Study on preheating ablative effects of two-mode Rayleigh-Taylor instability
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摘要: 针对双模扰动下的烧蚀瑞利-泰勒不稳定性增长问题，采用高精度的数值计算方法，研究了不同预热程度下模耦合产生的多个高次谐波幅值的发展和演化问题。研究表明，三种预热烧蚀条件下，当扰动基模满足长波与短波耦合方式时，谐波中的长波模态占主导，而短波模发展明显受到抑制；当满足短波与短波耦合时，耦合结果带来了许多新的增长较快的长波模态，此时短波模增长呈现小幅震荡形式。比较两种耦合方式可以发现，长波结构在烧蚀瑞利-泰勒不稳定性弱非线性阶段都占主导地位，尤其是短波与短波耦合中气泡与尖钉表现出不同于两个基模的长波模结构。进一步分析预热效应对模耦合增长的影响，发现预热程度越强就越能削弱耦合谐波的增长，这说明预热对烧蚀瑞利-泰勒不稳定性具有致稳作用，这对惯性约束聚变工程中控制烧蚀瑞利-泰勒不稳定性发展具有重要意义。Abstract: Aiming at the growth of ablative Rayleigh-Taylor instability with two perturbations, the evolutions of the amplitudes of high-order harmonics excited by two-mode coupling under different preheating conditions are studied by using a high-precision numerical simulation method. When the fundamental modes are a long-wavelength and a short-wavelength mode, the long-wavelength modes of the excited harmonics are dominant, while the development of short-wavelength modes are obviously suppressed; when the fundamental modes are two short-wavelength modes, many fast-growing and long-wavelength modes are excited, and the growth of short-wavelength modes are in the form of small oscillation. By comparing the two different two-mode coupling cases, it is found that the long-wavelength structures are dominant in the weakly nonlinear stage. Especially, in the two short-wavelength modes coupling case, the bubbles and spikes show long-wavelength structures which are different from the two fundamental modes. By further comparing the three preheating ablative effects, it is found that the higher the preheat degree is, the more the coupled harmonics growth will be weakened. It is of great significance to control the development of ablative Rayleigh-Taylor instability in inertial confinement fusion engineering.
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Key words:
- two-mode perturbations /
- preheating /
- Rayleigh-Taylor instability /
- high-order harmonics /
- bubbles /
- spikes
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图 1 不同预热情况下的一维平衡流场的密度、速度和温度分布
Figure 1. Density, velocity and temperature distribution of one-dimensional equilibrium flow field under different preheating conditions
图 2 强、中和弱预热情况下的线性增长率
Figure 2. Linear growth rate under strong, medium and weak preheating
图 3 不同预热情况下
$ {\lambda }_{1}=10\;{\text{μ}}\rm{m} $ 与$ {\lambda }_{2}=40\;{\text{μ}}\rm{m} $ 双模扰动所激发的谐波的密度幅值随时间的演化Figure 3. Temporal evolution of the density amplitude of harmonics excited by the coupling of two modes (short-and long-wavelength
$ {\lambda }_{1}=10\;{\text{μ}}\rm{m} $ and$ {\lambda }_{2}=40\;{\text{μ}}\rm{m} $ ) in different preheating cases
图 4 不同预热情况下
$ {\lambda }_{1}=10\;{\text{μ}}\rm{m} $ 与$ {\lambda }_{2}=40\;{\text{μ}}\rm{m} $ 双模扰动下在t=7.5 ns时的密度等值线Figure 4. Density contours for
$ {\lambda }_{1}=10\;{\text{μ}}\rm{m} $ and$ {\lambda }_{2}=40\;{\text{μ}}\rm{m} $ mode coupling under different preheating at t=7.5 ns
图 5 不同预热情况下
$ {\lambda }_{1}=10\;{\text{μ}}\rm{m} $ 与$ {\lambda }_{2}=12\;{\text{μ}}\rm{m} $ 双模扰动所激发的谐波的密度幅值随时间的演化Figure 5. Temporal evolution of the density amplitude of harmonics excited by the coupling of two short-wavelength modes (
$ {\lambda }_{1}=10\;{\text{μ}}\rm{m} $ and$ {\lambda }_{2}=12\;{\text{μ}}\rm{m} $ ) in different preheating cases
图 6 不同预热情况下
$ {\lambda }_{1}=10\;{\text{μ}}\rm{m} $ 与$ {\lambda }_{2}=12\;{\text{μ}}\rm{m} $ 双模扰动下在t=7.5 ns时的密度等值线Figure 6. Density contours for
$ {\lambda }_{1}=10\;{\text{μ}}\rm{m} $ and$ {\lambda }_{2}=12\;{\text{μ}}\rm{m} $ mode coupling under different preheating at t=7.5 ns表 1 三种预热条件的参数设置
Table 1. Parameter settings of strong, medium and weak preheating conditions
case b c strong preheating (SP) 8.6 1.6 moderate preheating (MP) 2 0.4 weak preheating (WP) 0.86 0.24 
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