Detailed investigation of the iterative analysis for inertial confinement fusion target characterization

Tianliang Yan; Kai Wang; Zhongming Zang; An Lu; Xiaobo Hu; Nan Chen; Huxiang Zhang; Chong Liu; Dong Liu; Dong Liu

doi:10.1364/AO.409026

Applied Optics
Vol. 59,
Issue 34,
pp. 10880-10886
(2020)
•https://doi.org/10.1364/AO.409026

Detailed investigation of the iterative analysis for inertial confinement fusion target characterization

Tianliang Yan, Kai Wang, Zhongming Zang, An Lu, Xiaobo Hu, Nan Chen, Huxiang Zhang, Chong Liu, and Dong Liu

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Tianliang Yan, Kai Wang, Zhongming Zang, An Lu, Xiaobo Hu, Nan Chen, Huxiang Zhang, Chong Liu, and Dong Liu, "Detailed investigation of the iterative analysis for inertial confinement fusion target characterization," Appl. Opt. 59, 10880-10886 (2020)

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Abstract

The iterative algorithm based on optical path difference and ray deflection (IAORD) is investigated in detail, and an advanced version (AIAORD) is proposed to obtain the refractive indices of the shell and the ice layer of the inertial confinement fusion (ICF) target simultaneously. The concept of the fixed-point iteration is introduced in the advanced algorithm, and it is found that the right choice of the combination of the input values and the characteristic curves is the key to ensure convergence in the iteration. The test uncertainties of the index measurement are analyzed by simulations, and they show that the uncertainties of the refractive indices of the shell and ice layer are 9.94% and 1.20%, respectively. Characteristic curves of typical ICF targets are studied, from which we conclude that AIAORD is versatile and suitable for the applications with any two unknown target parameters to be solved.

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Unknowns To Be Solved	Independent Variable	Dependent Variable	Unary Function Equivalent to Eq. (1)	Unary Function Equivalent to Eq. (2)
$t_{2}$ , $n_{2}$	$t_{2}$	$n_{2}$	$f_{1}$	$f_{2}$
$t_{2}$ , $n_{2}$	$n_{2}$	$t_{2}$	$F_{1}$	$F_{2}$
$n_{2}$ , $n_{1}$	$n_{2}$	$n_{1}$	$g_{1}$	$g_{2}$
$n_{2}$ , $n_{1}$	$n_{1}$	$n_{2}$	$G_{1}$	$G_{2}$
$t_{1}$ , $n_{2}$	$t_{1}$	$n_{2}$	$h_{1}$	$h_{2}$
$t_{1}$ , $n_{2}$	$n_{2}$	$t_{1}$	$H_{1}$	$H_{2}$
$t_{2}$ , $t_{1}$	$t_{2}$	$t_{1}$	$u_{1}$	$u_{2}$
$t_{2}$ , $t_{1}$	$t_{1}$	$t_{2}$	$U_{1}$	$U_{2}$
$t_{2}$ , $n_{1}$	$t_{2}$	$n_{1}$	$v_{1}$	$v_{2}$
$t_{2}$ , $n_{1}$	$n_{1}$	$t_{2}$	$V_{1}$	$V_{2}$
$t_{1}$ , $n_{1}$	$t_{1}$	$n_{1}$	$w_{1}$	$w_{2}$
$t_{1}$ , $n_{1}$	$n_{1}$	$t_{1}$	$W_{1}$	$W_{2}$

	Outer Radius ( $µ m$ )	Thickness of Shell ( $µ m$ )	Thickness of Ice Layer ( $µ m$ )	Refractive Index of Shell (unit)	Refractive Index of Ice Layer (unit)
1	383	25	65	1.56	1.16
2	450	3	100	1.59	1.13
3	1000	50	150	1.50	1.14
4	2000	100	300	1.50	1.14

Uncertainty Sources	Uncertainties	Sensitivity Coefficient $c_{1}$	Effect to $n_{1}$	Sensitivity Coefficient $c_{2}$	Effect to $n_{2}$
Outer radius of the target, $R$	0.05%	14.49 (unit)	0.72%	2.30 (unit)	0.12%
Thicknesses of the shell, $t_{1}$	0.8%	1.41 (unit)	1.13%	0.14 (unit)	0.11%
Thicknesses of the ice layer, $t_{2}$	0.31%	2.72 (unit)	0.84%	0.37 (unit)	0.11%
Extraction of the first interference fringe, $r_{1}$	0.5%	3.31 (unit)	1.66%	0.07 (unit)	0.04%
Extraction of the second interference fringe, $r_{2}$	0.5%	6.88 (unit)	3.44%	0.14 (unit)	0.07%
Extract bright ring, $X_{2}$	0.1%	8.33 (unit)	0.83%	1.74 (unit)	0.17%
Position of the target	5 µm	0.22 (%/µm)	1.10%	0.06 (%/µm)	0.30%
Non-sphericity of the shell	0.14%	16.98 (unit)	2.38%	3.15 (unit)	0.44%
Total uncertainty	—	—	4.97%	—	0.60%

Unknowns To Be Solved	Independent Variable	Dependent Variable	Unary Function Equivalent to Eq. (1)	Unary Function Equivalent to Eq. (2)
$t_{2}$ , $n_{2}$	$t_{2}$	$n_{2}$	$f_{1}$	$f_{2}$
$t_{2}$ , $n_{2}$	$n_{2}$	$t_{2}$	$F_{1}$	$F_{2}$
$n_{2}$ , $n_{1}$	$n_{2}$	$n_{1}$	$g_{1}$	$g_{2}$
$n_{2}$ , $n_{1}$	$n_{1}$	$n_{2}$	$G_{1}$	$G_{2}$
$t_{1}$ , $n_{2}$	$t_{1}$	$n_{2}$	$h_{1}$	$h_{2}$
$t_{1}$ , $n_{2}$	$n_{2}$	$t_{1}$	$H_{1}$	$H_{2}$
$t_{2}$ , $t_{1}$	$t_{2}$	$t_{1}$	$u_{1}$	$u_{2}$
$t_{2}$ , $t_{1}$	$t_{1}$	$t_{2}$	$U_{1}$	$U_{2}$
$t_{2}$ , $n_{1}$	$t_{2}$	$n_{1}$	$v_{1}$	$v_{2}$
$t_{2}$ , $n_{1}$	$n_{1}$	$t_{2}$	$V_{1}$	$V_{2}$
$t_{1}$ , $n_{1}$	$t_{1}$	$n_{1}$	$w_{1}$	$w_{2}$
$t_{1}$ , $n_{1}$	$n_{1}$	$t_{1}$	$W_{1}$	$W_{2}$

	Outer Radius ( $µ m$ )	Thickness of Shell ( $µ m$ )	Thickness of Ice Layer ( $µ m$ )	Refractive Index of Shell (unit)	Refractive Index of Ice Layer (unit)
1	383	25	65	1.56	1.16
2	450	3	100	1.59	1.13
3	1000	50	150	1.50	1.14
4	2000	100	300	1.50	1.14

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Applied Optics