Illumination of a spherical fusion pellet displaced from the geometric foci of focused laser beams: vector-analysis method

The illumination of a spherical fusion pellet displaced from the foci of a refractive laser-fusion system is investigated based on the vector-analysis method. This method is more accurate than the phase-shift approximation for the spherical wave functions in the displaced frame and reduces the computation time and capacity more greatly than does the method of translational addition theorems for spherical wave functions. Two transformation matrices are derived through analyzing the EM-field vector in three different frames of coordinates. The two matrices are used to calculate the efficiency, kurtosis, and skewness of illumination distribution at the pellet surface. The numerical results of the illumination efficiency are in a good agreement with the results of othe workers. In addition, the pellet displacement corresponding to maximal illumination flatness near the focus is determined quantitatively. The illumination asymmetry that is due to the perpendicular pellet displacement is aggravated by using larger lens aperture or short light wavelength and/or by displacing the pellet on the positive axial side of the focus