Bragg reflection concentrators for hard x-ray astronomy

Herbert W. Schnopper

doi:10.1364/AO.20.001089

Applied Optics
Vol. 20,
Issue 6,
pp. 1089-1093
(1981)
•https://doi.org/10.1364/AO.20.001089

Bragg reflection concentrators for hard x-ray astronomy

Herbert W. Schnopper

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Herbert W. Schnopper, "Bragg reflection concentrators for hard x-ray astronomy," Appl. Opt. 20, 1089-1093 (1981)

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Abstract

The use of parabolic concentrators with mosaic Bragg crystals as reflectors to the problems of hard x-ray source and cyclotron line detection is discussed. The primary application of the instrument is to detect the broad continuum of hard x-ray sources at energies above ~5 keV where normal grazing incidence concentrators become inefficient. The sensitivity of the instrument is calculated for pyrolytic graphite and lithium fluoride reflectors. Sensitivity for sources with continuum fluxes 10⁻³ Crab in the >20-keV energy range is possible for observing times of 10⁴ to 10⁵ sec.

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								n_C,m cm⁻² s⁻¹
θ₁ deg	θ₂ deg	E₁ keV	E₂ keV	ΔE_1,2 keV	n_b s⁻¹	A_eff cm⁻²		10³s	10⁴s	10⁵s	n_crab cm⁻²s⁻¹
Graphite (002): R_c ≃ 4 × 10⁻³, 2d = 6.708Å, r₁ ≃ 100 cm, Δθ_c ≃ 0.°5, n_re ≃ 2
2	2	52.9	35.3	17.6	2.8×10⁻²	36		5.8×10⁻⁴	1.5×10⁻⁴	4.5×10⁻⁵	8.5×10⁻²
3	4	35.3	26.5	8.8	1.4×10⁻²	66		2.5×10⁻⁴	6.1×10⁻⁵	1.8×10⁻⁵	″
4	5	26.5	21.2	5.3	8.5×10⁻³	99		1.5×10⁻⁴	3.3×10⁻⁵	9.3×10⁻⁶	″
5	6	21.2	17.7	3.5	5.6×10⁻³	132		9.8×10⁻⁵	2.1×10⁻⁵	5.7×10⁻⁶	″
LiF(200): R_c ≃ 2.3 × 10⁻⁴, 2d = 4.027Å, r₁ = 100 cm, Δθ_c = 0.°05, n_re =20
4	5	44.1	35.3	8.8	1.4×10⁻²		57	2.9×10⁻⁴	7.1×10⁻⁵	2.0×10⁻⁵	5.1×10⁻²
5	6	35.3	29.4	5.9	9.4×10⁻³		76	1.8×10⁻⁴	4.4×10⁻⁵	1.3×10⁻⁵	″
6	7	29.4	25.2	4.2	6.7×10⁻³		95	1.4×10⁻⁴	3.1×10⁻⁵	8.7×10⁻⁶	″
7	8	25.2	22.1	3.1	5.0×10⁻³		115	1.1×10⁻⁴	2.2×10⁻⁵	6.2×10⁻⁶	″
LiF(220): R_c = 1 × 10⁻⁴, 2d = 2.898Å, r₁ = 100 cm, Δθ_c ≃ 0.°05, n_re ≃ 20
4	5	61.9	49.6	12.4	2.0×10⁻²		25	7.5×10⁻⁴	1.9×10⁻⁵	5.6×10⁻³	3.6×10⁻²
5	6	49.6	41.3	8.2	1.3×10⁻²		33	4.9×10⁻⁴	1.2×10⁻⁵	3.4×10⁻⁵	″
6	7	41.3	35.4	5.9	9.4×10⁻³		41	3.6×10⁻⁴	8.2×10⁻⁵	2.3×10⁻⁵	″
7	a	35.4	31.0	4.4	7.1×10⁻³		50	2.7×10⁻⁴	6.0×10⁻⁵	1.7×10⁻⁵	″
S	9	31.0	27.6	3.4	5.5×10⁻³		59	2.2×10⁻⁴	4.7×10⁻⁵	1.3×10⁻⁵	″
9	10	27.6	24.9	2.7	4.4×10⁻³		67	1.8×10⁻⁴	3.7×10⁻⁵	1.0×10⁻³	″
10	11	24.9	22.6	2.2	3.6×10⁻³		76	1.5×10⁻⁴	3.0×10⁻⁵	8.1×10⁻⁶	″
11	12	22.6	20.8	1.9	3.0×10⁻³		85	1.4×10⁻⁴	2.6×10⁻⁵	6.7×10⁻⁶	″

						n_C,m cm⁻² s⁻¹
s deg	E keV	ΔE_c keV	ΔE_d keV	n_b cm⁻² s¹	A_eff cm²	10³s	10⁴s	10⁵s	n_crab cm⁻²s⁻¹
Graphite (002): R_c ≃ 4 × 10⁻³, 2d = 6.7 08A, r₁ = 100 cm, Δθ_c = 0.°05, n_re = 2
2.5	42.3	a.5	0.33	5.3×10⁻⁴	18	5.3×10⁻⁴	7.1×10⁻⁵	1.5×10⁻⁵	1.7×10⁻³
3.5	30.3	4.3	0.29	4.7×10⁻⁴	33	2.9×10⁻⁴	3.8×10⁻⁵	7.7×10⁻⁶	2.9×10⁻³
4.5	23.5	2.6	0.27	4.3×10⁻⁴	49	1.9×10⁻⁴	2.5×10⁻⁵	5.1×10⁻⁶	4.4×10⁻³
5.5	19.3	1.8	0.25	4.0×10⁻⁴	66	1.4×10⁻⁴	1.8×10⁻⁵	3.7×10⁻⁶	6.1×10⁻³
LiF(200): R_c ≃ 2.3 × 10⁻⁴, 2d = 4.027Å, r₁ = 100 cm, Δθ_c = 0.°05, n_re ≃ 20
4.5	39.2	0.44	0.32	5.2×10⁻⁴	2.8	3.4×10⁻³	4.5×10⁻⁴	9.5×10⁻⁵	1.9×10⁻³
5.5	32.1	0.29	0.30	4.8×10⁻⁴	3.9	2.4×10⁻³	3.2×10⁻⁴	6.6×10⁻⁵	2.6×10⁻³
6.5	27.2	0.21	0.28	4.5×10⁻⁴	6.5	1.4×10⁻³	1.9×10⁻⁴	3.9×10⁻⁵	3.4×10⁻³
7.5	23.6	0.16	0.27	4.3×10⁻⁴	10.0	9.4×10⁻³	1.2×10⁻⁴	2.5×10⁻³	4.4×10⁻³
LiF(220): R_c = 1 × 10⁻⁴, 2d = 2.848Å, r₁ = 100 cm, Δθ_c = 0.°05, n_re ≃ 20
4.5	55.5	0.62	0.37	5.9×10⁻⁴	1.2	8.0×10⁻³	1.1×10⁻³	2.3×10⁻⁴	1.1×10⁻³
5.5	45.4	0.41	0.34	5.4×10⁻⁴	1.7	5.6×10⁻³	7.5×10⁻⁴	1.6×10⁻⁴	1.5×10⁻³
6.5	38.4	0.29	0.32	5.1×10⁻⁴	2.3	4.2×10⁻³	5.5×10⁻⁴	1.2×10⁻⁴	2.0×10⁻³
7.5	33.3	0.22	0.30	4.9×10⁻⁴	3.5	2.7×10⁻³	3.6×10⁻⁴	7.5×10⁻⁵	2.5×10⁻³
8.5	29.4	0.17	0.29	4.7×10⁻⁴	4.9	1.9×10⁻³	2.5×10⁻⁴	5.3×10⁻⁵	3.0×10⁻³
9.5	26.4	0.14	0.28	4.5×10⁻⁴	7.0	1.5×10⁻³	1.8×10⁻⁴	3.6×10⁻⁵	3.6×10⁻³
10.5	23.9	0.11	0.27	4.3×10⁻⁴	9.2	1.0×10⁻³	1.3×10⁻⁴	2.7×10⁻⁵	4.3×10⁻³
11.5	21.8	0.09	0.26	4.2×10⁻⁴	11.8	8.0×10⁻⁴	1.0×10⁻⁴	2.1×10⁻⁵	5.0×10⁻³

								n_C,m cm⁻² s⁻¹
θ₁ deg	θ₂ deg	E₁ keV	E₂ keV	ΔE_1,2 keV	n_b s⁻¹	A_eff cm⁻²		10³s	10⁴s	10⁵s	n_crab cm⁻²s⁻¹
Graphite (002): R_c ≃ 4 × 10⁻³, 2d = 6.708Å, r₁ ≃ 100 cm, Δθ_c ≃ 0.°5, n_re ≃ 2
2	2	52.9	35.3	17.6	2.8×10⁻²	36		5.8×10⁻⁴	1.5×10⁻⁴	4.5×10⁻⁵	8.5×10⁻²
3	4	35.3	26.5	8.8	1.4×10⁻²	66		2.5×10⁻⁴	6.1×10⁻⁵	1.8×10⁻⁵	″
4	5	26.5	21.2	5.3	8.5×10⁻³	99		1.5×10⁻⁴	3.3×10⁻⁵	9.3×10⁻⁶	″
5	6	21.2	17.7	3.5	5.6×10⁻³	132		9.8×10⁻⁵	2.1×10⁻⁵	5.7×10⁻⁶	″
LiF(200): R_c ≃ 2.3 × 10⁻⁴, 2d = 4.027Å, r₁ = 100 cm, Δθ_c = 0.°05, n_re =20
4	5	44.1	35.3	8.8	1.4×10⁻²		57	2.9×10⁻⁴	7.1×10⁻⁵	2.0×10⁻⁵	5.1×10⁻²
5	6	35.3	29.4	5.9	9.4×10⁻³		76	1.8×10⁻⁴	4.4×10⁻⁵	1.3×10⁻⁵	″
6	7	29.4	25.2	4.2	6.7×10⁻³		95	1.4×10⁻⁴	3.1×10⁻⁵	8.7×10⁻⁶	″
7	8	25.2	22.1	3.1	5.0×10⁻³		115	1.1×10⁻⁴	2.2×10⁻⁵	6.2×10⁻⁶	″
LiF(220): R_c = 1 × 10⁻⁴, 2d = 2.898Å, r₁ = 100 cm, Δθ_c ≃ 0.°05, n_re ≃ 20
4	5	61.9	49.6	12.4	2.0×10⁻²		25	7.5×10⁻⁴	1.9×10⁻⁵	5.6×10⁻³	3.6×10⁻²
5	6	49.6	41.3	8.2	1.3×10⁻²		33	4.9×10⁻⁴	1.2×10⁻⁵	3.4×10⁻⁵	″
6	7	41.3	35.4	5.9	9.4×10⁻³		41	3.6×10⁻⁴	8.2×10⁻⁵	2.3×10⁻⁵	″
7	a	35.4	31.0	4.4	7.1×10⁻³		50	2.7×10⁻⁴	6.0×10⁻⁵	1.7×10⁻⁵	″
S	9	31.0	27.6	3.4	5.5×10⁻³		59	2.2×10⁻⁴	4.7×10⁻⁵	1.3×10⁻⁵	″
9	10	27.6	24.9	2.7	4.4×10⁻³		67	1.8×10⁻⁴	3.7×10⁻⁵	1.0×10⁻³	″
10	11	24.9	22.6	2.2	3.6×10⁻³		76	1.5×10⁻⁴	3.0×10⁻⁵	8.1×10⁻⁶	″
11	12	22.6	20.8	1.9	3.0×10⁻³		85	1.4×10⁻⁴	2.6×10⁻⁵	6.7×10⁻⁶	″

						n_C,m cm⁻² s⁻¹
s deg	E keV	ΔE_c keV	ΔE_d keV	n_b cm⁻² s¹	A_eff cm²	10³s	10⁴s	10⁵s	n_crab cm⁻²s⁻¹
Graphite (002): R_c ≃ 4 × 10⁻³, 2d = 6.7 08A, r₁ = 100 cm, Δθ_c = 0.°05, n_re = 2
2.5	42.3	a.5	0.33	5.3×10⁻⁴	18	5.3×10⁻⁴	7.1×10⁻⁵	1.5×10⁻⁵	1.7×10⁻³
3.5	30.3	4.3	0.29	4.7×10⁻⁴	33	2.9×10⁻⁴	3.8×10⁻⁵	7.7×10⁻⁶	2.9×10⁻³
4.5	23.5	2.6	0.27	4.3×10⁻⁴	49	1.9×10⁻⁴	2.5×10⁻⁵	5.1×10⁻⁶	4.4×10⁻³
5.5	19.3	1.8	0.25	4.0×10⁻⁴	66	1.4×10⁻⁴	1.8×10⁻⁵	3.7×10⁻⁶	6.1×10⁻³
LiF(200): R_c ≃ 2.3 × 10⁻⁴, 2d = 4.027Å, r₁ = 100 cm, Δθ_c = 0.°05, n_re ≃ 20
4.5	39.2	0.44	0.32	5.2×10⁻⁴	2.8	3.4×10⁻³	4.5×10⁻⁴	9.5×10⁻⁵	1.9×10⁻³
5.5	32.1	0.29	0.30	4.8×10⁻⁴	3.9	2.4×10⁻³	3.2×10⁻⁴	6.6×10⁻⁵	2.6×10⁻³
6.5	27.2	0.21	0.28	4.5×10⁻⁴	6.5	1.4×10⁻³	1.9×10⁻⁴	3.9×10⁻⁵	3.4×10⁻³
7.5	23.6	0.16	0.27	4.3×10⁻⁴	10.0	9.4×10⁻³	1.2×10⁻⁴	2.5×10⁻³	4.4×10⁻³
LiF(220): R_c = 1 × 10⁻⁴, 2d = 2.848Å, r₁ = 100 cm, Δθ_c = 0.°05, n_re ≃ 20
4.5	55.5	0.62	0.37	5.9×10⁻⁴	1.2	8.0×10⁻³	1.1×10⁻³	2.3×10⁻⁴	1.1×10⁻³
5.5	45.4	0.41	0.34	5.4×10⁻⁴	1.7	5.6×10⁻³	7.5×10⁻⁴	1.6×10⁻⁴	1.5×10⁻³
6.5	38.4	0.29	0.32	5.1×10⁻⁴	2.3	4.2×10⁻³	5.5×10⁻⁴	1.2×10⁻⁴	2.0×10⁻³
7.5	33.3	0.22	0.30	4.9×10⁻⁴	3.5	2.7×10⁻³	3.6×10⁻⁴	7.5×10⁻⁵	2.5×10⁻³
8.5	29.4	0.17	0.29	4.7×10⁻⁴	4.9	1.9×10⁻³	2.5×10⁻⁴	5.3×10⁻⁵	3.0×10⁻³
9.5	26.4	0.14	0.28	4.5×10⁻⁴	7.0	1.5×10⁻³	1.8×10⁻⁴	3.6×10⁻⁵	3.6×10⁻³
10.5	23.9	0.11	0.27	4.3×10⁻⁴	9.2	1.0×10⁻³	1.3×10⁻⁴	2.7×10⁻⁵	4.3×10⁻³
11.5	21.8	0.09	0.26	4.2×10⁻⁴	11.8	8.0×10⁻⁴	1.0×10⁻⁴	2.1×10⁻⁵	5.0×10⁻³

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Equations (19)

Applied Optics