Weakly nonlinear hydrodynamic instabilities in inertial fusion

Abstract

For many cases of interest to inertial fusion, growth of Rayleigh–Taylor and other hydrodynamic instabilities is such that the perturbations remain linear or weakly nonlinear. The transition to nonlinearity is studied via a second-order solution for multimode classical Rayleigh–Taylor growth. The second-order solution shows how classical Rayleigh–Taylor systems forget initial amplitude information in the weakly nonlinear phase. Stabilized growth relevant to inertial fusion is qualitatively different, and initial amplitudes are not dominated by nonlinear effects. In all systems with a full spectrum of modes, nonlinear effects begin when mode amplitudes reach about 1/Lk2, for modes of wave number k and system size L.

Bell-Plessett effect on harmonic evolution of spherical Rayleigh-Taylor instability in weakly nonlinear scheme for arbitrary Atwood numbers

“…25,26 When the perturbation amplitude is close to its wavelength, the second harmonic, third harmonic and so on are generated successively, and then the perturbation goes into the weakly nonlinear regime. [12][13][14] In the third-order weakly nonlinear theory, [4][5][6][7] the interface position at time t can be expressed as the form of gðx; tÞ ¼ P 3 i¼1 g i cosðikxÞ with g i being the amplitude of the ith harmonic…”

“…[1][2][3] The RTI has been extensively investigated theoretically, [4][5][6][7][8][9][10][11][12][13][14] experimentally, 15,16 and numerically. [17][18][19][20] Before the RTI enters a strong nonlinear stage, [21][22][23][24] it will undergo a linear stage, and then a weakly nonlinear stage.…”

Gated x-ray detector for the National Ignition Facility

“…Additionally, the instrument is intended to acquire 2D spatially or 1D spectrally time resolved images of target features. Some specific examples are: spectral emission from targets 2 , spatially resolved foil trajectories 3 , hydrodynamic instability growth information 4 , shock front propagation 5 and x-ray time history for ignition physics 6 .…”

The Gated X-ray Detector for the National Ignition Facility

“…Additionally, the instrument is intended to acquire 2D spatially or 1D spectrally time resolved images of target features. Some specific examples are: spectral emission from targets 2 , spatially resolved foil trajectories 3 , hydrodynamic instability growth information 4 , shock front propagation 5 and x-ray time history for ignition physics 6 . The GXD specifications include spectral sensitivities from 200 nm to 17.5 keV, photocathode active area of 30 mm square, four 10 ohm 7.5 mm striplines, temporal window adjustable from 70 ps to 1500 ps, independent gain for each stripline, spatial resolution of 50 µm, independent strip delays up to 44 ns and pulsed phosphor.…”