平面几何条件下的流体力学不稳定性分析
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摘要
流体力学不稳定性是惯性约束核聚变的重要研究课题,它能破坏靶丸的对称性和完整性,使得点火失败,惯性约束聚变靶在内爆阶段是不稳定的,特别是瑞利-泰勒不稳定性,在内爆的开始阶段它破坏靶的球壳,而在内爆后期它又阻碍中心热斑的形成。因此深入了解流体力学不稳定的增长过程,对于实现点火和高增益是至关重要的。中心热斑点火目标的实现最关键的步骤就是实现对流体力学不稳定性的控制。本文采用两种方法来对调制平面靶的扰动增长进行观测,并且对系统的调制传递函数进行了研究。
本文利用面向背光照相技术对正弦调制平面靶的瑞利-泰勒不稳定性增长进行了实验研究,得到了清晰的时空分辨图像;通过采用傅里叶变换取基模法和求波峰波谷差值法分析了实验结果;两种方法得到的靶扰动增长因子相同。同时,对实验中平面靶扰动增长较小可能的原因给出了定性解释。
侧向背光照相能直接反映靶表面扰动幅度的变化情况。在神光Ⅱ装置上,实验利用侧向背光照相技术,对烧蚀面扰动引起的内界面扰动增长进行了观测。实验结果表明,观察到的内界面扰动幅度大于期望值。分析认为,造成内界面较大扰动增长的原因主要是2维效应。因为样品盖住了黑腔的诊断孔, X光福照的只是对应开孔部分的样品,烧蚀面扰动引起的内界面的扰动就呈现出一幅从中间的扰动区域逐渐过渡到四周的图像。由此,提出了新的靶优化设计方案,即应减小沿背光方向的样品尺寸。
在流体力学不稳定性实验中,X光强度分布经过成像系统后在像面上的成像强度会发生变化,所以要准确得到靶扰动的变化情况,还需要对成像系统的调制传递函数进行研究。本文通过测量刀边像得到系统的边缘扩散函数,进而得到系统的调制传递函数。在面向背光照相实验中,只须找出相应空间频率的调制传递函数值,即可得到X光强度的实际分布。系统的调制传递函数等于各个分系统的调制传递函数的乘积,本文利用菲涅尔-基尔霍夫衍射理论与锐利-索末菲衍射理论对针孔相机的点扩散函数进行了模拟,再经傅立叶变化得出了针孔相机的调制传递函数。
The hydrodynamic instability has been a focus of research in Inertial Confinement Fusion (ICF). It can destroy the symmetry and integrity of the capsule, and even fail the ignition. Inertial confinement fusion capsule implosions are inherently unstable. In particular, the Rayleigh-Taylor instability (RTI) tends at first to destroy the imploding shell and later hinders the formation of the central hot spot. The understanding of the growth of perturbations is of extreme important for achieving the ignition and high gain. It should be clear that the goal of central hot spot ignition depends most critically on how to control the instability. This paper makes use of two methods to measure the perturbation growth of sine modulated surface target and explore the system modulation transfer function (MTF).
This paper makes use of face-on photography technology to investigate the Rayleigh-Taylor instability of sine modulated surface target and gain a vivid space and time resolved image. The experimental result are analyzed by using two method: 1.Figure out fundamental mode Fourier coefficient; 2. Figure out the D-value of wave crest and wave hollow, the two methods obtain the same perturbation growth factor. Moreover, the possible reasons for the little growth have been discussed and give the qualitative interpretation.
Side-on radiography technology can directly demonstrate the change of perturbation amplitude on target surface. In the experiment at Shenguang II laser facility, this technology is used to detect rear surface perturbation caused by the ablation surface perturbation. The perturbation amplitude observed in the experiment is higher than expected. According to our analysis, two-dimensional effect is the main reason for larger perturbation growth of the rear surface. Because the target is set on the diagnosis hole of the holhraum, X-ray irradiate the part of the target corresponding to diagnostic hole. The rear surface perturbation, which is caused by the ablation surface perturbation, exists in the center and gradually spreads around. Based on above discussion, an optimized target design is presented at last, which suggests the target size along the direction of backlighting transmit should decrease.
X-ray intensity distribution will have a change when it passes through the optical system in the hydrodynamic instability experiments, in order to get the perturbation change information,the system modulation transfer function should be investigated This chapter makes use of the knife-edge image to get the brim spread function, then the system modulation transfer function can be derived from the brim spread function. When the system modulation transfer function is known, the practical X-ray intensity distribution can be obtained through image intensity. Moreover, the product of subsystem modulation transfer function is the system modulation transfer function, this paper employs Fresnel-Kirchhoff’s law of diffraction and Rayleigh -Sommerfeld’s law of diffraction to simulates pinhole camera’s point spread function (PSF), then gains this pinhole camera’s modulation transfer function through Fourier analysis.
本文利用面向背光照相技术对正弦调制平面靶的瑞利-泰勒不稳定性增长进行了实验研究,得到了清晰的时空分辨图像;通过采用傅里叶变换取基模法和求波峰波谷差值法分析了实验结果;两种方法得到的靶扰动增长因子相同。同时,对实验中平面靶扰动增长较小可能的原因给出了定性解释。
侧向背光照相能直接反映靶表面扰动幅度的变化情况。在神光Ⅱ装置上,实验利用侧向背光照相技术,对烧蚀面扰动引起的内界面扰动增长进行了观测。实验结果表明,观察到的内界面扰动幅度大于期望值。分析认为,造成内界面较大扰动增长的原因主要是2维效应。因为样品盖住了黑腔的诊断孔, X光福照的只是对应开孔部分的样品,烧蚀面扰动引起的内界面的扰动就呈现出一幅从中间的扰动区域逐渐过渡到四周的图像。由此,提出了新的靶优化设计方案,即应减小沿背光方向的样品尺寸。
在流体力学不稳定性实验中,X光强度分布经过成像系统后在像面上的成像强度会发生变化,所以要准确得到靶扰动的变化情况,还需要对成像系统的调制传递函数进行研究。本文通过测量刀边像得到系统的边缘扩散函数,进而得到系统的调制传递函数。在面向背光照相实验中,只须找出相应空间频率的调制传递函数值,即可得到X光强度的实际分布。系统的调制传递函数等于各个分系统的调制传递函数的乘积,本文利用菲涅尔-基尔霍夫衍射理论与锐利-索末菲衍射理论对针孔相机的点扩散函数进行了模拟,再经傅立叶变化得出了针孔相机的调制传递函数。
The hydrodynamic instability has been a focus of research in Inertial Confinement Fusion (ICF). It can destroy the symmetry and integrity of the capsule, and even fail the ignition. Inertial confinement fusion capsule implosions are inherently unstable. In particular, the Rayleigh-Taylor instability (RTI) tends at first to destroy the imploding shell and later hinders the formation of the central hot spot. The understanding of the growth of perturbations is of extreme important for achieving the ignition and high gain. It should be clear that the goal of central hot spot ignition depends most critically on how to control the instability. This paper makes use of two methods to measure the perturbation growth of sine modulated surface target and explore the system modulation transfer function (MTF).
This paper makes use of face-on photography technology to investigate the Rayleigh-Taylor instability of sine modulated surface target and gain a vivid space and time resolved image. The experimental result are analyzed by using two method: 1.Figure out fundamental mode Fourier coefficient; 2. Figure out the D-value of wave crest and wave hollow, the two methods obtain the same perturbation growth factor. Moreover, the possible reasons for the little growth have been discussed and give the qualitative interpretation.
Side-on radiography technology can directly demonstrate the change of perturbation amplitude on target surface. In the experiment at Shenguang II laser facility, this technology is used to detect rear surface perturbation caused by the ablation surface perturbation. The perturbation amplitude observed in the experiment is higher than expected. According to our analysis, two-dimensional effect is the main reason for larger perturbation growth of the rear surface. Because the target is set on the diagnosis hole of the holhraum, X-ray irradiate the part of the target corresponding to diagnostic hole. The rear surface perturbation, which is caused by the ablation surface perturbation, exists in the center and gradually spreads around. Based on above discussion, an optimized target design is presented at last, which suggests the target size along the direction of backlighting transmit should decrease.
X-ray intensity distribution will have a change when it passes through the optical system in the hydrodynamic instability experiments, in order to get the perturbation change information,the system modulation transfer function should be investigated This chapter makes use of the knife-edge image to get the brim spread function, then the system modulation transfer function can be derived from the brim spread function. When the system modulation transfer function is known, the practical X-ray intensity distribution can be obtained through image intensity. Moreover, the product of subsystem modulation transfer function is the system modulation transfer function, this paper employs Fresnel-Kirchhoff’s law of diffraction and Rayleigh -Sommerfeld’s law of diffraction to simulates pinhole camera’s point spread function (PSF), then gains this pinhole camera’s modulation transfer function through Fourier analysis.
引文
[1] 张钧,常铁强. 激光核聚变靶物理基础. 北京:国防工业出版社,2004,256-299
[2] 叶文华. 激光烧蚀 RT 不稳定性线形增长率和非线性行为的数值研究.强激光与粒子束,1998,10(4):567-572
[3] 张钧,赖东显,张维岩. 辐射烧蚀界面的单模 Rayleigh-Taylor 不稳定性分析.计算物理,1998,15(4):483-488
[4] 江少恩,李文洪,孙可煦,等. “神光Ⅱ”上冲击波法测量黑腔辐射温度. 高压物理学报,2005,19(4):289-292
[5] 李熙,朱华庆. 瑞利-泰勒不稳定性的实验研究及数值模拟. 科技导报,2005,23(11): 30-32
[6] 李三伟,冯杰,丁永坤,等. 强激光烧蚀平面靶的实验研究. 原子与分子物理学报,2000,17(2):204-210
[7] 吴俊峰,叶文华,张维岩. 柱几何 Rayleigh-Taylor 不稳定性数值模拟. 强激光与粒子束,2003,15(1):64-68
[8] 齐进,叶文华. 三维激光烧蚀瑞利-泰勒不稳定性并行计算.计算物理,2002,19(5):388-392
[9] 叶文华,张维岩,贺贤土. 烧蚀瑞利-泰勒不稳定性线形增长率的预热致稳公式. 物理学报,2000,49(4):763-767
[10] 李维新. 一维不定常流与冲击波. 北京:国防工业出版社,2003,1-80
[11] Fujioka S, Sunahara A, Ohnishi N, et al. Suppression of Rayleigh-Taylor instability due to radiative ablation in brominated plastic targets. Phys. plasmas, 2004, 11(5): 2814-2822
[12] Piriz A R, Sanz J, Lbanez L F. Rayleigh-Taylor instability of steady ablation fronts: The discontinuity model revisited. Phys. Plasmas, 1997, 4(4): 1117-1126
[13] Glendinning S G, Dixit S N, Hammel B A, et al. Measurement of a Dispersion Curve for Linear-Regime Rayleigh-Taylor Growth Rates in Laser-Driven Targets. Physical Review Letters, 1997, 78(17): 3318-3321
[14] Pawley C J, Bodner S E, Dahlburg J P. Observation of Rayleigh-Taylor growth to short wavelengths on Nike. Phys. Plasmas, 1999, 6(2): 565-570
[15] Lindl J D, Amendt P, Berger R L, et al. The physics basis for ignition using indirect-drive targets on the National Ignition Facility. Phys. plasmas, 2004, 11(2): 441-459
[16] Goncharov V N, Betti R, McCrory R L, et al. Self-consistent stability analysis of ablation frontswith large Froude number. Phys. Plasmas, 1995, 3(4): 1402-1414
[17] Farley D R, Peyser T A, Logory L M, et al. High Mach number mix instability experiments of an unstable density interface using a single-mode, nonlinear initial perturbation. Phys. Plasmas, 1999, 6(11): 4304-4317
[18] Schneider M B, Dimonte G, Remington B. Large and small Scale Structure in Rayleigh-Taylor Mixing. Physical Review Letters, 1998, 80(16): 3507-3510
[19] Peyser T A, Miller P L, Stry P E, et al. Measurement of Radiation-Driven Shock-Induced Mixing from Nonlinear Perturbations. Physical Review Letters, 1995, 75(12): 2332-2335
[20] Remington B A, Haan S W, Glendinning S G, et al. Large Growth Rayleigh-Taylor Experiments Using Shaped Laser Pulses. Physical Review Letters, 1991, 67(23): 3259-3262
[29] Weber S V, Remington B A, Haan S W. Modeling of Nova indirect drive Rayleigh-Taylor experiments. Phys.Plasmas,1994, 1(1): 3652-3661
[21] Shigemori K, Azechi H, Nakai M, et al. Measurement of Rayleigh-Taylor Growth Rate of Planar Targets Irradiated Directly by Partially Coherent Light. Physical Review Letters, 1997, 78(2): 250-253
[22] Sakaiya T, Azechi H, Matsuoka M, et al. Ablative Rayleigh-Taylor Instability at Short Wavelengths Observed with Moire Interferometry. Physical Review Letters, 2002, 88(14): 145003
[23] Fujioka S, Sunahara A, Nishihara K, et al. Suppression of Rayleigh-Taylor Instability due to Self-Radiation in a Multiablation. Physical Review Letters, 2004, 92(19): 195001
[24] Taylor R J, Dahlburg J P, Iwase A, et al. Measurement and simulation of laser Imprinting and Consequent Rayleigh-Taylor Growth. Physical Review Letters, 1996, 76(10): 1643-1646
[25] Knauer J P, Betti R, Bradley D K, et al. Single-mode, Rayleigh-Taylor growth-rate measurements on the OMEGA laser system. Phys. Plasmas, 1999, 7(1): 338-345
[26] Aglitskiy Y, Velikovich A L, Karasik M, et al. Direct Observation of Mass Oscillations Due to Ablative Richtmyer-Meshkov Instability in Plastic Targets. Physical Review Letters, 2001, 87(26): 265001
[27] Fujioka S, Shiraga H, Nishikino M, et al. Side-on measurement of hydrodynamics of laser-driven plasmas with high space- and time-resolution x-ray imaging technique. Review of Scientific Instruments, 2003, 74(3): 2198-2201
[28] 张钧,常铁强.烧蚀引起 R-T 不稳定性实验条件的初步研究.强激光与粒子束,1995,7(4):601-607
[29] Remington B A, Weber S V, Marinak M M, et al. Single-mode and multimode Rayleigh-Taylor experiments on Nova. Phys. plasmas, 1995, 2(1): 241-255
[30] Smitherman D P, Chrien R E, Hoffman N M, et al. The feedout process: Rayleigh-Taylor and Richtmyer-Mshkov instabilities in uniform, radiation-driven foils. Phys. Plasmas, 1999, 6(3): 932-939
[31] Smitherman D P, Chrien R E, Hoffman N M, et al. Feedout coupling of Richtmyer-Meshkov and Rayleigh-Taylor instabilities in stratified, radiation-driven foils. Phys.Plasmas, 1999, 6(3): 940-946
[32] Ishizaki R, Nishihara K. Model of hydrodynamic perturbation growth in the start-up phase of laser implosion. Physical Review E, 1998, 58(3): 3744-3767
[33] Betti R, Lobatchev V, McCrory R L. Feedout and Rayleigh-Taylor Seeding Induced by Long Wavelength Perturbations in Accelerated Planar Foils. Physical Review Letters, 1998, 81(25): 5560-5563
[34] Shigemori K, Azechi H, Nakai M, et al. Perturbation transfer from the fronts to rear surface of laser-irradiated targets. Physical Review E, 2002, 65(4): 045401
[35] 叶文华,张维岩,陈光南,等.激光烧蚀瑞利-泰勒不稳定性数值研究.强激光与粒子束,1999,11(5):613-618
[36] Kilkenny J D, Glendinning S G, Haan S W, et al. A review of the ablative stabilization of the Rayleigh-Taylor instability in regimes relevant to inertial confinement fusion. Phys. plasmas, 1994, 1(5): 1379-1389
[37] Shigemori K, Nakai M, Azechi H, et al. Feedout of Rear Surface Perturbation due to Rarefaction Wave in Laser-Irradiated Targets. Physical Review Letters, 2000, 84(23): 5331-5334
[38] Li X L. A numerical study of three-dimensional bubble merger in the Rayleigh- Taylor instability. Phys. Fluids, 1995, 8(2): 336-343
[39] 安连生. 应用光学.北京:北京理工大学出版社,2003,146-169
[40] 王仕璠,朱自强. 现代光学原理. 成都:电子科技大学出版社,2000,131-164
[2] 叶文华. 激光烧蚀 RT 不稳定性线形增长率和非线性行为的数值研究.强激光与粒子束,1998,10(4):567-572
[3] 张钧,赖东显,张维岩. 辐射烧蚀界面的单模 Rayleigh-Taylor 不稳定性分析.计算物理,1998,15(4):483-488
[4] 江少恩,李文洪,孙可煦,等. “神光Ⅱ”上冲击波法测量黑腔辐射温度. 高压物理学报,2005,19(4):289-292
[5] 李熙,朱华庆. 瑞利-泰勒不稳定性的实验研究及数值模拟. 科技导报,2005,23(11): 30-32
[6] 李三伟,冯杰,丁永坤,等. 强激光烧蚀平面靶的实验研究. 原子与分子物理学报,2000,17(2):204-210
[7] 吴俊峰,叶文华,张维岩. 柱几何 Rayleigh-Taylor 不稳定性数值模拟. 强激光与粒子束,2003,15(1):64-68
[8] 齐进,叶文华. 三维激光烧蚀瑞利-泰勒不稳定性并行计算.计算物理,2002,19(5):388-392
[9] 叶文华,张维岩,贺贤土. 烧蚀瑞利-泰勒不稳定性线形增长率的预热致稳公式. 物理学报,2000,49(4):763-767
[10] 李维新. 一维不定常流与冲击波. 北京:国防工业出版社,2003,1-80
[11] Fujioka S, Sunahara A, Ohnishi N, et al. Suppression of Rayleigh-Taylor instability due to radiative ablation in brominated plastic targets. Phys. plasmas, 2004, 11(5): 2814-2822
[12] Piriz A R, Sanz J, Lbanez L F. Rayleigh-Taylor instability of steady ablation fronts: The discontinuity model revisited. Phys. Plasmas, 1997, 4(4): 1117-1126
[13] Glendinning S G, Dixit S N, Hammel B A, et al. Measurement of a Dispersion Curve for Linear-Regime Rayleigh-Taylor Growth Rates in Laser-Driven Targets. Physical Review Letters, 1997, 78(17): 3318-3321
[14] Pawley C J, Bodner S E, Dahlburg J P. Observation of Rayleigh-Taylor growth to short wavelengths on Nike. Phys. Plasmas, 1999, 6(2): 565-570
[15] Lindl J D, Amendt P, Berger R L, et al. The physics basis for ignition using indirect-drive targets on the National Ignition Facility. Phys. plasmas, 2004, 11(2): 441-459
[16] Goncharov V N, Betti R, McCrory R L, et al. Self-consistent stability analysis of ablation frontswith large Froude number. Phys. Plasmas, 1995, 3(4): 1402-1414
[17] Farley D R, Peyser T A, Logory L M, et al. High Mach number mix instability experiments of an unstable density interface using a single-mode, nonlinear initial perturbation. Phys. Plasmas, 1999, 6(11): 4304-4317
[18] Schneider M B, Dimonte G, Remington B. Large and small Scale Structure in Rayleigh-Taylor Mixing. Physical Review Letters, 1998, 80(16): 3507-3510
[19] Peyser T A, Miller P L, Stry P E, et al. Measurement of Radiation-Driven Shock-Induced Mixing from Nonlinear Perturbations. Physical Review Letters, 1995, 75(12): 2332-2335
[20] Remington B A, Haan S W, Glendinning S G, et al. Large Growth Rayleigh-Taylor Experiments Using Shaped Laser Pulses. Physical Review Letters, 1991, 67(23): 3259-3262
[29] Weber S V, Remington B A, Haan S W. Modeling of Nova indirect drive Rayleigh-Taylor experiments. Phys.Plasmas,1994, 1(1): 3652-3661
[21] Shigemori K, Azechi H, Nakai M, et al. Measurement of Rayleigh-Taylor Growth Rate of Planar Targets Irradiated Directly by Partially Coherent Light. Physical Review Letters, 1997, 78(2): 250-253
[22] Sakaiya T, Azechi H, Matsuoka M, et al. Ablative Rayleigh-Taylor Instability at Short Wavelengths Observed with Moire Interferometry. Physical Review Letters, 2002, 88(14): 145003
[23] Fujioka S, Sunahara A, Nishihara K, et al. Suppression of Rayleigh-Taylor Instability due to Self-Radiation in a Multiablation. Physical Review Letters, 2004, 92(19): 195001
[24] Taylor R J, Dahlburg J P, Iwase A, et al. Measurement and simulation of laser Imprinting and Consequent Rayleigh-Taylor Growth. Physical Review Letters, 1996, 76(10): 1643-1646
[25] Knauer J P, Betti R, Bradley D K, et al. Single-mode, Rayleigh-Taylor growth-rate measurements on the OMEGA laser system. Phys. Plasmas, 1999, 7(1): 338-345
[26] Aglitskiy Y, Velikovich A L, Karasik M, et al. Direct Observation of Mass Oscillations Due to Ablative Richtmyer-Meshkov Instability in Plastic Targets. Physical Review Letters, 2001, 87(26): 265001
[27] Fujioka S, Shiraga H, Nishikino M, et al. Side-on measurement of hydrodynamics of laser-driven plasmas with high space- and time-resolution x-ray imaging technique. Review of Scientific Instruments, 2003, 74(3): 2198-2201
[28] 张钧,常铁强.烧蚀引起 R-T 不稳定性实验条件的初步研究.强激光与粒子束,1995,7(4):601-607
[29] Remington B A, Weber S V, Marinak M M, et al. Single-mode and multimode Rayleigh-Taylor experiments on Nova. Phys. plasmas, 1995, 2(1): 241-255
[30] Smitherman D P, Chrien R E, Hoffman N M, et al. The feedout process: Rayleigh-Taylor and Richtmyer-Mshkov instabilities in uniform, radiation-driven foils. Phys. Plasmas, 1999, 6(3): 932-939
[31] Smitherman D P, Chrien R E, Hoffman N M, et al. Feedout coupling of Richtmyer-Meshkov and Rayleigh-Taylor instabilities in stratified, radiation-driven foils. Phys.Plasmas, 1999, 6(3): 940-946
[32] Ishizaki R, Nishihara K. Model of hydrodynamic perturbation growth in the start-up phase of laser implosion. Physical Review E, 1998, 58(3): 3744-3767
[33] Betti R, Lobatchev V, McCrory R L. Feedout and Rayleigh-Taylor Seeding Induced by Long Wavelength Perturbations in Accelerated Planar Foils. Physical Review Letters, 1998, 81(25): 5560-5563
[34] Shigemori K, Azechi H, Nakai M, et al. Perturbation transfer from the fronts to rear surface of laser-irradiated targets. Physical Review E, 2002, 65(4): 045401
[35] 叶文华,张维岩,陈光南,等.激光烧蚀瑞利-泰勒不稳定性数值研究.强激光与粒子束,1999,11(5):613-618
[36] Kilkenny J D, Glendinning S G, Haan S W, et al. A review of the ablative stabilization of the Rayleigh-Taylor instability in regimes relevant to inertial confinement fusion. Phys. plasmas, 1994, 1(5): 1379-1389
[37] Shigemori K, Nakai M, Azechi H, et al. Feedout of Rear Surface Perturbation due to Rarefaction Wave in Laser-Irradiated Targets. Physical Review Letters, 2000, 84(23): 5331-5334
[38] Li X L. A numerical study of three-dimensional bubble merger in the Rayleigh- Taylor instability. Phys. Fluids, 1995, 8(2): 336-343
[39] 安连生. 应用光学.北京:北京理工大学出版社,2003,146-169
[40] 王仕璠,朱自强. 现代光学原理. 成都:电子科技大学出版社,2000,131-164