An efficient radiation analysis approach through compressive model for laser driven inertial confinement fusion

Abstract

Radiation symmetry evaluation is critical to the laser driven Inertial Confinement Fusion (ICF), which is usually obtained through a view-factor equation model. The model is nonlinear, and its equation number can be very large when the size of discrete mesh element is very small to achieve a prescribed accuracy, which may lead to an intensive equation solving process. In this paper, an efficient radiation symmetry analysis approach is presented through equation model compression, in which, (1) the radiation symmetry analysis is carried out for two kinds of geometric shapes: cylindrical capsule and spherical capsule. For the structure of cylindrical capsule, the Legendre–Fourier basis and Zernike basis are applied to represent the radiation flux of the capsule. And for the structure of spherical capsule, the spherical harmonics is employed to sparsely represent the radiation flux on the capsule and spherical cavity. Then the nonlinear energy equilibrium equations are transformed into the equations with sparse coefficients, which means there are many redundant equations, (2) Only a few equations are uniformly selected to recover such sparse coefficients with a Latin hypercube sampling scheme, (3) A Modified Conjugate Gradient-Iteration Hard Thresholding (MCG-IHT) algorithm is then given to rapidly solve such sparse coefficients equations with as few as possible iterations. Finally, the presented approach is validated with two experiment targets for Shenguang III-YX and Shenguang II laser facilities in China. The equation model is reduced much more, only a few of equations are required to achieve the radiation flux with comparable accuracy within much less of computation time. And the solution is much more efficient as the size of discrete mesh element decreases, in which, almost 1.1% computation time is required to obtain the comparable result.