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The hook method under transverse concentration gradient conditions
Volume 39A, number 2
PHYSICS LETTERS
24 April 1972
THE HOOK METHOD UNDER TRANSVERSE CONCENTRATION GRADIENT CONDITIONS I.P. YAVOR and Yu.L. SEROV
loffe Physical TechnicalInstitute, USSR Academy of Sciences, Leningrad, USSR Received 14 February 1972 Distortion of hooks under conditions of a large transverse (relative to the optical axis) atom concentration gradient has been observed. Formulas for determining concentration gradient from hook distortion are given.
The hook method has been employed to obtain the distribution of non-excited Cs-atom concentration in narrow interelectrode spacing of a planar diode with a hot cathode. The adjustment of the interferometer providing necessary space resolution was made according to the scheme, recommended in ref. [1]. The spacing image and the interference fringes, localized in the spacing, were focused in the plane of a spectrograph slit. The narrowing of the projecting aperture achieved by means of a split diaphragm parallel to the edges of the interelectrode spacing permitted to attain resolution of an order of 0.15 mm across the spacing. When positioning the spectrograph slit perpendicularly to the spacing image distortion of the hooks was observed. Distorted hooks near Cs resonance line 8521 A are shown in fig. 1. The lower edge of the interferogram corresponds to the cathode, the upper one to the anode. The interferogram was obtained at Cs-vapour pressure PC~ = 1.1 mm Hg, interelectrode distance d = 1.5 mm, cathode temperature Tk = 1570°K, anode temperature Ta = 700°K and current through the diode i = 0. The effect of hook distortion allows us to make not only a qualitative conclusion about the existence of transverse atom concentration gradient, but also a
quantitative estimation of its value. An expression for the difference in phases of interfering beams as proposed in ref.[2] but taking into account a change in atom concentration N in the y-direction normal to the spacing is as follows:
~o= ~ - N(y)B.XyXj
;
(1)
here ~b is the total phase difference which is due to a plane-parallel glass plate making the interference fringes to incline and to geometrical difference in paths of interfering beams; ~/is the absorption line wavelength. B = e2fl/4nmc 2, where f i s the oscillator strength and l is the vapour column length. If y-axis is directed from the cathode to the anode, then at Tk > Ta,dN/dy > 0 and the rate of phase difference change along y is
a__
ay ay
x-x/
(2)
On the interferogram of fig. 1 X increases from the left to the right and BCJ/dy is positive, since the order of fringe interference increases in the direction of short waves and, consequently, from the cathode to
Fig. 1. 109
Volume 39A, number 2
PHYSICS LETTERS
the anode. Besides, in the spectrum region, where the hooks are observed, a¢/dy weakly depends on X and y and it may be assumed that a~k/dy = const. Therefore, for a given AX = IX-Xjl the rates of the change in the phase difference to the left and to the right from the absorption line are higher and lower, respectively, by the same magnitude of (dN/dy) X
8 (xp 2/A~. The total phase change from the cathode to the anode measured by the number of fringes in the region of the hooks on the left side (X < Xj) is m = k + ANB(Xi)2/AX, and on the right side (X > Xi) is n = k - ANB(Xi)2/AX. If the difference in the atom concentration near the anode and the cathode AN= 0, then the number of hooks to the left and to the right is m = n = k, i.e. k is the number of hooks for a homogeneous vapour column. In the presence an atom concentration gradient the number of hooks on the left side increases, while on the right side it decreases. A readjustment of the interferometer and the resulting inversion of the slope of interference fringes leads to inversion of the pattern observed, i.e. the number of hooks to the left becomes smaller, while to the right it becomes larger, due to the change of the sign of
a~/ay. Thus, the transverse atom concentration gradient leads to redistribution of the hooks to the left and to the right from the absorption line, but their total number remains constant and equal to the total number of
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24 April 1972
the hooks near the line considered in the case of homogeneous vapour column under the equivalent conditions. The average value of the atom concentration gradient in the spacing is
dN
~-=
m-n 2Bd
AX
(X/)2"
(3)
For the right side of the interferogram (fig. 1) the second term in eq. (2) is negative and its absolute value increases with decreasing X, the number of interference fringes, which are crossed by y-axis, being decreased. If dN/dy does not depend on y, then at a~o/dy = 0 a vertical line will be observed crossing the entire spacing in the direction from the cathode to the anode. In fig. 1 values a~o/dy = 0 are observed only at the fixed values o f y . This indicates that dN/dy increases in the direction of the anode. The authors are grateful to G.K. Tumakayev for helpful discussions.
References [1] G.K. Tumakaev and V.R. Lazovskaya, Aerofizicheskie issledovaniya sverchzvukovych techeniy, Izd. Nauka, USSR (1967) 79. [2] A.M. Schuchtin, Spektroskopiya gazorazriadnoy plazmy, Izd. Nauka, USSR (1970) 110.
PHYSICS LETTERS
24 April 1972
THE HOOK METHOD UNDER TRANSVERSE CONCENTRATION GRADIENT CONDITIONS I.P. YAVOR and Yu.L. SEROV
loffe Physical TechnicalInstitute, USSR Academy of Sciences, Leningrad, USSR Received 14 February 1972 Distortion of hooks under conditions of a large transverse (relative to the optical axis) atom concentration gradient has been observed. Formulas for determining concentration gradient from hook distortion are given.
The hook method has been employed to obtain the distribution of non-excited Cs-atom concentration in narrow interelectrode spacing of a planar diode with a hot cathode. The adjustment of the interferometer providing necessary space resolution was made according to the scheme, recommended in ref. [1]. The spacing image and the interference fringes, localized in the spacing, were focused in the plane of a spectrograph slit. The narrowing of the projecting aperture achieved by means of a split diaphragm parallel to the edges of the interelectrode spacing permitted to attain resolution of an order of 0.15 mm across the spacing. When positioning the spectrograph slit perpendicularly to the spacing image distortion of the hooks was observed. Distorted hooks near Cs resonance line 8521 A are shown in fig. 1. The lower edge of the interferogram corresponds to the cathode, the upper one to the anode. The interferogram was obtained at Cs-vapour pressure PC~ = 1.1 mm Hg, interelectrode distance d = 1.5 mm, cathode temperature Tk = 1570°K, anode temperature Ta = 700°K and current through the diode i = 0. The effect of hook distortion allows us to make not only a qualitative conclusion about the existence of transverse atom concentration gradient, but also a
quantitative estimation of its value. An expression for the difference in phases of interfering beams as proposed in ref.[2] but taking into account a change in atom concentration N in the y-direction normal to the spacing is as follows:
~o= ~ - N(y)B.XyXj
;
(1)
here ~b is the total phase difference which is due to a plane-parallel glass plate making the interference fringes to incline and to geometrical difference in paths of interfering beams; ~/is the absorption line wavelength. B = e2fl/4nmc 2, where f i s the oscillator strength and l is the vapour column length. If y-axis is directed from the cathode to the anode, then at Tk > Ta,dN/dy > 0 and the rate of phase difference change along y is
a__
ay ay
x-x/
(2)
On the interferogram of fig. 1 X increases from the left to the right and BCJ/dy is positive, since the order of fringe interference increases in the direction of short waves and, consequently, from the cathode to
Fig. 1. 109
Volume 39A, number 2
PHYSICS LETTERS
the anode. Besides, in the spectrum region, where the hooks are observed, a¢/dy weakly depends on X and y and it may be assumed that a~k/dy = const. Therefore, for a given AX = IX-Xjl the rates of the change in the phase difference to the left and to the right from the absorption line are higher and lower, respectively, by the same magnitude of (dN/dy) X
8 (xp 2/A~. The total phase change from the cathode to the anode measured by the number of fringes in the region of the hooks on the left side (X < Xj) is m = k + ANB(Xi)2/AX, and on the right side (X > Xi) is n = k - ANB(Xi)2/AX. If the difference in the atom concentration near the anode and the cathode AN= 0, then the number of hooks to the left and to the right is m = n = k, i.e. k is the number of hooks for a homogeneous vapour column. In the presence an atom concentration gradient the number of hooks on the left side increases, while on the right side it decreases. A readjustment of the interferometer and the resulting inversion of the slope of interference fringes leads to inversion of the pattern observed, i.e. the number of hooks to the left becomes smaller, while to the right it becomes larger, due to the change of the sign of
a~/ay. Thus, the transverse atom concentration gradient leads to redistribution of the hooks to the left and to the right from the absorption line, but their total number remains constant and equal to the total number of
110
24 April 1972
the hooks near the line considered in the case of homogeneous vapour column under the equivalent conditions. The average value of the atom concentration gradient in the spacing is
dN
~-=
m-n 2Bd
AX
(X/)2"
(3)
For the right side of the interferogram (fig. 1) the second term in eq. (2) is negative and its absolute value increases with decreasing X, the number of interference fringes, which are crossed by y-axis, being decreased. If dN/dy does not depend on y, then at a~o/dy = 0 a vertical line will be observed crossing the entire spacing in the direction from the cathode to the anode. In fig. 1 values a~o/dy = 0 are observed only at the fixed values o f y . This indicates that dN/dy increases in the direction of the anode. The authors are grateful to G.K. Tumakayev for helpful discussions.
References [1] G.K. Tumakaev and V.R. Lazovskaya, Aerofizicheskie issledovaniya sverchzvukovych techeniy, Izd. Nauka, USSR (1967) 79. [2] A.M. Schuchtin, Spektroskopiya gazorazriadnoy plazmy, Izd. Nauka, USSR (1970) 110.