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A microwave spectroscope at one centimetre wavelength Thomas, Blodwen 1948

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JSp  '9*-* & sr  A MICROWAVE SPECTROSCOPE AT ONE CENTIMETRE WAVELENGTH. by Blodwen Thomas  A thesis submitted i n p a r t i a l fulfilment of the requirements for -the degree of MASTER OF ARTS i n the Department of PHYSICS  The University of B r i t i s h Columbia  ABSTRACT  The object of t h i s research was the construction of a microwave spectroscope at 1.25 cm. wavelength. The double modulation method, which was used here, i s discussed. The system was tested with ammonia, and the inversion spectrum identified.  The effect  of using various harmonies of detection i s shown.  AC KNCWLE DGMENT.  I am pleased to express my thanks to Dr. A . Van der Ziel, under whose direction this research was carried on. I would also like to acknowledge the help of Mr. D. Scovil, who built part of the equipment. This project has been conducted by myself with the aid of a National Research Council Bursary and a Defence Research Board grant. In addition, the Defence Research Board provided a grant for buying the microwave equipment.  TABLE OF CONTENTS. 1.  INTRODUCTION. A. Application of molecular spectroscopy to the study of molecular structure B. Present state of microwave research C. Object of the research at U.B.C.  .... .... ....  1 2 3  11. THEORY. A. B. C. D. E. F. G. H.  Types of molecular symmetry Linear molecules Symmetric top molecules Spherical top molecules Asymmetrical top molecules Isotope effect Hyperfine structure Ammonia: inversion doubling and hyperfine structure I. Stark & Zeeman effects J. Intensity and shape of lines  111.  IV)  14 15  A. Electronic apparatus i ) Klystron and power supply i i ) Low frequency sawtooth modulation i i i ) Radio frequency o s c i l l a t o r iv) Attenuation v) Waveguide absorption c e l l v i ) Crystal detection v i i ) ladio frequency amplifier v i i i ) Frequency measurements  .... .... .... .... .... .... .... ....  18 20 20 21 21 22 23 23  B. Vacuum technique  ....  24  ....  26  ....  30  ....  30  ....  32  EXPERIMENTAL PROCEDURE  RESULTS A. Ammonia inversion lines B. Effect of harmonic detection on line shape C. Effect of radio frequency modulation voltage on line shape  VI)  10 11 11  APPARATUS.  A. Single and double modulation methods V)  7  CONCLUSIONS  V i i ) BIBLIOGRAPHY  .... 35 . . . . ' 36  ILLUSTRATIONS  1. Klystron power supply c i r c u i t 2. Block diagram of vacuum system  following page 18 "  "  2k  "  "  27  "  "  28  " "  " "  28 JO  3. Block diagram of double modulation spectroscope k.  Picture of equipment  5. Close-up picture of klystron, attenuators, and controls 6 . Ammonia inversion lines  A MICROWAVE SPECTROSCOPE AT ONE CENTIMETRE WAVELENGTH  1.  INTRODUCTION  A. Application of molecular spectroscopy to the study of molecular structure. Molecular spectroscopy i s the determination of energy levels i n molecules for the purpose of investigating their molecular structure.  These levels may be divided conveniently into  three types: electronic, vibrational and rotational levels.  Trans-  i t i o n s between electronic levels form absorption or emission lines and bands i n the v i s i b l e region; vibrational lines and vibrationrotation bands appear i n the infra-red; rotational lines are i n the millimetre and centimetre (microwave) region. The high frequency oscillators necessary as sources for the microwave region are recent developments i n electronics, and are helping to remove the l i m i t a t i o n of optical methods at the low energy levels. If a molecule has an e l e c t r i c dipole moment, transitions are possible between rotational energy levels, and a series of rotational absorption lines appears i n the microwave region. The line frequencies determine the moments of i n e r t i a and internuclear spacings of the simple molecules. Rotational line series also indicate the presence of isotopes, owing to the s l i g h t l y differing moments of inertia.  A rotational line may have hyperfine structure i f one of the  nuclei i n the molecule has an e l e c t r i c quadrupole moment. The quadrupole coupling coefficient iri the molecule can be calculated from  the spacing of the hyperfine components, and the nuclear spin from the number of these components. Thus rotational lines are a measure of moment of i n e r t i a , bond spacing, nuclear quadrupole moment, nuclear spin and isotopic mass ratios. B. Present state of microwave research. Since 19^-6 molecules with electric dipole moments have been investigated mainly i n the cm. region.  Linear and symmetric  top molecules have simpler line structures than the more common asymmetric top because of the higher symmetries of the former.  The  bond distances of such molecules as OCS have been measured by Dakin, Good, and Cole (9) and Townes, Holder and Merritt (26).  The spectrum  of NH^ i s an example of inversion doubling and i t s lines are measured by Good and Coles (13), Strandberg et al (220>, Simmons and Gordy (21). The interaction energy f o r quadrupole coupling i s given by FJeld ( 1 1 ) , and Bardeen and Townes ( 2 ) .  The nuclear spin and quadrupole moment of  CI, N, Br, and I are measured by Townes et a l ( 2 5 ) , Gordy et a l (15). A transition has been found i n Cv, due to i t s magnetic dipole moment by Beringer ( 3 ) .  Water absorption has a peak at 1.3^4- cm. - Autler et a l  ( 1 ) , Townes and Merritt (23).  Townes et a l (26) have found lines for  several suitable linear molecules, Dailey and Wilson (8) f o r polyatomic asymmetric molecules by Stark effect.  Rotating molecules which have an  electric dipole moment show Stark and Zeeman effects i n applied f i e l d s . Both have been boserved: i n NH^ by Coles and Good (6), methyl alcohol and S0 by Dailey and Wilson (7) and ( 8 ) , Jen ( 1 9 ) . 2  The earliest microwave absorption measurements were made by Cleeton and Williams  (5)  i n 193^-. They found a broad absorption  line i n HH, at 1.25 cm. with a Hertzian o s c i l l a t o r .  Recently several  methods with balanced c i r c u i t detection for comparing absorption i n a wave guide were used by Beringer  (3),  Good  (12),  and Townes  (2i|.).  Later (27)  improvements are those of Gordy and Kessler (lij.), Watts and Williams  Hughes and Wilson ( 1 8 ) . Gordy and Kessler f i r s t used a method of single frequency modulation of a reflex klystron, and demonstrated a graph of absorption versus frequency on a cathode ray oscilloscope.  Since then,  they and several others have used double modulation of the klystron. The additional modulation i s at radio frequency i n order to increase the sensitivity of the spectrograph by increasing the signal to noise ratio at the crystal detector. Hughes and Wilson measure the Stark effect with an equally sensitive method employing radio modulation of the line frequencies.  Jen has adapted the method of Gordy and Kessler  to high temperature by replacing the waveguide absorption c e l l with a resonant cavity for convenience of application of the magnetic f i e l d i n the Zeeman effect.  The cavity i s also suitable for heating molecules  to the desired energy levels.  The accuracy of microwave frequency  measurements i s very good: 10 kc. at 25,000 Mc. or better than 1 i n  10^.  The high accuracy frequency standards are b u i l t by multiplying a standard quartz c r y s t a l . C.  High resolution i s also obtained: separations of 200 kc.  Object of this research. When t h i s project was. started last f a l l , i t was  decided to build a microwave spectograph at 1 . 2 5 cm.  From t h i s wave-  length the project can be extended into the millimetre region i n the future.  The double modulation method was chosen for good s e n s i t i v i t y  and for the simplicity of the system.  Microwave plumbing and klystron  tubes were obtained from de Mornay Budd and Raytheon.  The electronic  equipment and vacuum system have been constructed and assembled here.  k  The vacuum system i s b u i l t to allow investigation of absqption at pressures down to 1 0 mm. of mercury, The spectrograph i s now completed with signal detection at the second harmonic frequency.  The klystron  frequency may be swept from 2 2 , 0 0 0 to 2 5 , 0 0 0 Mc. or further, depending on the tubes.  The frequency i s measured to four figures with a  transmission type wavemeter. A frequency standard, being completed here, w i l l be accurate to s i x figures. With the spectrograph i t was planned to measure the inversion spectrum of ammonia, and this has been done. By comparing our results with those of Strandberg et al ( 2 2 ) , and Good and Coles ( 1 5 ) , the accuracy and sensitivity of t h i s spectrograph could be tested. The effect of double modulation on line shape has also been studied with detection at several harmonic frequencies. From the results with ammonia, i t i s seen that some improvements can be made to the system in order to increase the signal to noise r a t i o .  In addition, f a m i l i a r i t y  with the techniques at this frequency w i l l lead to work at higher frequencies where many interesting molecules may be investigated. 11.  THEORY  A. Types of molecular symmetry. Molecules may be classed according to their degrees of symmetry into the types: l i n e a r , symmetrical top or rotator, spherical top, and asymmetrical top. Linear molecules, including a l l diatomic ones, have a zero moment of i n e r t i a about t h e i r internuclear axis, and non zero but equal moments of i n e r t i a about any two other mutually perpendicular axes.  A l l other molecules have non zero moments  of i n e r t i a about the three principal axes.  I f a l l three moments of  5  i n e r t i a are equal, the molecule i s a spherical tops i f two are equal - a symmetric top, i f a l l unequal - an asymmetric top. The rotational spectra are typical of the various types of symmetries, and may be interpreted to give information about the molecular structure by the The main reference i s Hefczberg ( 1 7 )  following theoretical development. B.  Linear molecules. If the angular momentum of the electrons about the  internuclear axis i s zero (as i s the case f o r the unexcited ground state of the molecules), and i f the molecule i s i n the zero vibrational state, then a linear molecule may be considered as a simple vibrator with zero moment of i n e r t i a about the figure axis.  The angular momentum of the  rotating molecule i s quantised: p = h / J (J •+ 1) From this the energy of the various levels i s given as s E  J " JL  "  J (J + 1) h  21  8  -7T2  2  I  or E where I •  s BJ (J + 1)  =Vr  B-  mfr? i s the t o t a l moment of i n e r t i a of the molecule about  an axis perpendicular to the internuclear axis for this particular case of the simple linear rotator.  The mass of the electrons can be taken  into account s u f f i c i e n t l y accurately by using the mass of the neutral atom rather than the nucleas as V . completely r i g i d .  The molecule, however, i s not  The influence of centrifugal force results i n a s l i g h t  increase i n the internuclear distances when the molecule i s rotating. The following correction can.be made to the energy of the levels: _E_  he  = BJ (J + 1 )  - DJ  2  (J+1)  2  where D^.B.  This extra factor i s negligible for linear molecules. The t o t a l eigenf unction of linear molecules i s  IfJs 1^ 2}/ i(l the product of electronic, vibrational, and rotational v  r  eigenfunctions.  The rotational level of a molecule i s called positive  or negative depending on whether ihe t o t a l eigenfunction remains the same or changes sign by r e f l e c t i o n of a l l particles at the centre of mass. /* If  and Jfl are unchanged by t h i s symmetry operation, the symmetry v  character depends only on i ^ . : even J rotational levels are positive, odd J are negative.  I f the linear molecule has a centre of symmetry, i t also  has the property symmetric or antisymmetric re exchange of identical nuclei.  The t o t a l eigenfunction remains the same or changes sign when a l l  nuclei on one side of the centre of mass are simultaneously exchanged with corresponding ones on the other side.  In linear molecules alternate  levels are symmetric and antisymmetric. If the linear molecule has no centre of symmetry, the s t a t i s t i c a l weight of a rotational l e v e l i n a symmetric electronic state Cf)  i s g j B 2 J -f1, the number of orientations of J i n a magnetic  f i e l d (which i s developed by the rotational motion).  If the molecule  has a centre of symmetry, then ihe nuclear spin of the identical pairs of nuclei has an influence on the s t a t i s t i c a l weight. The even and odd levels each have a different weight factor which depends on the spins and must be multiplied to the term  2J+-1.  I f a l l pairs of identical  nuclei have zero spin, alternate levels w i l l be entirely missing. I f non zero spin, the ratio of intensities i s determined by their spin. However, a linear molecule with a centre of symmetry cannot have an e l e c t r i c dipole moment, so i s of no interest i n the microwave region since i t cannot have rotational transitions.  One case has been observed  7  of a homohuclear diatomic molecule which shows transitions due to magnetic dipole moment - Cvj. The thermal distribution of these levels combines the Boltzmann factor and the s t a t i s t i c a l weight of each l e v e l .  The  population of a rotational level i s N, <~*> g, e - §<J . For the linear kT  molecule with no centre of symmetry, g j r 2J +1 as above. The graph of Nj versus J increases at f i r s t due to g j then decreases due to the exponential factor. The solution of the matrix elements shows that for e l e c t r i c dipole radiation a molecule must have a dipole moment i n order for the transition probability to be observable. The selection rule i s 4J  B  0, 1 1 .  The symmetry selection rules are: transitions can occur  only from a positive (even j ) level to a negative (odd J) l e v e l , and only between states with the same symmetry (a jump cannot occur between a symmetric and antisymmetric l e v e l ) .  These two rules show why a linear  molecule with a centre of symmetry cannot have rotational l i n e s , since they automatically eliminate the transitions  - +1,  However, a  linear molecule with no centre of symmetry (i.e. one with a permanent e l e c t r i c dipole moment) can have lines. Considering y  (cm"') »  - -M, the absorption wave number i s :  2B (J-H)  where J refers to lower l e v e l .  - Ifi) ( J - M )  5  This i s an almost equidistant line  series, and characterizes linear molecules. Examples of such molecules are OCS, C.  C1CN.  Symmetric top molecules. The symmetric top molecule has a non zero moment of  i n e r t i a about i t s figure axis i n addition to equal moments of i n t e r t i a  about two other perpendicular axes. Ig, the third 1 ^ .  The two equal moments w i l l be called  The t o t a l angular momentum represented by the quantum  number J miist be perpendicular to the figure axis i n a linear molecule, but a symmetric top can have a constant component of angular momentum along the figure axis.  Examples are NH , the methyl halides.  The  figure axis natates about the constant J direction, and at the same time the molecule rotates about the figure axis.  The component of J along  the figure axis i s called K, and K may take the values X , J - 1 , ... - J. Again assuming no electronic angular momentum, the energy of the levels i s E. JK he  BJ ( J  where B = h  (A - B)  +1)  A  8TT cI 2  8 i r 2 ( j I B  A  It i s evident that a l l states with KfO are doubly degenerate. 4 L, the molecule i s a prolate symmetric top, i f I > I °  A  B  If - I,  i t i s oblate.  Taking into account the effect of centrifugal force on a non r i g i d rotator, the energy levels are corrected! E  JK  he  « BJ  (J+ 1 ) -f (A-B)  where C^B  K  2  - Dj J  2  (J-M)  2  - D J J R  (Jfl) K  2  -  DgK^  or A. The number of molecules i n a given J , K level i s  ^JK^JK  6  - E idP^ kx  where the factors of g have been discussed. There . JK  i s a series of graphs of N  JK  versus J f o r each value of K.  the t o t a l number of molecules i n a given J  Since J^K,  level i s not a smooth  function, compared with the distribution i n linear molecules. The symmetric top molecule must have a permanent dipole moment to allow dipole radiation, as for the linear molecule. Due to the symmetry i n this case, the moment w i l l l i e along the figure  axis.  ^ J - 0 i 1, <a K = 0.  The selection rules are  The l a t t e r ruie  i s necessary because rotation about the figure axis does not change any component of the dipole moment along a given fixed direction.  Again  the symmetry selection rules are: transitions are allowed only between a positive and negative l e v e l , and between levels which have the same s t a t i s t i c a l weight factor due to nuclear spin.  The f i r s t r e s t r i c t i o n  always permits transitions i n prolate symmetric tops, but only i n oblate tops which have double levels (for each K value) due to inversion doubling. The absorption frequencies are: V  (cm"') a  2B (j+1)  - 2i> K JK  2  (J + 1)  - ^/>. J  (J^1)  5  This i s a series of approximately equidistant bands -which may be resolved into very small fine structure s p l i t t i n g (for example, 20 cm"' i n  HH^)  due to the term containing K, when the effect of centrifugal force on a non r i g i d rotator i s considered. Each J level has J+1 2J+1, because of K degeneracy.  components, not  In NH^ each fine structure line i s  double due to the separation of inversion levels ( .8 cm '). -  As for linear molecules, the rotational levels of the symmetric top are either positive or negative as the t o t a l eigenfunction i s unchanged or changes sign on r e f l e c t i o n of a l l particles at -the centre of mass. The s t a t i s t i c a l weight g  i s a more complicated factor since i t JK  must account for inversion doubling, two f o l d K degeneracy, and effect of nuclear spin.  A non planar symmetric top has a " l e f t " and "right"  form of the molecule.  I f the potential energy h i l l separating the  two  positions i s not i n f i n i t e l y high, a slight s p l i t t i n g occurs into two almost coinciding energy levels - inversion doubling, which i s discussed more f u l l y i n later section.  One level i s positive, the oiher negative.  In addition to t h i s s p l i t t i n g , each level with KfOis doubly degenerate as  seen from the formula for E .  In addition, a true symmetric top has  JK  an axis of symmetry, and the nuclear spin of the identical nuclei causes differences i n the s t a t i s t i c a l weights of the levels.  For a molecule  with a three f o l d axis of symmetric i n a t o t a l l y symmetric electronic and vibrational state, the levels with K r 0 , 3 , 6 . . have greater s t a t i s t i c a l weight than with K - 1,2,k,5,..• I f the spin of the l i k e nuclei is zero, the levels with K = 1,2,4.. are missing entirely. of H i n NH 2:1.  3  i s h.  The spin  and the ratio of intensities for this molecule i s  The weight factor includes 2 J + 1  i f K = 0 or 2 (2J + 1 ) ,  K^O,  the nuclear spin factor, and the inversion doubling i f i t s separation i s negligible. D.  Spherical top molecules. The moment of i n e r t i a about any axis through the  centre of mass of a spherical top molecule i s the same. Since t h i s type has an i n f i n i t e number of non coinciding axes of symmetry, the dipole moment must always be zero.  Therefore no rotational dipole  radiation i s possible for such molecules. level formulas as linear molecules. E.  They have the same energy  Examples are: CH^, CCi^, SF^.  Asymmetric top molecules. As usual the t o t a l angular momentum J i s constant  for a given l e v e l .  A l l three principal moments of i n e r t i a are  different, and the double degeneracy due to K i s removed to give 2J -f-1 levels for each J value. E  -  The energy of the levels: f ( I , I , I , J) A  B  c  i s more d i f f i c u l t to represent by quantitative rules. tops, levels are positive or negative.  As f o r symmetric  However, the p o s s i b i l i t y of  inversion doubles each level into two of opposite symmetry. I f there  11  are also identical muclei i n the molecule, the e i f s are symmetric or antisymmetric on exchange of pairs, and the s t a t i s t i c a l weights depend on the spins. As before, the molecule must have a permanent moment to have rotational lines.  The selection rule i s 4J - 0 ±l . t  The motion  of "the asymmetric rotator no longer requires the r e s t r i c t i o n on the axial component: of momentum of the symmetric top. A complicated sprectrum i s allowed, because of the removal of degeneracy i n the fine structure, and the symmetry selection rules seldom r e s t r i c t .  Examples  of asymmetric top molecules with a permanent dipole moment ares H 2 0 , D  2  0,  E CO. 2  P. Isotope effect. I f one of the nuclei i n a molecule has isotopes, there w i l l be separate series of lines due to the different moments of inertia.  The position and spacing of the lines differ s l i g h t l y . The  mass ratios of -the isotopes can be calculated very accurately from rotational spectre. I f the masses of isotopes are already known, the isotope effect can be used to calculate the distance of the isotopic nucleas from the centre of mass of the molecule.  Since this distance i s  not appreciably affected by the different masses, ihe line s h i f t gives the difference i n moments of i n e r t i a and hence the distance measurement: A.  I = 4 on . f -  X  G. Hyperfine structure. If one of the nuclei has an e l e c t r i c quadrupole moment, (in addition t o the molecular dipole moment) there i s an electrostatic interaction energy between the quadrapole moment and the gradient of the molecular electric f i e l d at the nucleus.  This causes a small s p l i t t i n g  of the energy levels due to I J coupling into 21 + 1 ( i f I < J) or 2J+• 1  12 (J<^l) levels - the so called hyperfine structure. For a linear or symmetric top, the interaction energy i s t  1where  3K  3/L1P ( C t l ) - I (1*1) J (J+1) J (J +1) 21 (21 - 1) (2J - 1) 2J + 3) 2  C = F (F •+1) - I (I +1) - (J +1) Fr  |j-f-11 , | j + I - l | ,  •• •  [J - 11  and where Q i s the quadrupole moment of the nucleus, V i s the electrostatic potential at the nucleus due to the other charges i n the molecule, K. i s the component of J on the figure axis (called z here), I i s the spin of the nucleus which has the quadrupole moment, F a J +-I. The interaction i s calculated from the quantized angle between I and J Feld (tl), Bardeen and Townes ("2>). The new quantum number F i s the resultant of the nuclear spin momentum and the molecular rotational momentum. The selection rules for transitions are <3F » o ,±7, d j - o, ^1, &K a 0. Thus the number of components i n a t r a n s i t i o n determines the nuclear spin. Since F » ( J + l ) . . j j - l | the number of lines observed at a single transition i s the minimum of ^1 - t i ,  ^ J -tl.  The separation  of the hyperfine structure determines the quadrupole coupling coefficient Q —i . A rotational line with t h i s hyperfine structure i s characterized 02  by a strong central line with weak s a t e l l i t e s symmetrically placed on either side. In order to have this quadrupole s p l i t t i n g , i t i s necessary that I ^ 1, J >1. H. Ammonia inversion doubling and hyperfine structure. A l l non planar molecules have two identical potential minima corresponding to the two equilibrium positions of the nuclei resulting from inversion at the centre of mass.  I f the potential h i l l  between the two minima i s i n f i n i t e l y high, there can be no transition  13  from one configuration to the other, and the energy levels of each form are i d e n t i c a l .  However, i f the potential h i l l i s not i n f i n i t e l y high,  by quantum mechanics the molecule w i l l transfer from one equilibrium position to the other after a certain time, and the energy levels are s p l i t into close doublets.  In the case of ammonia the N nucleus has  two positions with identical potential minima along the figure axis. There i s an equal probability of the N nucleus being on either side of the plane of the hydrogen nuclei.  Because the two potential  wells are symmetrical about the o  zero plane the eigenf unctions can  Distance  ft~o»Yt zero pl£U\c  be the same or opposite i n sign when the N isreflected at the origin. Therefore there i s a possible symmetric and antisymmetric combination of the separate o s c i l l a t o r functions of each minimum, which correspond to the two s l i g h t l y s p l i t levels.  Since the probability of finding  the nucleus i n either minimum i s equal, the population of the two levels i s according to the Boltzmann distribution for thermal equilibrium}  orN  the two levels have s l i g h t l y different energy and  therefore different population. Inversion doubling i s described by Herzberg ( 1 7 ) and Dennison ( 1 0 ) . Transition from the lower to upper level can be observed i n ammonia. The jump & J = 0 , 4 K B 0 now emits a quantum because of inversion doubling. I f the gas i s i n the zero vibrational state, tJie s p l i t t i n g i s small, about ,8cm. for a l l J , K values. The energy difference depends s l i g h t l y on J and K since the small  14 rotational energy has an effect on the shape of the molecule and hence on the height of the potential h i l l .  The dependence is given empirically lii  by many of the references mentioned f o r ammonia. Since N  H  has a quad-  rupole moment and a spin of 1, these transitions are not single l i n e s , but have the hyperfine structure previously described.  The diagram indicates  the jump due to the selection rule 4P » 0, £1  F = 7+l  The separation J + 1 —» J i s not equal to  J  J -* J - 1  so there i s a strong central  J-l  |^  line with 2 longer and 2  —  shorter wavelength s a t e l l i t e s .  1  F  7+I  =  7  T-l  Actual photographs of these lines are found i n the results. I.  Stark and Zeeman effects.. "When an e l e c t r i c f i e l d i s applied to a molecule, a  dipole moment i s induced which can take up various directions with respect to the f i e l d .  The interaction energy depends on the orientation  of the orbitalangular momentus vector re the applied f i e l d .  Thus tiie  Stark effect i s a s p l i t t i n g of the rotational levels into multiplets, and can be used for measuring the strength of the e l e c t r i c dipole  and  i t s orientation re the figure axis of the molecule. Most molecules have an even number of electrons,  and  therefore a zero magnetic moment. But, i f a molecule i s rotating, a weak magnetic f i e l d i s generated by the orbital motion of the atoms and i s proportional to the speed of rotation.  Therefore the Zeeman effect  15 may be observed.  The applied magnetic f i e l d interacts with the rotational  magnetic f i e l d , and the rotational levels are s p l i t into multiplets, depending on the orientation of the applied f i e l d re the o r b i t a l angular momentum vector. Refer (6), (7), (19) f° experimental results i n r  microwave spectroscopy. J.  Intensity and shape of lines. The intensity of absorption at a given frequency  depends on the number of molecules i n the i n i t i a l and f i n a l states, and the probability of transition from the i n i t i a l to f i n a l state.  The - E_ population N of the various rotational levels i s K ^ g „ e 1?.JK JK JK kT TTr  for linear and symmetric top molecules, where g  &  K  T  i s tlge s t a t i s t i c a l  JK.  weight of the level with energy E  . The absorption coeffient at any  frequency i s given by Van Vleck and Weisskopf (27), They calculate oC (absorption coefficient per cm.) c l a s s i c a l l y from the Hamiltonian and electromagnetic theory, then generalize to a quantum mechanical system.  They assume adiabatic c o l l i s i o n s as the means of restoring  thermal equilibrium, i . e . the time interval of c o l l i s i o n i s much less than tiie interval between c o l l i s i o n s for a molecule.  They apply a  correction to the theory of Lorentz since certain app roximations usually made are no longer v a l i d i n the microwave region, inhere the c o l l i s i o n frequency i s of the order of magnitude of the absorption frequency.  They obtain: 06-  8j£ji 6hc -  ^_ kT  2f.£  —  \* /v j-f(vcj,v)e rfi  ;  J  V l  t  C  where y=incident frequency, y.. =frequ3ncy of the absorption l i n e , and  ^  k 1  '  •f(Vijy)±s the structure factor which, gives the shape of the l i n e  This formula holds i n the microwave region where rotational energy i s much less -than thermal energy. The structure factor determines the shape of the line i n terms of the half width  . The main limitation on the shepe of the  line or the half width i s the length of the wave t r a i n absorbed by the molecule between c o l l i s i o n s : Dennison (10). It i s seen that the half width i s the reciprocal of the time interval between c o l l i s i o n s :  =^  . Therefore, from kinetic theory, the half  width of a line i s directly proportional to pressure i n the region from about 10 microns to 10 cm Penrose  , as measured experimentally by Bleaney and  The absorption at the centre of the l i n e i s : V*  Since a^and N  3KT A V are each directly proportional to pressure under the  conditions usually holding i n microwave measurements, i t follows that the height of the absorption line is independent of pressure, though the line width decreases with decreasing pressure.  For good resolution  i n absorption measurements i t i s necessary to work at  .01 - .001 mm Hg  pressure. At low pressures or at high intensity of radiation the height of the absorption l i n e does decrease at low pressure. i s explained as saturation broadening.  This  When the c o l l i s i o n frequency i s  so low that i t becomes comparable with the rate of transitions per molecule to the upper level by absorption of energy, then the distribution of molecules between ground and excited states i s disturbed by the excess  17  power.  The rate of return of molecules to the lower l e v e l by c o l l i s i o n i s  comparatively  slow, so that the d i s t r i b u t i o n of molecules becomes that  corresponding to a higher temperature, and the absorption falls.  coefficient  This e f f e c t i s greater at the centre of the l i n e than at the sides  and therefore the l i n e appears t o be broadened.  18  111.  APPARATUS  A. Electronic apparatus. i)  2K33  fclystron and power supply.  The  2K33 reflex  klystron ocsillates at 1.25 cm. and  has a power output of ij.0 milliwatts.  I t s frequency of o s c i l l a t i o n  can be altered by e l e c t r i c a l and mechanical tuning over a range of at least  3000 megacycles.  This tube has a wave guide output at one side  and a tunable plunger at the other.  The power supply must be voltage  controlled: i t requires about - 1800 volts for the cathode which accelerates the electron beam, the grids of the resonator or tuned cavity are at ground, the focussing grid controls the current flow and i s at -1800 - -2000 volts variable, (the klystron operating current i s made variable since tube, characteristics vary s l i g h t l y ) , the reflector i s at -1800 -  -2300 volts  variable. This l a t t e r range usually covers the most  e f f i c i e n t modes of o s c i l l a t i o n .  The c i r c u i t diagram i s shown on the  following page. The modulation voltages are applied to the klystron reflector directly at the supply.  The output power i s more than  sufficient for absorption measurements. The theory of operation of r e f l e x klystrons i s well developed by Pierce and Shepherd (20). A direct current beam i s accelerated from the cathode, controlled by -the focussing g r i d , and i t passes through the resonator grids into the d r i f t space containing the reflector electrode.  I f there i s a radio frequency voltage on the  resonator the elctrons w i l l become velocity modulated when passing through it.  The length of time spent by the electrons i n the d r i f t space i s  KLYSTRON  POWER SUPPLY  KLYSTRON CONNECTIONS 1. C A T H O D E 2. G R I D 3 REFLECTOR  MODULATION  S. H E A T E R fe. HEATER  19  controlled by the reflector, which reverses their direction.  By the  time -that -the beam has returned to the resonator i t has become density modulated.  The slow electrons catch up to the faster ones i n the d r i f t  space since the latter travel a longer distance before turning back. I f the phase relations are right, the beam w i l l give up energy to the resonator and build up oscillations i n i t .  The natural frequency of  o s c i l l a t i o n of the klystron i s obviously determined by t h i s resonant circuit.  I t s equivalent capacity i s formed mainly by the two close  p a r a l l e l grids, and i t s induetince by the surrounding loop.  These factors  indicate a method of tuning the klystron. I f the g r i d separation i s made mechanically variable, as i n the 2K33 tube, then the klystron frequency can be altered over a f a i r l y large range - several thousand megacycles. A decrease i n spacing causes an increase i n capacity and, therefore, an increase i n frequency of o s c i l l a t i o n . Solution of the transconductance  of the reflex  klystron shows that the tube w i l l oscillate most easily when f . t e  n+x,  where f i s the klystron frequency, i t i s the time spent i n the d r i f t space, and n i s the number (integral) of the mode, t i s inversely proportional to the reflection voltage V . R  Then, i f the reflection  voltage i s , for example, increased s l i g h t l y , t w i l l decrease, and the conductance w i l l contain a small capacitive term - i n t h i s case negative. This term has the effect of decreasing the tuning capacity of the oscillator c i r c u i t , and therefore increasing the frequency.  This means  that, over a small range of variation of V , the tube w i l l t r y to maintain the maximum conductance possible i . e . f . t = n + f-. This range of o s c i l l a t i o n i s c a l l e d a mode and may be 10 - 50 megacycles wide.  The  maximum power i s developed at the centre of the mode. I f the reflector  20 voltage i s varied over a wide range, many modes of o s c i l l a t i o n appear. The mode with smallest  (n r 1) gives most power output, but the  o s c i l l a t i o n i s most stable at higher modes since the real part of the conductance increases with n. This property of klystron tubes makes them ideally suited for frequency modulation by sweep voltages. A low frequency linear sawtooth voltage i s applied to the reflection to sweep the klystron frequency through the whole or part of a mode so that part of a spectrum can be traced out on a scope.  In the double modulation method, a much  smaller radio frequency sine voltage i s also applied to the reflector to modulate the absorption over a small range while the sawtooth gradually sweeps the position over the whole range, ii)  Low frequency sawtooth modulation. The low frequency sawtooth o s c i l l a t o r i s a gas triode  as usual, and was b u i l t with, a cathode follower c i r c u i t to increase linearity.  Its frequency i s easily varied from 1 - 100 cps. The  amplitude required to cover a complete mode of o s c i l l a t i o n i s from 20 - 80 v o l t s , but i s reduced to about 5 volts for studying absorption i n order to decrease the required band width of the amplifier and thus reduce crystal detection noise. The sawtooth voltage i s also used as the horizontal sweep on the oscillope which i s used to observe the absorption.  The frequency has been kept at L\.0 - 60 cps for easy viewing  on the scope screen, but better results can be obtained at much lower frequencies with a persistent screen scope, as explained under crystal detection (vi) iii)  Radio frequency o s c i l l a t o r . A standard tuned plate tuned grid o s c i l l a t o r was  21  b u i l t to operate at 8 6 kc.  The output coupling gives a variable voltage  up to 1 volt since a fraction of a volt i s necessary for radio frequency modulation of the klystron for accurate reproduction of the absorption l i n e s . The double modulation method i s described i n the experimental procedure. iv)  Attenuation. Two attenuators were bought from de Mornay Budd.  One i s a standard 11 decibel, tlie other i s a variable calibrated attenuator to 3 5 db. I t has been found preferable to attenuate the o s c i l l a t o r signal rather strongly, and then use high amplification after detection.  I f the input power i s too high, saturation broadening occurs.  In addition, the signal t o noise ratio of the crystal has an optimum value at a certain low power l e v e l .  The crystal noise seems to increase  more than the detected signal at high power levels, whereas the signal becomes smaller than the noise at too low power levels. v) Waveguide absorption c e l l . *  The absorption c e l l consists of two five feet sections of 1 . 2 5 cm waveguide ( 2 3 , 0 0 0 - 2 7 , 0 0 0 mc) with cross section. It i s gold plated to prevent corrosion. For convenience a U bend i s placed halfway along the guide to bring the tunable crystal mount up to the other controls. The guide i s closed at both ends with thin mica windows, as described i n section B, and a short s l i t cut along one side for evacuation and f i l l i n g . There i s an optimum length of waveguide to give maximum sensitivity (for measurement of small absorption coefficients) as calculated by Hershberger ( 1 6 ) . I f the c e l l i s too short, l i t t l e power w i l l be absorbed by the gas; i f too long, the losses i n the  22  waveguide become excessive. In order for the change i n power reaching the crystal to be a maximum at an absorption l i n e , the optimum length for the c e l l may be shown to be that where the power reaching the crystal has f a l l e n to l/e of the incident power at beginning due to waveguide losses.  This occurs when / = i - where OL i s the power absorption ««-  C  C  coefficient which accounts for losses i n the guide walls or i n any d i e l e c t r i c material.  For copper waveguide at 1.25 cm. the optimum  length i s about 10 metres.  However, the function which determines the  point of ^ R v ^ ,* has a broad maximum: the 10 feet used here does not cause an appreciable decrease i n s e n s i t i v i t y . vi)  Crystal detection. The crystal diode i s the s i l i c o n 1N26. We have  bought tunable crystal mounts. The input power on the crystal i s held well below the burnout value by the attenuators. output goes to a radio frequency amplifier.  The crystal  Crystal noise during  detection i s high. I t i s necessary to consider how t h i s noise may be reduced since i t greatly decreases the sensitivity of the spectrograph. "When detecting a small repeated signal on top of a constant microwave power l e v e l , the crystal noise i s inversely proportional to frequency. For a small frequency interval A)/, the noise electromotive force developed effectively i n series with the crystal i s e f r k ^  . I  n  the method of single modulation (discussed l a t e r ) , the t o t a l noise i s calculated by adding these emfs quadratically over the -whole frequency band between upper and lower l i m i t s determined by the audio amplifier band width.  J  u  17  23 Thus the noise i s independent of the frequency of the sweep voltage when only singly modulated, because both of the sweep frequency. e  and  w i l l be multiples  In double modulations -  2  kB  where B i s the band width of the radio frequency amplifier, since Po (rf modulation frequency) i s almost constant compared with the small band width centred at V . Therefore the crystal noise level can be 0  made much smaller i n the double modulation method by taking from the crystal only a small band of frequencies at.radio frequency. Since a l l frequencies occurring i n the radio frequency signal must be multiples of the low sawtooth frequency, the band width necessary to reproduce the signal w i l l be proportional to the sawtooth frequency which i s therefore a means of reducing the noise level.  Sweep frequencies of 1 cps have been used  by some researchers t o improve sensitivity i n t h i s way. vii)  Radio frequency amplifier. The radio frequency amplifier contains three tuned  stages of amplification with automatic volume control, and a diode detector.  The gain i s 1 0 , and the band width 1 0 kc.  I t i s tuned  to 1 7 2 kc to receive the second harmonic of the o s c i l l a t o r frequency the purpose of this i s simply to increase the signal to noise ratio at the crystal.  I t s input i s matched to the c r y s t a l , the output goes to a  scope. viii)  Frequency measurement.  A calibrated transmission type tunable cavity wavemeter from de Mornay Budd i s accurate to four figures at 2 5 , 0 0 0 Mc. Another project being completed i n t h i s department i s the construction  2k  of a microwave frequency standard. A 200 kc temperature controlled quartz crystal i s multiplied and mixed with a variable accurate signal generator to give a continuously variable frequency standard at 25,000 mc. This standard w i l l be accurate to s i x figures. B. Vacuum technique. A block diagram of the vacuum system i s shown on the following page. A mercury diffusion pump i s used t o evacuate the waveguide absorption c e l l .  A P h i l i p s and Pirani guage give continuous  pressure readings over the required range.  The waveguide i s sealed at  the two ends with thin mica windows. I t was found that beeswax and rosin i s most convenient for sealing these windows to the guide.  The U  bend halfway was completely sealed from the outside with low vapor pressure Apiezon sealing wax. A brass block was soldered onto the s#lit i n the waveguide; the glass tubing from the pump i s sealed into a hole d r i l l e d i n the block, again with Apiezon wax. The gas f i l l i n g system consists of a 3 gallon reservoir bottle and a p a r t i a l l y closed off stop cock which feeds into the waveguide at the same point at the pump. The bottle i s evacuated, then f i l l e d with several cms of gas.  The stop cock inner bore i s  blocked to halfway with a low vapor pressure wax. The open half i s turned toward the gas supply, then turned through 180° so that a very small volume of gas at several cms pressure i s released t o the much larger volume of waveguide. The pressure i n the guide may thus be regmlated from .01 micron to 10 micron i n small steps. The pump i s closed off to make a static system i n the guide at constant pressure for any length of time during which absorption measurements may be made. The minute amounts of gas thus used are not sufficient to injure the gaages or forepump. So f a r the i n i t i a l gas supply has been anhydrous  BLOCK DIAGRAM OP VACUUM SYSTEM WINDOW  MICA  -TP—  3<Z TWO  5'  X MICA WINDOW  SECTIONS  OF WAVEGUIDE  3C BRASS  BLOCK  =0  =0 PHILIPS GAUGE PIRANI GAUGE  » J 1 1) 1 URY :ETER  wen HAKOi  3 GALLON BOTTLE GAS RESERVOIR!  ZE  MERCURY TRAP  MERCURY DIFFUSION PUi.;P  S T O P COCK . SEALED END  POREPU:.'.P  GAS SUPPLY  ammonia only. other gases.  The system w i l l , however, be satisfactory f o r most  26  IY* EXPERIMENTAL PROCEDURE A.  Single and double modulation methods. Although the double modulation method i s used here,  i t i s an added improvement to the single modulation method, so the l a t t e r w i l l be described f i r s t .  The klystron i s frequency modulated  by applying the low frequency sawtooth voltage to the reflector electrode.  The modulated microwave power passes through the attenuator  and waveguide absorption c e l l to the crystal diode detector. The crystal output passes through an audio amplifier to the v e r t i c a l plates of a scope to be used for viewing absorption. The horizontal deflection of the scope i s obtained directly from the sawtooth voltage. Since the klystron frequency i s proportional to the sweep voltage, the scope shows a graph of absorption versus frequency. The absorption lines are much sharper than the gradual change of the contour of the mode of o s c i l l a t i o n , so that the mode may be cut out by a high pass f i l t e r before the amplifier, or, instead of a f i l t e r , two differentiating c i r c u i t s at the amplifier w i l l pass only the highest frequency components. Two are necessary t o give a symmetrical pattern almost indentical to the original line shape.  Reflections i n the guide are also broad, low frequency  signals and are eliminated by the above devices. The limitation i n sensitivity of this method i s due to the r e l a t i v e l y high crystal detection noise at the low frequency. The single modulation method was t r i e d here f i r s t with a three stage audio amplifier and a high pass f i l t e r with cutoff at 100 cps.  I t was not successful because the high gain amplifier  distorted the signals, and the f i l t e r introduced further distortion.  In addition, more careful design i s necessary to eliminate blocking of the amplifier tubes. A better system appears to be a three stage audio amplifier with a differentiating c i r c u i t between each tube.  The c i r c u i t  constants must again be chosen carefully t o prevent distortion. In addition to the low frequency sweep used i n the single modulation method, a small radio frequency sine voltage i s also applied to the reflector for double modulation.  This system i s now  being used here, and a block diagram i s found on tine following page. The radio voltage sweeps over a small frequency range which i s gradually moved acros s the mode by the low frequency sawtooth.  Thus the power  received at the detector becomes modulated by the radio frequency, so that, after detection, a radio frequency amplifier i s used i n place of an audio amplifier.  After amplification the radio frequency signal  i s detected and placed on the scope to give a trace of absorption versus frequency as before. Since the effect of the radio frequency modulation and detection on the absorption i s similar to differentiation, the low frequency mode contour and reflections do not appear very large at the output. However, the beginning and end of the mode are usually sharp enough to give strong signals: these are useful as markers of the position of the mode. The greatly increased detection frequency over the siggle modulation method increases the signal to noise ratio at the crystal diode considerably. In t h i s experiment the o s c i l l a t o r i s at 86 kc and the radio frequency amplifier i s tuned t o the second harmonic, 172 kc. Oscillators at 172 kc, 57 kc and 1+3 kc were also tested to observe the effect of the f i r s t , third and fourth harmonic detection on the l i n e shape, but the best results so f a r have been obtained at the second harmonic.  BLOCK DIAGRAM OF MICROWAVE SPECTROGRAPH  R.E. OSCILLATOR  POWER SUPPLY  KLYSTRON  SAW TOOTH OSCILLATOR  PUMP  ATTENUATOR - WAVE GUIDE  J CRYSTAL DETECTOR R .F. AMPLIFIER  OSCILLOSCOPE.  The low frequency voltage i s variable, but usually held at 5 - 1 0 volts since a small klystron frequency sweep permits a small band width f o r the amplifier and hence less noise. variable up t o several volts.  The radio frequency voltage i s  I t must be sufficiently small that i t  sweeps across only a fraction of the absorption line i n one cycle, because the r f output shape depends on the size of this voltage as well as the original shape of the l i n e .  The effect of various voltages on  line shape i s shown i n the results. To sweep over a spectrum, the klystron i s tuned mechanically from i t s lower to upper l i m i t of o s c i l l a t i o n .  As the  klystron i s tuned i n small steps (the intervening frequencies are covered by the width of the mode), the t o t a l length of the waveguide system must be adjusted each step for maximum output by the tuning plungers at each end.  The 2K33 :klystron w i l l o s c i l l a t e from 2 2 , 0 0 0  to 2 5 , 0 0 0 Mc or further ,in t h i s way.  A brass block and screw with  d i a l was constructed to f i t on the tube for tuning by hand, and i s shown i n the pictures of the apparatus on the following pages. The f i r s t plate shows a l l the electronic and vacuum equipment. The microwave plumbing i s seen better i n the close-up following.  At the  front are the klystron and attenuators leading to the waveguide! the crystal detector mount i s d i r e c t l y behind at the other end of the waveguide. The anplifier (rf) and high voltage control panel are also shown. The connection from the waveguide t o the glass evacuating and f i l l i n g system is. seen i n one corner. .The contour of the mode i s not completely cut out by the double modulation system.  In addition to the expected sharp  signals at the beginning and end of the mode, the shape of the whole  29 mode i s not entirely flattened out. When absorption lines appear on a slope, they become distorted.  The double modulation method does,  however, completely cut out reflections, because these are very broad signals and therefore have no high frequency components. A wave reflected from the end of the crystal mount, the mica windows, or U bend w i l l pass back and forth i n the waveguide. This path length w i l l cause the incident and reflected waves to add i n phase at some frequencies to form standing waves, but to cancel at other frequencies. Thus a standing wave pattern should appear as background on the absorption versus frequency graph on the scope. However the pattern i s very wide except for very long absorption paths so that the signal can not pass through the r f amplifier. In our waveguide of 1 0 feet, a complete cycle of reflections from one maximum to the next would cover about 5 0 Mc variation of the klystron frequency. The effects of pressure and saturation broadening have been discussed i n the theory.  Both were observed here.  I t was  found necessary to measure absorption below . 0 1 mm pressure i n order to resolve "the ammonia lines.  The gas pressure i s easily regulated  as previously explained. At higher pressures the double modulation method i s not so useful since the lines are too broad.  At low pressures,  saturation broadening i s observed unless the input power i s s u f f i c i e n t l y low.  The input variable attenuation of k5 db i s high enough so f a r to  prevent t h i s effect.  i  30  A.  V. RESULTS. Ammonia inversion lines. A l l the ammonia lines i n the region 23,000 -  2lj.,700 Mc have been found and i d e n t i f i e d .  Their frequencies have been  measured by Good and Coles (13) and Strawdberg et al (22) more accurately than i s yet possible here.  A typical l i n e with satellites due to nuclear  quadrupole coupling i s photographed from the oscilloscope and shown i n figure 1 on the following page. This is -the general appearance of the lines at second harmonic detection. At large J,K values the hyperfine structure becomes too small to observe; the s a t e l l i t e s were seen here up to 5,5.  They could not be observed on the weakest l i n e s , although  of low J,K values, partly because insufficient radio frequency amplification before the diode detector causes small signals to be detected quadratically, and partly because the noise level has not been reduced to the absolute minimum. B.  Effect of harmonic detection on line shape. The radio frequency modulated signal may be amplified  and detected at the fundamental or at the harmonic* frequencies. 'When the radio frequency modulation voltage sweeps across fen absorption l i n e , the size of the fundamental signal i s proportional to the rate of change of absorption (i.e. the slope of the l i n e ) .  Therefore the output at this  frequency should have the shape of the line differentiated once.  The  envelope of this signal, after detection, is that seen on the scope there i s a dip at the central frequency of the l i n e . twice the fundamental frequency  I f detection i s at  (second harmonic), the signal expected  i s the absorption line differentiated twice;  at the t h i r d harmonifi i t  appears differentiated three times, etc.  These expected line shapes may-  be calculated from an analysis of the effect of double modulation on the absorption.  I f the detection i s linear, the odd harmonics have a zero  amplitude at the centre of the line with a sharp discontinuity of slope. The even harmonics have a maximum at the centre.  If the signal reaching  the detector i s small, the detection w i l l be quadratic.  In the case of  odd harmonics, the consequent mixing then causes a small signal at the centre.of the line so that there i s a smooth dip with positive amplitude instead of a sharp cusp at zero level.  Figure 2 represents detection at  the fundamental (odd harmonics) and may be compared with figure 1 , detection at second harmonic. The even harmonics s t i l l have maxima at the centre but -the small hyperfine structure i s decreased. Figures 3 and k represent the same line but 1 2 db attenuation at the input has been added for figure 1+. Thus reduction of the power level has placed the s a t e l l i t e s at ihe quadratic detection l e v e l and they are much more reduced than the main l i n e .  The sidebands on the second harmonic picture  were suppressed i n figure 1 , by using a small radio frequency voltage, but may be seen i n figure 5 .  The line shapes at t h i r d , fourth, f i f t h ,  and sixth harmonics were also investigated on the scope with a variable oscillator.  As expected, the number of side bands continually increased,  while a l l odd harmonics had a dip, and even harmonics a maximum at the centre of the structure. However, the amplitude of the signal decreases as the number of the harmonic increases, so there i s no advantage i n working at higher harmonics. The f i r s t harmonic i s the largest, and therefore should have relatively laarger s a t e l l i t e s since the signals could be kept more easily above, the quadratic detection level of the diode.  However, one  32  problem arising at fundamental detection i s that the dip at the centre of the main line does not always show up. When the line occurred along a slope of the mode contour, one of the' sidebands was suppressed and the line appeared single.  For frequency measurements the central frequency  must be sharply defined and i t would be wrong to use the top of the single l i n e .  To overcome this d i f f i c u l t y , a double differentiating  c i r c u i t may be added to the radio frequency amplifier.  Then a sharp  signal should appear at the position of ine slope discontinuity at the centre of the line regardless of the distortion of the sidebands due to the mode contour. I f the sharp point has been smoothed out by quadratic detection, then the doubly differentiated signal w i l l be smaller. However, i t s position w i l l s t i l l be independent of the slope of mode, so that frequency measurements may be made accurately.  This method of detection  w i l l be t r i e d here i n the future. C. Effect of radio frequency modulation voltage on the line shape. If the radio frequency modulation voltage i s so small that i t sweeps over only a fraction of the line width per cycle, then the line shape i s reproduced without distortion.  I f , however, the frequency  sweep i s of the same order of magnitude as the l i n e width, then the structure i s broadened and distorted.  The dependence of the width of the  observed signal structure on radio frequency amplitude may be easily shown. Let the absorption line f a l l t o zero amplitude at f i n i t e frequencies f  1  and f , so that the difference gives the line width a = f - f-j. 2  If a  linear sweep only i s applied to the klystron, then absorption appears only during the time interval required to sweep from f^ to f^. I f a small radio frequency voltage i s added, the klystron frequency w i l l reach f^ at an earlier time represented by the frequency sweep of one half cycle  33  of the radio frequency, and the klystron frequency will s t i l l be at f^ at a later time when radio frequency is furthest negative. Therefore the absorption signal appears to be of width a -f»2b where b is the amplitude of the radio frequency (in terms of frequency sweep). The pictures taken at second harmonic detection show this broadening effect due to increasing radio frequency sweep voltage, and also the distortion effects which occur in this case. Figures 3 ~ 6 were all taken at sufficiently low pressure to eliminate collision broadening. Figure 3 has a small radio frequency sweep, and the input power i s high enough to show the satellites. Since the radio frequency sweep i s low, i t does not broaden the line appreciably, but, in this case, the line i s broadened by the high power level - saturation. In figure h the input power has been reduced by 1 2 db, so that the satellites, quadratically detected, are too small to observe. The radio frequency sweep is not changed in figure U» Very small sidebands are distortion introduced by the radio frequency sweep as mentioned in section B. In figure 5 the radio frequency voltage has been increased, and the 1 2 db retained. The width of the structure is observed to increase over figure k as discussed above. In addition, further distortion occurs: the two sidebands, formerly very small, have increased. As the radio frequency sweep is increased further in figure 6, the width increases, and the two sidebands become larger than the central band. Figures 3 and U demonstrate saturation broadening. When the microwave power used for the line of figure 3 is reduced by 12 db, the line becomes narrower as in figure 1+. The amplification of the scope after detection was increased. This narrow line was maintained as a reference for figures 5 and 6, when the radio frequency  sweep was increased to show i t s effect on the width of the structure. It may be noted that the lines are well above noise level i n general.  VI.  CONCLUSIONS.  The 1.25 cm spectroscope has been tested with ammonia and found satisfactory i n most respects. A l l of the ammonia lines i n the frequency sweep of our klystron were detected and identified.  The second harmonic detection i s more accurate  at present than the f i r s t harmonic, but the sensitivity of the system would be increased by changing to the f i r s t harmonic and using differentiating c i r c u i t s as discussed i n the results. The limitations on the magnitudes of pressure, input power, and radio frequency voltage have been indicated.  At present  the accuracy of frequency measurements i s only to four figures, but further work i s being done here on a microwave frequency standard.  In order to increase the size of the hyperfine structure  more radio frequency amplification i s necessary to make the detection linear.  36  BIBLIOGRAPHY. 1. S.H. Autler, G.E. Becker, J.M.B. Kellogg ... Phys Rev 69, 69k, I9I+6. 2.  J. Barden, CH. Townes ... Phys Rev 73, 97,  3.  R. Beringer ... Phys Rev 69, 693, I9J4.6.  19(48.  70, 2 1 3 , 1946.  1+.  B. Bleaney, R.P. Penrose ... Proc Phys Soc 5 9 , 1+18, 1947. 60,  83, 19I+8.  5. C E . Clecton, W.H. Williams ... Phys Rev 1+5, 23!+, I93I+. 6.  D.K. Coles, W.E. Good ... Phys Rev 70 , 979, I9I+6.  7.  B.P. Dailey ... Phys Rev 72, 8l+, 191+7.  8.  B.P. Dailey, E.B. Wilson ... Phys Rev 72, 522, I9I+7.  9/  T.W. Dakin, W.E. Good, D.K. Coles ... Phys Rev 71, 61+0, I9I+7.  10.  D.M. Dennison ... Rev Mod Phys 3, 280, 1931. 12, 175, 191+0  Phys Rev 31, 503, 1928. 11.  B.T. Feld ... Phys Rev 72, 1116, I9I+7.  12. W.E. Good ... Phys Rev 6 9 , 539, 19U6. 70, 213, 191+6. 13.  W.E. Good, D.K. Coles ... Phys Rev 71, 383, 191+7.  11+.  W. Goody, M. Kessler ... Phys Rev 71, 61+0, 191+7. 72, 61+1+, 191+7.  15.  W. Gordy, J.W. Simmons, A.G. Smith ... Phys Rev 72, J>hk> 191+7.  16. W.D. Hershberger ... J l Appl Phys 19, 1+11, I9I+8. 17. G. Herzberg ... "Molecular Spectra and Molecular Structure" Vol. 1 and 2, Chapter 1 18. R.H. Hughes, E.B. Wilson ... Phys Rev 71, 562, I9I+7. 19.  C.K. Jen ... Phys Rev 72, 986, I9I+7.  Van Nostrand.  Bibliography .. continued. 20.  J.R. Pierce, W.G. Shepherd ... B e l l Sys Tech J l 2 6 , 4 6 0 , 1947.  21.  J.W. Simmons, W. Gordy ... Phys Rev 7 3 , 713, I9J48.  22.  M.W.P. Strandb'erg, R. Kyhl, T. Wentink, R.E. Hillger ... Phys Rev 7 1 , 3 2 6 , 19^4-7.  23.  C.H. Townes,S.R. Merritt ... Phys Rev 7 0 , 558, 1946.  2l+.  C.H. Townes ... Phys Rev 7 0 , 6 6 5 , 1946.  25.  C.H. Townes, A.N. Holder, J . Bardeen, F-.R. Merritt ... Phys Rev 71, 6i)4, 1947.  26.  C.H. Townes, A.N. Holder, F.R. Merritt ... Phys Rev 72, 5 1 3 , 1  27.  J.H. Van Vleck, V.F. Weisskopf ... Rev Mod Phys 17 , 227, 1945.  28. R.J. Watts, D. Williams ... Phys Rev 7 2 , 2 6 3 , 1947. 7 2 , 1122,  1947.  


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