Instability analysis of pointing accuracy and power imbalance of spherical hohlraum

Abstract

An analytic model to describe the statistic behavior of flux asymmetry on the capsule shell under the influence of random fluctuation of laser spots' position and laser energy is developed. Based on our previous work [Duan et al., Phys. Plasmas 22, 092704 (2015)] and a diagram technique, the expectation, variance, and probability density function of flux asymmetry raised by laser pointing accuracy and laser power imbalance of 4, 6, and 8 laser entrance holes (LEHs) spherical hohlraums are shown. For spherical hohlraums with different numbers of LEHs, it is found that the random part of flux asymmetry is proportional to the ratio between laser energy and square root of total spots' number ELaser/Nt, and angle-of-incidence θ0, which indicates that a choice of small θ0 and a great number of Nt can reduce the random flux asymmetry. In order to achieve a cumulative probability in which each l-order flux asymmetry can meet corresponding requirements [Gu et al., Phys. Plasmas 21, 012704 (2014)] beyond 90% in the condition of a 1000 μm capsule and 4000 μm hohlraum, the power imbalance, i.e., the ratio between standard derivation and expectation of laser spots power ΔF/Fspot for 4, 6, and 8 LEHs spherical hohlraums must not exceed 8.1%, 9.1%, and 8.5%, corresponding pointing accuracy rHΔθ must not exceed 79 μm, 102 μm, and 96 μm along the êθ direction, and rH sin 2θ0Δϕ must not exceed 77 μm, 99 μm, and 94 μm along the êϕ direction, respectively.