Abstract
1 Introduction
Due to Rayleigh–Taylor instability during inertial confinement fusion (ICF) experiment, the imperfection of capsule surface degrades the final symmetry of the implosion and creates mix at the pusher–fuel interface, potentially quench the ignition[
In the 1990s, Lawrence Livermore National Laboratory (LLNL) and General Atomics (GA) developed an atomic force microscope (AFM)-based spheremapper, for mapping the outer surface profiles of ICF capsule[
With the progress in capsule fabrication techniques and the increasing requirements for capsule precise characterization in ICF experiments, several surface analysis methods have been developed since 1999[
Sign up for High Power Laser Science and Engineering TOC. Get the latest issue of High Power Laser Science and Engineering delivered right to you!Sign up now
2 Profilometer
The AFM is an effective tool for characterizing the topography of ICF capsules, due to its nanometer resolution and tiny acting force. However, the limited scanning range restricts its application for capsule surface profile measurement. A motion system with nanometer precision is indispensable to cooperate with AFM.
The capsule profilometer setup is shown in Figure
The small-sized air bearing is composed of aerostatic bearing, torque motor, and circular grating for high precise rotation. The radial rotation error is less than 30 nm. The typical rotational speed is 1–10 rpm. Uniform positioning for more than 36,000 positions of the circumference is realized, with an angular accuracy of less than
Figure
2.1 Fast alignment to rotation axis
Before the profile measurement, the capsule center has to be aligned to the rotation axis of the air bearing. In this way, the surface fluctuations of rotated capsule will not exceed the AFM measuring range due to capsule off centeredness. The limited measuring range of AFM and the small diameter of ICF capsule make the aligning process a time-consuming and difficult task, which influences the efficiency of capsule measurement.
To solve this problem, an alignment method of capsule rotation center based on CCD image is proposed, which makes the alignment simple and fast. The aligning process is shown in Figure
After the aligning step, the eccentricity of the capsule center is restricted to less than
2.2 Automatic recording of surface traces
In order to improve the profiling efficiency, automatic measurement of surface traces is essential. In 3D reconstruction, we use several orbits to cover the entire capsule, and each orbit contains large amount of parallel traces. Automatic measurement of traces enlarges the covering area in single orbit, thus shortens the time for complete coverage measurement and ensures the reconstruction accuracy.
An algorithm is developed to center the AFM tip on the capsule’s equator before measurement, by operating the motorized
With the developed algorithm, the surface traces in one orbit are measured automatically so long as the separation and the number of traces are set. A set of 150 measured traces with
2.3 Precise capsule reorientation
The standard procedure to acquire surface power spectrum of one capsule is to calculate the fluctuation power from the average of the Fourier transform of nine surface profiles[
The reorientation accuracy is the key to ensure the complete surface mapping and 3D surface reconstruction. There is always a slight bobble in picking up and replacing the capsule, which influences the reconstruction accuracy. Therefore, the reorientation accuracy needs exact determination.
The suction force of the vacuum chuck is set appropriate to avoid capsule deformation and ensure the flexible operation in capsule repositioning. Based on calculations and experimental results, we designed and built a vacuum chuck with tiny suction force, which is through the shaft center. The capsule deformation caused by vacuum chuck is estimated to be one order of magnitude lower than capsule sphericity error.
The two orthogonal shafting are repeatedly adjusted according to the feature points on capsule surface, which finally guarantees the precise reorientation of the capsule. Two micropores are imposed on capsule surface by femtosecond laser ablation. As shown in Figure
2.4 Noise power spectrum
Noise power spectra are shown in Figure
3 Surface topography characterization
Based on the developed profilometer and measured surface traces of the capsule, surface geometry parameters including 1D mode-power spectrum, surface roughness, and roundness can be calculated. With the complete mapping data, the entire capsule surface can be reconstructed and 2D power spectrum is plotted. Therefore the characterization of the entire surface is realized and the capsule surface quality can be evaluated.
3.1 Complete surface measurement and 3D reconstruction
Complete surface measurement is based on precise capsule reorientation and automatic recording of surface traces. After the recording of circumference traces in one orbit, the capsule is orientated several times with equal interval angle by the operation of two orthogonal shafting, to cover the entire surface. As shown in Figure
The complete mapping data needs preprocessing before surface reconstruction. Profilometer only measures the deviation from a circle, not the radius itself. As a result, mode 0 (the average radius) and mode 1 (circle center) must be first retrieved for each trace to minimize the radius discrepancy and trace intersections[
After data preprocessing, all orbit data is combined and aligned according to initial measured positions, and the spherical surface map
After the spherical harmonic expansion, the entire capsule surface is reconstructed with different orders, as shown in Figure
3.2 Surface characterization with mode-power spectrum
The surface traces measured by profilometer reflect the characteristic of capsule surface. Different modes (frequencies) of capsule surface fluctuations have diverse effects on the hydrodynamic instability in implosion. To exactly evaluate the influence, the amplitude of fluctuations at each concerned mode must be acquired. Therefore, the mode-spectrum curve which gives the relationship between surface fluctuation mode and its amplitude becomes a significant parameter to estimate the capsule performance in ICF experiment.
The circumferential trace data by profile measurement is a one-dimensional discrete time sequence. The harmonic component at each mode can be obtained by Fourier transform. The 1D mode-power spectrum is plotted with the mode as horizontal coordinate and the square of the amplitude for each harmonic component as the longitudinal coordinate[
The measured profile traces of capsule surface and the calculated mode-power spectrum curves are shown in Figure
Compared with 1D power spectrum, 2D power spectrum is more effective for characterization of the entire capsule surface. Based on the spherical harmonic analysis of complete mapping data, the 2D power spectrum is calculated for entire surface evaluation.
For a 2 mm diameter GDP capsule, the spherical surface map
As shown in Figure
3.3 Application
The successful establishment of capsule surface profilometer greatly promotes the fabrication of ICF capsules. On the other hand, the precise characterization of capsule surface ensures capsule quality for ICF experiments, and provides complete capsule morphology parameters for numerical simulation research. As shown in Figure
The initial morphology of the capsule is the vital factor that affecting the implosion performance. The capsule power spectra obtained by profilometer provide significant import data for quantitative interpretation of various non-one-dimensional factors on implosion performance, and comparison between the experimental results and numerical simulations.
4 Conclusion
Based on AFM and high-precision rotary air bearing, a capsule profilometer is developed with nanometer resolution for surface profile measurement of ICF capsule. To evaluate the capsule quality, 1D and 2D power spectra are calculated with the measured surface traces with measurement uncertainty of 1.7 nm and capsule reorientation error of less than
References
[1] R. B. Stephens, S. W. Hann, D. C. Wilson.
[2] S. W. Haan, P. A. Amendt, T. R. Dittrich. Fusion Sci. Technol., 45, 69(2004).
[3] R. C. Cook, R. L. McEachern, R. B. Stephens. Fusion Sci. Technol., 35, 224(1999).
[4] S. W. Haan, J. D. Salmonson, D. S. Clark. Fusion Sci. Technol., 59, 1(2011).
[5] N. A. Antipa, S. H. Baxamusa, E. S. Buice. Fusion Sci. Technol., 63, 151(2013).
[6] K. A. Moreno, S. Eddinger, J. Fong. Fusion Sci. Technol., 55, 349(2009).
[7] B. Li, Z. Zhang, Z. He. High Power Laser Part. Beams, 27(2015).
[8] X.-S. Zhao, T. Sun, Y.-D. Yan. Key Eng. Mater., 315–316, 796(2006).
[9] X.-S. Zhao, T. Sun, X.-J. Ma. At. Energy Sci. Technol., 42, 833(2008).
[10] X.-S. Zhao, D.-Z. Gao, X.-J. Ma. At. Energy Sci. Technol., 46, 1014(2012).
[11] R. B. Stephens, D. Olson, H. Huang. Fusion Sci. Technol., 45, 210(2004).
[12] H. Huang, R. B. Stephens, J. B. Gibson. Fusion Sci. Technol., 49, 642(2006).
[13] D. Garcia. Comput. Stat. Data Anal., 54, 1167(2010).
[14] H. Groemer. Geometric Applications of Fourier Series and Spherical Harmonics(1996).
Set citation alerts for the article
Please enter your email address