Internal absorption cross sections in a stratified sphere

D. W. Mackowski; R. A. Altenkirch; M. P. Menguc

doi:10.1364/AO.29.001551

Applied Optics
Vol. 29,
Issue 10,
pp. 1551-1559
(1990)
•https://doi.org/10.1364/AO.29.001551

Internal absorption cross sections in a stratified sphere

D. W. Mackowski, R. A. Altenkirch, and M. P. Menguc

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D. W. Mackowski, R. A. Altenkirch, and M. P. Menguc, "Internal absorption cross sections in a stratified sphere," Appl. Opt. 29, 1551-1559 (1990)

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Abstract

Series expressions for the radially dependent absorption cross section and angle-averaged absorption heat source function within a stratified sphere are presented. A numerically stable and accurate algorithm for computation of the internal radiative properties, as well as the overall scattering and extinction of a stratified sphere having an arbitrary number of layers is developed. The results allow for direct estimation of the degree of penetration and intensity of radiative heating in radially inhomogeneous spherical particles, and also provide an estimate of the thermal emission coefficient of particles having a radial temperature distribution.

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			This Study		Reference 12

a₁/a₃	a₂/a₃	x₃	Q_abs,1	Q_abs,3	Q_abs,1	Q_abs,3
0.792	0.794	29.93	1.642	2.748 × 10⁻⁵	1.658	2.676 × 10⁻⁵
0.784	0.804	30.23	1.493	3.688 × 10⁻⁵	1.538	3.623 × 10⁻⁵
0.766	0.824	30.94	1.114	3.415 × 10⁻⁵	1.125	3.688 × 10⁻⁵
0.749	0.843	31.65	1.019	6.606 × 10⁻⁵	1.025	6.533 × 10⁻⁵
0.704	0.880	33.67	0.9673	4.628 × 10⁻⁵	0.9675	4.528 × 10⁻⁵
0.622	0.933	38.11	1.021	7.394 × 10⁻⁵	1.021	7.566 × 10⁻⁵
0.551	0.964	43.03	0.9618	1.385 × 10⁻⁵	0.9613	1.455 × 10⁻⁵
0.493	0.985	48.13	0.9864	7.280 × 10⁻⁶	0.9853	7.251 × 10⁻⁶

	Q_ext	Q_sca	Q_abs	Q_back
Case 1: f_v(r) = const. = ${\bar{f}}_{v}$	2.090	1.117	0.9731	0.0301
Case 2: core absorption	2.207	1.873	0.3340	2.625
Case 3: shell absorption	2.099	1.294	0.8058	0.1995
Case 4: f_v(r) = 4/3r/a_L ${\bar{f}}_{v}$	2.089	1.122	0.9672	0.0340
Case 5: f_v(r) = 1/4(1 − r/a_L) ${\bar{f}}_{v}$	2.100	1.287	0.8121	0.1725

			This Study		Reference 12

a₁/a₃	a₂/a₃	x₃	Q_abs,1	Q_abs,3	Q_abs,1	Q_abs,3
0.792	0.794	29.93	1.642	2.748 × 10⁻⁵	1.658	2.676 × 10⁻⁵
0.784	0.804	30.23	1.493	3.688 × 10⁻⁵	1.538	3.623 × 10⁻⁵
0.766	0.824	30.94	1.114	3.415 × 10⁻⁵	1.125	3.688 × 10⁻⁵
0.749	0.843	31.65	1.019	6.606 × 10⁻⁵	1.025	6.533 × 10⁻⁵
0.704	0.880	33.67	0.9673	4.628 × 10⁻⁵	0.9675	4.528 × 10⁻⁵
0.622	0.933	38.11	1.021	7.394 × 10⁻⁵	1.021	7.566 × 10⁻⁵
0.551	0.964	43.03	0.9618	1.385 × 10⁻⁵	0.9613	1.455 × 10⁻⁵
0.493	0.985	48.13	0.9864	7.280 × 10⁻⁶	0.9853	7.251 × 10⁻⁶

	Q_ext	Q_sca	Q_abs	Q_back
Case 1: f_v(r) = const. = ${\bar{f}}_{v}$	2.090	1.117	0.9731	0.0301
Case 2: core absorption	2.207	1.873	0.3340	2.625
Case 3: shell absorption	2.099	1.294	0.8058	0.1995
Case 4: f_v(r) = 4/3r/a_L ${\bar{f}}_{v}$	2.089	1.122	0.9672	0.0340
Case 5: f_v(r) = 1/4(1 − r/a_L) ${\bar{f}}_{v}$	2.100	1.287	0.8121	0.1725

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Applied Optics