An investigation on the precision mounting process of large-aperture potassium dihydrogen phosphate converters based on the accurate prediction model
Introduction
Inertial confinement fusion (ICF) is a method that can achieve controllable nuclear fusion [1], therefore, it has been a major research focus in many countries [[2], [3], [4]]. In order to obtain short-wavelength lasers, the converters in ICF facilities play an important role by converting long-wavelength lasers into short-wavelength lasers. Potassium dihydrogen phosphate (KDP) crystal is an ideal material for use in converters because of its high laser damage threshold and second harmonic generation(SHG) efficiency [5,6]. Though KDP converters have a large aperture (over 330 mm), they have a small thickness (no more than 12 mm), which could result in weak stiffness and large distortion under an external force. Eventually, distortion of a few microns will induce great changes in the phase matching angle and lead to a decrease in the beam quality and SHG efficiency [[7], [8], [9]]. In order to improve the SHG efficiency of KDP converters, various facilities have put forward extremely strict requirements for surface distortion. In ICF facilities, the additional surface distortion of KDP converters after mounting is required to be no more than 5λ (3.2 μm), which is a great challenge during the mounting process.
In the beam path of inertial confinement fusion, all KDP converters are installed obliquely with a tilted angle of 15–60°, and the changes of the surface figure are the result of the combined action of the gravity and clamping forces. Because of the different positions and compact installation conditions in the final optics assembly, it is impossible to measure the surface distortion of online KDP converters prior to installation in the facility. Numerical simulation is the only way to effectively predict and analyze the distortion of KDP converters under various installation positions. Thus many researchers established the mechanical model to predict and calculate the variation in surface distortion. Barker et al. pointed out that the distortion of the crystal surface is mainly caused by gravity and the process of mounting the crystal, and the distortion under simply support on four corners was calculated [10]. Auerbach et al. analyzed the influence of gravity on the surface shape of KDP converters under different conditions. Results had proved the theoretical control effect of the configurations in National Ignition Facility (NIF) [11]. Lubin et al. established an optomechanical model of the KDP converters in Laser Megajoule (LMJ) to predict the influence of gravity on SHG efficiency [12]. Moreover, Li et al. studied effective support ways to reduce PV value of large scale optics, they designed a radial multisegmental support to decrease surface deformation of the large-aperture optics, and proposed a novel dynamic analysis method to access the surface deformations [13,14]. Zhang et al. proposed a theoretical structure applying the Lever Principle to control the distortion and they modeled the adaptive optics mounting method to study the influence of clamping force on the distortion of KDP converters [15,16].
Effective support ways can contribute to the good performance of a large-scale optical system. An adjustable three-segment surface-contact radial support way is proposed to facilitate the movement process of a large-scale rotating mirror. Under a most dangerous working condition, the supporting angle is optimized by a two-step optimization method, which makes the maximum PV value reduce by 10.26% relative to that before optimization and that the maximum von Mises stress has a very little increase. Moreover, the coupling analysis of thermal stress in the rotating mirror caused by some thermal factors, such as motor heat, is carried out to validate the assembly design. The supporting way, as an effective radial mounting for dynamic optical elements, can be valuable for the reference of similar opto-mechanical design.
In the process of modeling and analyzing KDP converters, the accuracy of the simulation model directly determines the analysis result [17]. To further improve the accuracy of numerical simulation, many researchers have proposed methods for optimizing modeling. Wang et al. [18] classified the distortion of KDP crystal as a small deformation problem of elastic thin plate, and emphasized on the orthotropic properties of the KDP crystal. They transformed the original material stiffness matrix by coordinate transformation, and obtained the stiffness matrix of KDP crystal in a global coordinate system. In addition, Su et al. [19] used a Gaussian distribution to generate key points to establish an analytical model of non-ideal surfaces, in order to analyze the effect of contact surface topography on the crystal's distortion, stress and conversion efficiency. Liu et al. [20] used the fractal theory to analyze and reconstruct contact surfaces and created a more accurate finite element analysis model.
Therefore, it is necessary to study in detail the mechanical modeling and distortion prediction methods of KDP converters. Considering the mounting process of in-service KDP converters in ICF facilities, we establish a prediction model for the mounting process of KDP converters. Furthermore, in order to optimize the model, accurate displacement and force boundary conditions are set in the model according to the configuration, which further reflects the real conditions during the mounting process. The stiffness coefficients of KDP crystal are measured by ultrasonic resonance spectrum analysis, which improves the accuracy of the model. We apply the finite element method to assist calculations and divide fine meshes in the computational model. Then we use the simulation results as a reference to clarify the influence of key factors in the mounting process on surface distortion. Additionally, we prepare a prototype configuration for the experiment, and perform an on-site mounting process and surface measurement experiment in an optical assembly building, verifying the effect of clamping force on the surface distortion of the KDP crystal. Based on the modified model and considering the effect of non-ideal surface contact on theoretical simulation, we effectively predict the deformation of KDP converters before and after mounting. At last, we aim to verify the prediction model by measurements in the vertical placement state, and then apply this model to predict the deformation of KDP converters in other installation attitudes. The simulation results of various installation attitudes will be applied for the improvement of the mounting process.
Section snippets
Optical setup
As shown in Fig. 1, the frequency conversion system consists of a type I KDP crystal and a type II dKDP crystal. The basic frequency laser is linearly polarized along the o-axis of the KDP crystal, and a frequency doubled effect occurs in a type I KDP crystal, through which the basic frequency laser is converted into a beam of second harmonic polarized along the o axis and a beam of basic frequency laser polarized along the e axis of dKDP crystal. The two beams interact in the dKDP crystal and
Theoretical model
KDP converters have a large aperture-to-thickness ratio, so plate theory can be applied for mechanical analysis. According to plate theory and the generalized form of Hooke's law, and considering the balance of forces, the differential equation for the bending of an anisotropic plate can be obtained.
KDP crystal belongs to the tetragonal system, so the stress-strain relationship can be obtained from the generalized form of Hooke's law. Assume that the stiffness matrix of KDP material is [D] = [D
Settings of numerical simulation
When analyzing the distortion of KDP converters under actual working conditions, it is very difficult to get an analytical solution because the boundary conditions and the forces are very complicated. Therefore, we need to assist calculations with numerical solution methods, and the finite element method(FEM) is an effective tool to solve this problem. According to the analysis object, we have established a finite element analysis model as shown in Fig. 5. First of all, we set the material
Key factors analysis
Employing the established prediction model, we can obtain the surface distortion (peak-valley value) of KDP converters under various conditions. Thus we use the simulation results as a reference to analyze the influence of main factors on surface distortion. Because the KDP converters applied in our experiments have a large aperture (330 mm) but a small thickness (12 mm), clamping forces are undoubtedly the root cause of surface distortion. In addition, by analyzing the mounting process, we
Conclusions
In this article, in order to effectively predict and analyze the surface distortion of KDP converters during mounting, based on plate theory and the generalized form of Hooke's law of anisotropic materials, we propose a prediction model for KDP converters and their mounting process applied in ICF facilities. Based on the prediction model, we analyze the influence of the three key factors on the surface distortion. The surface distortion and maximum stress increase when the clamping force
Acknowledgement
This research is supported by National Natural Science Foundation of China (Grant No.51575310) and Natural Science Foundation of Beijing (Grant No. 3162014). The authors also appreciate the contributions and efforts of the researchers and engineers in the Research Center of Laser Fusion, China Academy of Engineering Physics.
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