Compressive Sensing For The Symmetry Distribution Analysis In Inertial Confinement Fusion Simulation

One of the key factors with the successful achievement of Inertial ConfinementFusion(ICF) is the achievement of high energy symmetry on the surface of the sphericaltarget containing the fuel. Numerical methods have been developed to calculate the energydistribution inside the hohlraum. The energy-balance model divides the interior wall of thehahlraum into spot area and non-spot area, and assume the energy of each area is uniform.According to the energy balance inside the hohlraum, the energy of both areas iscalculated, so we can calculate the energy received by any area on the surface of the targetwith view factor method.The analytic view factor method is useful for hohlraums of certain shape, but notapplicable to arbitrarily shaped ones. The discrete view factor method solves this problem,it divides the interior wall of the hohlraum and the surface of the target into small gridsand calculate the energy radiation between them. But the major problem of this approachis the large amount of calculation. Finding an optical approach which reduces thecalculation significantly but does not cause much error is the main motivation of thisthesis.A new method called compressive sensing was raised in2006which points out thatwe can recovery a signal from only a few random samples only if the signal is sparse. Inthis thesis, we point out the sparsity of the spherical harmonic(SH) coefficients of theenergy distribution on the target surface, and design a random sample approach. Aweighting matrix is introduced to form a sampling matrix that satisfies the restrictedisometry property(RIP),which is a key property for exact recovery. Using the CS approach,only a few grids on the target need to be sampled randomly and uniformly, and theoriginal signal can be recovered and the drive symmetry of the target can be calculatedexactly.The new approach is used to calculate the energy symmetry of the target for severaltypical radiation situations inside the hohlraums, and the accuracy, efficiency and stabilityof the new approach are discussed.This CS based new approach is used in an ICF simulation software named Rad-3D.In the end of this thesis, the frame and working process of the software are introduced anda typical example of optimization for the ICF device is given out.