The Evaporation Rate of Filament Material from Alternating Current Heated Filaments

A. D. Wilson

doi:10.1364/AO.2.001055

Applied Optics
Vol. 2,
Issue 10,
pp. 1055-1059
(1963)
•https://doi.org/10.1364/AO.2.001055

The Evaporation Rate of Filament Material from Alternating Current Heated Filaments

A. D. Wilson

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A. D. Wilson, "The Evaporation Rate of Filament Material from Alternating Current Heated Filaments," Appl. Opt. 2, 1055-1059 (1963)

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Abstract

The operation of an incandescent filament on alternating current of the form, i = i₀ sinωt, is reviewed. A model for the ac evaporation rate, in a vacuum of a uniformly heated straight wire, is presented in terms of: (1) The known temperature fluctuations, and (2) The evaporation rate evaluated at the do and the ac mean filament temperatures. It is shown that the ac evaporation rate can be significantly greater than the dc evaporation rate. A method of evaluating the ac evaporation rate in terms of the spectral modulation is developed.

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T_m(°K)	B_m	$Error \approx B_{m} {(\frac{Δ T_{0}}{T_{m}})}^{2} (Percent)$
2000	48.3	48.3
2400	40.2	40.2
2800	34.4	34.4
3200	30.1	30.1

T_m₁ (°K)	$\begin{array}{l} B \approx \frac{ν}{T_{m 1}} \\ = \frac{q_{0}}{K T_{m 1}} \end{array}$	∊	H¹ × 10⁷ (ergs/cm³⁻°K	R(T_m₁) (g cm⁻² sec⁻¹)	$Δ T_{0} (\frac{f}{P / A}) (^{\circ} K - cm - cps)$	$α (\frac{f}{P / A}) \times 10^{2} (cm - cps)$	ψ(P/A) × 10² (cm rad/sec)	$\frac{f_{min}}{(P / A) \times 10^{3} (cm - cps)}$
2000	48.3	0.259	2.66	7.48 × 10⁻¹⁴	0.552	1.33	1.40	3.51
2400	40.2	0.294	2.87	2.32 × 10⁻¹⁰	1.22	2.02	2.54	6.37
2800	34.4	0.321	3.07	7.20 × 10⁻⁸	2.28	2.80	4.12	10.32
3000	32.2	0.334	3.18	7.14 × 10⁻⁷	3.02	3.23	5.07	12.75
3200	30.1	0.341	3.22	5.33 × 10⁻⁶	3.95	3.72	6.23	15.65
3400	28.4	0.348	3.38	3.14 × 10⁻⁵	4.88	4.06	7.25	18.20

	ΔT₀ (°K)			α			I₀(α)

T_m₁ (°K)	f_min	2f_min	3f_min	f_min	2f_min	3f_min	f_min	2f_min	3f_min
2000	157	78.5	51	3.80	1.90	1.27	9.53	2.13	1.45
2400	191	95.5	63.5	3.17	1.59	1.06	5.56	1.72	1.29
2800	221	110	73.6	2.71	1.36	0.91	3.84	1.52	1.22
3000	237	118	79	2.54	1.27	0.85	3.39	1.45	1.17
3200	252	126	84	2.38	1.19	0.78	2.94	1.40	1.15
3400	268	134	89.5	2.23	1.12	0.75	2.66	1.32	1.14

T_m(°K)	B_m	$Error \approx B_{m} {(\frac{Δ T_{0}}{T_{m}})}^{2} (Percent)$
2000	48.3	48.3
2400	40.2	40.2
2800	34.4	34.4
3200	30.1	30.1

T_m₁ (°K)	$\begin{array}{l} B \approx \frac{ν}{T_{m 1}} \\ = \frac{q_{0}}{K T_{m 1}} \end{array}$	∊	H¹ × 10⁷ (ergs/cm³⁻°K	R(T_m₁) (g cm⁻² sec⁻¹)	$Δ T_{0} (\frac{f}{P / A}) (^{\circ} K - cm - cps)$	$α (\frac{f}{P / A}) \times 10^{2} (cm - cps)$	ψ(P/A) × 10² (cm rad/sec)	$\frac{f_{min}}{(P / A) \times 10^{3} (cm - cps)}$
2000	48.3	0.259	2.66	7.48 × 10⁻¹⁴	0.552	1.33	1.40	3.51
2400	40.2	0.294	2.87	2.32 × 10⁻¹⁰	1.22	2.02	2.54	6.37
2800	34.4	0.321	3.07	7.20 × 10⁻⁸	2.28	2.80	4.12	10.32
3000	32.2	0.334	3.18	7.14 × 10⁻⁷	3.02	3.23	5.07	12.75
3200	30.1	0.341	3.22	5.33 × 10⁻⁶	3.95	3.72	6.23	15.65
3400	28.4	0.348	3.38	3.14 × 10⁻⁵	4.88	4.06	7.25	18.20

Abstract

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Tables (3)

Equations (19)

Applied Optics