of the interface perturbation and the driven asymmetry in cylindrical geometry.(A)The thin shell model describes the nonlinear evolution of the Rayleigh-Taylor(RT)instability.For the initial small-amplitude perturbation,the linear growth rates from our model agree well with those from Mikaelian's work[Phys.Fluids 17,094105(2005)]but are slightly larger than those from the classical prediction for the low-mode perturbations.The perturbation ampli-tudes from our model is general agreement with that from the weakly nonlinear model[L.F.Wang et al.,Phys.Plasmas 20,042708(2013)].Moreover,on account of the force analysis of the thin shell model,the present model can investigate the deformation and the nonlin-ear evolution of the shell initialized by the largc-amplitudc and multi-mode perturbations in cylindrical geometry.(B)The thin shell model describes the evolution of the interface perturbation,which the perturbed thin shell is driven by the uniform pressure.It is found that the interface perturbation is amplified by the compression,and the outward and inward parts of the deformed shell develop into the peak and valley,respectively.(C)The thin shell model describes the evolution of the drive asymmetry,which the unperturbed thin shell is driven by a nonuniform pressure difference with a spatial modulation.It is found that the thin shell generates the spatial fundamental modulation,second and three harmonics.With a same pressure difference,the amplitude at any position of the shell are consistent.It is found that the amplitude of the pcak-to-vallcy for the low-mode drive asymmetry is depen-dent on the pressure dittcrcnce.(D)The thin shell model describes Che evolution of the interface perturbation and the drive asymmctry which the perturbed thin shell is driven by a nonuniform pressure difference with a spatial modulation.It is found that the deformation of the thin shell tends to be serious with the mode-coupling between the drive asymmetry and the interface perturbation,which not only produces,the spatial fundamental modulation and the fundamental interface perturbation,but also produces the coupling modes and the second harmonic.Furthermore,the phase difference between the interface perturbation and the spatial modulation is briefly discussed by the present model.[More detailed results in Phys.Plasmas 25,092703(2018)](3)A thin shell model generalizes the thin layer model in planar geometry to the case of the two-dimensional spherical geometry.The present model describes the evolution of the in-terface perturbation and the driven asymmetry in two-dimensional spherical geometry.(A)The thin shell model describes the nonlinear evolution of the Rayleigh-Taylor(RT)instabil-ity in two-dimensional spherical geometry.For the initial small-amplitude perturbation,the linear growth rates from our model agree well with those from Mikaelian's theory[Phys.Rev.Lett.65,992(1990);Phys.Rev.A 42,3400(1990)]but are slightly larger than those from the classical prediction for the low-mode perturbations.The perturbation amplitudes and bubble velocities from our model are in general agreement with those from the weakly nonlinear model[J.Zhang,Phys.Plasmas 24,062703(2017)]and Layzer's model[As-trophys.J.122,1(1955)],respectively.Moreover,the present model can investigate the deformation and the nonlinear evolution of the shell initialized by the large-amplitude and multi-mode perturbations in two-dimensional spherical geometry.(B)The thin shell model describes the evolution of the interface perturbation in two-dimensional spherical geometry.It is found that the perturbation is amplified by the compression,and the outward and inward parts of the deformed shell develop into the peak and valley,respectively.(C)The thin shell model describes the evolution of the drive asymmetry in two-dimensional spherical geome-try.It is found that the thin shell can not only generates the spatial fundamental modulation,second and three harmonics,which is same as that in cylindrical geometry,but also gener-ates other modes.With a same pressure difference,the amplitude at any position of the shell are consistent.It is found that the amplitude of the peak-to-valley for the low-mode drive asymmctry is dependent on the pressure difference.(D)The thin shell model describes the evolution of the interface perturbation and the drive asymmetry in two-dimensional spheri-cal geometry.It is found that the deformation of the thin shell tends to be serious with the mode-coupling between the drive asymmetry and the interface perturbation,which not only produces the spatial fundamental modulation and the fundamental interface perturbation,but also produces the coupling modes and the second harmonic.[More detailed resutls in Phys.Plasmas 26,022710(2019)](4)A thin shell model generalizes the three-dimensional theory[Phys.Rev.Lett,53,446(1984);Phys.Fluids 27,2164(1984)]to the case of the three-dimensional spherical geom-etry.The present model describes the evolution of the interface perturbation and the driven asymmetry in three-dimensional spherical geometry.On the basis of the thin layer approxi-mation,the governing equations for the shell motion and the deformation are obtained ana-lytically and solved numerically.(A)The present model describes the nonlinear evolution of the RT instability in three-dimensional spherical geometry.For the initial small-amplitude perturbation,the linear growth rates from our model agree well with the thin shell model in two-dimensional spherical geometry.Moreover,the present model can investigate the deformation and the nonlinear evolution of the shell initialized by the large-amplitude and multi-mode perturbations in three-dimensional spherical geometry.(B)The thin shell mod-el describes the evolution of the low-mode drive asymmetry in three-dimensional spherical geometry,containing the single-mode and multi-mode drive asymmetries.According to the half of the ignition threshold factor(ITF),we use the thin shell model to obtain the toler-ability of the low-order spherical harmonic Y10?Y20?Y30?Y40?Y44 and Y4-4 for the drive asymmetry.(C)We apply the thin shell model to research the real implosion experiments.It is found that the results agree well with the physical experiments and numerical simulations.For the ICF implosion in three-dimensional spherical geometry,we carry out a detailed and deeply study with the physical decomposition,and obtain the behaviour of the drive asymmetry and the interface perturbation.The presented results play an important scientific significance and application value in understanding the hot-spot of the ICF implosion. |
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