EXPERMENTAL RESULTS WITH ATOMIC HYDROGEN STORAGE BEAM SYSTEMS*

Helmut Hellwig and Howard E. Bell Atomic Frequency and Time Standards Section National Bureau of Standards Boulder,Colorado 80302 USA

Summary hydrogen atoms1 is an appealing design [2], [S]. For such a device, operating far below oscillation threshold, Two atomic hydrogen storage beam devices are the cavity pulling factor F1 is very favorable [l], [6]: described, one based on the detection of hydrogen atoms, the other on the detection of changes in the microwave signal due to the hydrogen resonance.

Electron bombardment ionization is used for the detection of a omic hydrogen. Detector efficiencies of up to 5 X IO-‘ are measured using a method which is where QC and Q are the cavity and line quality factors, 1 based on the study of pulse decay at maser oscillation respectively.However, an efficient, low-background threshold. Quantitative measurements of the atomic hydrogen detector is essential to exploit the advantage hydrogen beam intensity as a function of source pres- given by hydrogen atom detection as compared to the sure and RF discharge power are given. The overall detection of the microwave power. efficiency of the atomic hydrogen detection in the 8 hydrogen storage beam device is estimated at about 10- . For a passive device, based on detecting the Ways to increase the efficiency are indicated. microwave signal which is transmitted through the cavity containingthe hydrogen atoms, J. Viemet, c. Audoin, The second device, which is based on microwave and M. Desaintfuscien have shown [l] that the cavity detection, closely resembles a hydrogen maser oscil- pulling factor F2 is lator with a low-Q cavity below oscillation threshold. Cavity pulling can be reduced to a point where environ- mental temperature fluctuations limit the stability mainly via the second-order Doppler effect. A quartz crystal oscillator is locked to the hydrogen hyperfine transition using the dispersion of this resonance. Locking to the Here, Ly is a gain parameter [for negligible saturation dispersion feature eliminates the need for frequency thegain is equal to (1 - CY)-’ atresonance]. Information modulation in order to find line-center. The stability of on the hydrogen line can be obtained by detecting either the frequency standard was measured against crystal the microwave intensity or the dispersion signal. Since oscillators and cesium beam frequency standards; the dispersion signal contains the frequency information, stabilities of 4 X wererecorded for sampling times its use avoids the need for frequency modulation of the of 30 seconds and of 3 hours. slaved quartz crystal oscillator; however, the hydrogen flux has to be modulatedin order to subtract--in first KeyWords (for information retrieval): Atomic approximation- -the dispersive characteristic of the hydrogen beam, Atomic hydrogen generation, Dispersion, microwave cavity. Frequencystability, Frequency standard, Hydrogen atom detection, Hydrogen flux calibration, Hydrogen In the following, WC report in Part 1 our results maser, Relaxation measurements, Spinexchange. with a system employing the detection of hydrogen atoms, and in Part 2 we discuss the design and performance of Introduction a system employing microwave signal detection.

As compared to the hydrogen maser oscillator, a 1. HydrogenAtom Detection passive hydrogen standard offers a significant reduction in cavity pulling [l], [2]. This, together with the 1. l Beamintensity calibration elimination of the requirement to obtain self-oscillation, offers considerable design advantages, might lead to In order to evaluate the efficiency of an atomic improved long-term stability, and possibly offers greater hydrogen detector it is necessary to know the hydrogen flexibility to evaluate the frequency bias due to wall- beam intensity. We used a hydrogen maser oscillator to collisions of the stored hydrogen atoms (wallehift)[3].

Based on certain theoretical considerations, a hydrogen storage beam tube employing the detection of

l Experiments with stored beams have been done earlier; *Contribution of the National Bureau of Standards, for example, an experiment using cesium is described not subject to copyright. in Ref.[4].

242 calibrate the intensity of the hydrogen beam. We then (d) the maser was brought far below oscillation used the beam system of the maser oscillator to evaluate threshold by detuning the microwave cavity, yz was the performance of our hydrogen atom detector.2 measured by observing the pulse decay (Fig. la); (e) the hydrogen beam intensity was reduced to a level The beam intensity at oscillation threshold of the where no spin-exchange occurred, the pulse decay was hydrogen maser [7] is given by againmeasured (Fig. lb). and yZsE wasobtained as the difference between this measurement and the one according to (d) above; (f) Ith was calculated using eqs (3) and (5).

We used this procedure to measure the beam 22 withc E hVf8r p RV, where V isthe volume, Q the intensity as a function of the atomic hydrogen source loaded quality facfor, and r] the filling factor [7 J of the parameters. The source was a pyrex glass bottle with cavity; p is the magnetic dipole moment of the transi- a collimator opening consisting of a bundle of channels tion,h is Planck'sconstant, and y therelaxation with about 40 pm diameter each and a length of 0.6 mm. constant. One has to distinguish caPefully between the The total diameter of the bundle was 1. 3 mm. The relaxation of the population difference described by y dissociating discharge was driven by a ZOO-MHz RF 1' and the relaxation of the oscillating magnetic moment generator. Figure 2a shows that the beam intensity 4 described by y2. It can beshown that [8] depends linearly on the source pr sure at constant RF power, and reaches more than lof* atoms per second. It should be noted that typical beam intensities for 2 Yo = YlY2 hydrogen maser oscillator operation are about lo1 atoms per second. Figure 2b depicts the dependence of the beam intensity on the RF power of the discharge at where y1 and y2 are each the sum of all corresponding constant source pressure. This curve essentially shows relaxation processes. We now assume that all relaxa- the degree of dissociation into atomic hydrogen and tion processes other than hydrogen-hydrogen spin indicates a leveling off of the dissociation with higher RF exchangecan be described by y = and that for power. spin-exchange y = 2yzsE Tk!s allowstous 1SE rewrite eq (4): The atomic hydrogen detector was a commercial residual gas analyzer, i.e., an electron bombardment ionizer followed by a quadrupole mass spectrometer and 2 an electron multiplier. The ionizer emits a sheet of electrons, about 2 mm high (along the beam axis), across the hydrogen beam. For highest ionization efficiency, If y is measured, the threshold beam intensity the electron voltage is chosen to yield the maximum can be ca1:ulated from eq (3) since the constant c is ionization cross-section for hydrogen (approx. 70 V). known.3 The relaxation constants can be measured by We measured the electron multiplier gain and obtained observing the decay of the radiation intensity in the from the comparison between the detected current and maser cavity after applying a suitable, stimulating the calibrated hydrogen beam intensity (corrected for microwave pulse. The maser cavity was equipped with geometrical factors, and the presence of atoms in the two coupling loops; the pulse was applied to one, the F = 1, m = 1 level) an efficiency of 1.5 X 10-5 at an radiative decay observed at the other using a three-stage electron emission current of l mA. The efficiency in- superheterodyne receiver. The pulse was generated by creased near1 linearly with the electron current to Y 5 pulsing a frequency synthesizer whose frequency (about reach 5 X 10- at maximum emission current (3 mA). 20 MHz) was subtracted from quartz crystal controlled 1440 MHz to match the atomic hydrogen resonance 1.2Operation of thebeam frequency. Two important items must be considered: (1) When pulsed, the maser must be far below oscillation The hydrogen storage beam tube system which we threshold.(2) Only y is directlyobservable; in order used is shown in Fig. 3. A hydrogen maser oscillator to obtain y [see eq (5)4 one must also determine y was modified by adding a second output opening to the 2SE' The follow& measurement procedure was therefore storage bulb, followed by a dipole magnet as the second established: (a) the maser was made to oscillate; state selector and the atomic hydrogen detector which (b) the maser was tuned to maximum oscillation ampli- was positioned at the proper deflection angle. A beam tude; (c) the maser oscillator was brought as accurately stop was placed in the center of the bulb to prevent the as possible to oscillation threshold by introducing a direct passage of the hydrogen beam. Differential suitable inhomogeneity in the axial DC magnetic field in pumping decoupled the detector vacuum chamber from order to fulfill the conditions on which eq (3) is based; themain vacuum chamber byabout a factor of In operation, the vacuu-Toat the detector was measured to beapproximately 10 torr (m 10-8N/m2). 2Care has to be taken that identical geometries are used in the maser oecillator mode and in the particle detec- The beam intensity is always measured after the tion mode. In our experiments we always used a 4-mm aperture mentioned in footnote 2. Also, it must be diameter circular aperture at the entrance of the noted that we are only observing the difference in the storage bulb or the detector entrance, respectively, intensities of the F = 1, m = 0 and F = 0, m = 0 states. and always positioned at a distance of 45 cm from the The massresolution of the mass spectrometer was exit of the state selector magnet. chosen to be as low as possible in order to increase We first tested our system with a direct hydrogen Fig. 5 are the isolators, necessary to decouple the beam (beam stop removed). A microwave signal was circuits connected to the output of the microwave cavity swept across the hydrogen resonance and the detector from those at its input, and the phase-shifters. current measured. The resulting resonance curve with a linewidth of about 10 kHz is depicted in Fig. 4. A post- The output of the phase-sensitive detector is detection bandwidth of about 1 Hz was used. The ionizer proportional to the imaginary part of the total complex efficiency was set at-about 2.5 X cavity response. If the cavity contains state-selected hydrogen atoms and is tuned to their transition frequency, For the case of storage of hydrogen in the bulb we the hydrogen resonance is observable at the output of the estimated an efficiency of inthe reformation of an phase-sensitive detector as a phase-change due to the exiting beam, i. e. , we expected a beam intensity of corresponding dispersion. In order to obtain the fre- about lo9 atoms per second at the detector with an initial quency pulling factor of eq (2). i. e., in order to subtract beam intensity at the input of the storage bulb of lo1' the cavity response, we modulate the hydrogen beam atoms per second. Thus, with a detector efficiency of intensity at a relatively low rate, e. g., 1 Hz. Theoutput aboutthe detected part'cle count was expected to be of the phase-sensitive detector which contains the phase marginalwith only about 104 atomsper second. Never- information about the hydrogen resonance (now modulated theless, we operated such a complete system (Fig. 3) also at 1 Hz) is fed into a synchronous detector ("lock-in and detected a microwave response in the beam intensity amplifier"). Its amplified and filtered output serves as with a signal-to-noise ratio of about one to one at 100 S the correcting voltage for the crystal oscillator. The averaging time. The limiting noise was apparently shot locking criterion is thusa nulling of the phase-change noise due to an atomic hydrogen background. This back- under modulation of the intensity of the hydrogen beam ground is produced by dissociation of residual, hydrogen- entering the cavity. The hydrogen beam apparatus containing gases in the system as wellas molecular resembles closely a conventional hydrogen maser oscil- hydrogen which diffuses from the source to the detector lator except for the lower cavity-Q which places it region or, more important, is produced by the hot metal significantly below threshold (see Section 2. 2). components of the detector (mostly stainless steel) itself. We tried a more efficient ionizer with a space charge At this point it should be noted that in storage limited electron emission current of 50 mA. The effici- devices such as ours, the strength of the signal due to encywas measured to be 5 X but itsapplication as the hydrogen atoms as well as the associated linewidth a detector brought no advantage because of its corres- will increase as the interrogating power increases; there pondingly larger background signal. A reduction in the is no optimum power [6],[93 as in beam tubes (see electron accelerating voltage of the ionizer will reduce Appendix). h the Appendix we show that a typical power thebackground, However, the ionization cross-section P can be defined for which the transition probability is of hydrogen diminishes correspondingly, and the signal l,f4 and the linewidth is to noise remains nearly unchanged. 6

We judgedfromtheseresults that a majoreffort (6) W=t Jzn ye on the design of the exiting beam system (beam optics and detector) was called for. In view of our limited resourceswe decided to temporarily discontinue this where y isthe escape relaxation constant for the stored work and to proceed with the alternate detection method: hydroge: atoms. All other relaxation processes are m icro w ave detection. here assumed to be insignificant.assumption beThismicrowave assumeddetection. to here is a good approximation if relatively short escape relaxation M ic row av e Detection times are used (see below). (see used2. areMicrowave Detectiontimes

2. 1 Apparatus 2. 2 Experiments

The block diagram of our apparatus is depicted in We used in our first experiments a storage bulb of Fig. 5. The 5-MHz signal from a quartz crystal oscil- 10 cm diameter with a relatively short excape relaxation lator is multiplied by a factor of 288 and mixed with a time (calculated) of 0.1 S. The corresponding linewidth signal from a synthesizer (about 19. 594 MHz) to gener- at the typical power Pt follows from eq (6) as W = 4.5 Hz. We operated at beam intensities which are ate a signal at approximately the hydrogen transition t frequency. This signal, which can be swept across the comparable to those used in hydrogen maser oscillators. hydrogen resonance by sweeping the synthesizer fre- From previous experience we know that the cavity-Q for quency, is transmitted through the microwave cavity and an oscillation threshold beam intensity Ith at storage mixed again with the signals from the multiplier and times of about 1 S is approximately 30 000. Since the synthesizer. Amplification before the last miving yields oscillation threshold condition depends on the square of a good output at the last mixer (phase-sensitive detector) the storage time [eq (3) J, the (fictitious) threshold thus avoiding possible limitations due to low frequency cavity-Q for our device operating at beam intensities of noise (flicker noise) in the output of the phase-sensitive about 30 isapproximately QC th (J 90 000, We re- detector and in the circuits following it. Not shown in duced our cavity-Q to QC % 2500' by over-critically coupling to the output load of the cavity. Thus, our ~ system was operating at the fraction We obtained a maximum in the signal to noise at about (Y = Qc/Qc, th W 0.028 of oscillation threshold. 23 V accelerating voltage, This maximum is about 2.5 times larger than the signal to noise at 70 V acceleratingvoltage. However, the ionizer efficiency at 23 V accelerating voltage is only about one-half of the value at 70 V.

244 From eq (2) we calculate the pulling factor to be Dispersion-locking of a crystal oscillator to the F p: 4 x 10-6. This is one order of magnitude less than atomic hydrogen hyperfine resonance resulted in a fre- in the case of a typical hydrogen maser oscillator. quency standard with a promising frequency stability Since environmental temperature fluctuations are the performance. The reduced cavity pulling factor may dominant cause for cavity frequency fluctuations, the lead to improved long-term frequency stability andfor to above pulling factor puts us close to a fractional fre- a simplified design of the apparatus as compared to the quencychange of 1 x perdegree kelvin for our hydrogen maser oscillator. The cavity pulling factor device due to its fused quartz ~avity.~ could be reduced to the p int where the second-order Dopplereffect (1.4 X perdegree) would determine The hydrogen dispersion signal, as measured at the requirements for thermal stabilization. The wall- the output of the phase-sensitive detector, is depicted in shift may become more conveniently evaluable; for this, Fig. 6. The horizontal scale is indicated on the figure; cavity pulling could be reduced further to allow changes the recording was made with a post-detection time con- of the shape of the storage bulb without the need for stant of s; thehydrogen beam was not modulated. retuning the cavity [ 111, [ 121 or perhaps with a simple A high-resolution recording of the output signal of the resetting of the cavity by external sensing of the detuning. synchronous detector is shown in Fig. 7. The horizontal scale is shown on the figure; a post-detection time con- The spin exchange frequency shift enters explicitly stant of10 s was used. The hydrogen beam was as a frequency bias which must be evaluated and which modulated by turning the hydrogen discharge in the can be evaluated with the device described in this paper. source on and off at a l-Hz frequency. The linewidth of However, this bias is expected not to exceed a few parts about 5 Hz agrees with the predicted value. in 1013 for typical operating conditions [ 131, and its direct, precise measurement appears to be desirable in We operated the system as a frequency standard, view of some doubts about the total validity of the com- i. e. , we locked the crystal oscillator to the resonance, pensation of spin exchange shift by cavity pulling in the as shown in Fig. 5. The frequency stability was meas- cavity tuning procedure of the maser oscillator [ 141. ured against (commercial) cesium clocks used in the NBS time scale and against crystal oscillators. A Acknowledgements typical result is depicted in Fig. 8 where the square root of the two-sample Allan variance [ lO]is plotted The authors would like to thank Roxanne M. Pierce versus the sampling time. The circles are values and James A. Morgan for their dedicated help in con- obtained against a cesium clock; the triangles represent struction and measurements. We appreciate the assist- a measurement against a crystal oscillator. The best ance of David W. Allan in the frequency stability stabilities,with values of 4 X weremeasured at comparisons and stimulating discussions with Giinter sampling times of 7 = 30 S and of T = 3 hours. Kramer and Donald Halford which helped shape this Basically, Fig. 8 depicts the performances of a partic- paper. ular crystal oscillator and a particular cesium beam frequency standard. The instability due to the atomic Appendix hydrogen storage beam frequency standard does not show up, i. e., its performance apparently is equal to--or The probability density f(t) for an atom to stay possibly better than--the crystal oscillator and the for some time t in the storage bulb is given by cesium beam frequency standard in their respective ranges. - Yet f(t) = y e Conclusions 8 We have described hydrogen storage beam devices where ye is the escape relaxation constant. based on hydrogen atom detection as well as on micro- wavedetection. Theoretically, hydrogen atom detection This exponential distribution function leads easily leads to a device of superior performance; however, to the transition probability T for an ensemble of stored inefficient detection and high background so far have atoms [7]. prevented us from completing such a frequency standard. Nevertheless, the concept appears promising: Straight- forward improvements in the efficiencyof the beam optics and the detector to an overall efficiency of at least as well as a reduction in the hydrogen background, appearfeasible. Also, otherdetection principles could where be utilized, e. g., detection based on the comparatively high recombination energy of hydrogen. We plan to resume work along these lines.

Strictly, eq (7) cannot be completely true because we have a cutoff at very short times due to the physical In our experiments the cavity was not thermally necessity for the atoms to traverse the storage bulb controlled. at least once before escaping.

245 In eq (9), p is the magnetic dipole moment of the transition and H is the average microwave signal ampli- tude in the interrogation region. The power delivered by the atoms to the cavity is then nThw where n is the flux of atoms in the upper state minus tge flux of atoms in the lower state. We see that at resonance T has no maximum but approaches asymptotically T = 112 for arbitrarily large excitation (x - OD). The line will broaden with increasing excitation. From eq (8) we get for the linewidth

1 2 29 W = -(y +x) ne .

We define a typical microwave power P with a t corresponding perturbation parameter x and a linewidth t Wt by setting

2 x; = ye .

This leadsto T = 1f4 at resonance,and W t t dLn 'e Fig.l Radiative decay after pulsing,used for beam intensity calibration. (a) decay under oscillation thresh- References old conditions, (b) decay at reduced beam intensity for determination of thespin-exchange relaxation. Horizon- c11 J. Viennet, C. Audoin,and M. Desaintfuscien, tal scale: 0. 1 s per division. Proc. 25th Annual Symposium on Frequency

Control, Fort Monmouth, N. J., 337 (1971). .5- Available from Electronics Industries Association, Washington, D. C. H. Hellwig,Metrologia 6, 56 (1970). c21 .a - c31 For a listing of most experiments up to 1970 which involve the wallshift, see: H. Hellwig,R. F. C. Vessot, M. Levine, P. W. Zitzewitz, D. W. Allan, and D. J. Glaze, IEEE Trans. Instr, and Meas. .5 - IM-19, 200 (1970). MEASUREDAT BW RF-POWER c41 H. M. Goldenberg, D. Kleppner,and N. F. Ramsey,Phys. Rev. 123, 530 (1961). 0 l I I I 0 100 200 300 400 c5 1 H. Hellwig,Metrologia 6, 1l9 (1970). SOURCEPRESSURE (mtorr)- C61 J. H. Hollowayand R. F. Lacey,Proc. CongrGs Internationalde Chronom&rie, Lausanne, Vol. 1, 317 (1964). -t o'6:0.5

Kleppner, H. M. Goldenberg,and F. .v) c71 D. N. X Ramsey,Phys. Rev. 126, 603 (1962). 2 0.4- 4 N c81 H. Hellwig,Phys. Rev. 166, 4 (1968). ," 0.3- N. F. Ramsey,Molecular Beams. Oxford: - c91 > Clarendon 1956. p. 118ff. c y) 0.2- r W c101 D. W. Allan,Proc. IEEE 54, 221(1966); also c MEASUREDAT 100 rntorr z SOURCEPRESSURE J. A. Barnes et al., IEEE Trans. Instr. and - 0.1- Meas. IM-20, 105 (1971). P. E. Debdly, Proc. 24thAnnual Symposium on c111 012345678 Frequency Control, Fort Monmouth, N. 259 J., SOURCEDISCHARGE POYER (U)- (1970).Available from Electronics Industries Association,Washington, D. C. Fig. 2 (a) Beamintensity as a function of thehydrogen c123 D. Brenner, J. Appl.Phys. 41, 2942 (1970). pressure in the source; RF power held constant, (b) beam intensity as a function of the RF discharge power in the H. Hellwig, NBS Technical Note No. 387 (1970). c131 source; source pressure held constant. The numerical 141 S. B. Crampton, J. A. Duvivier, G.S. Read,and values for the pressure are uncorrected .readings of a E.R.Williams, Phys. Rev. A5, 1752 (1972). thermocouple gauge.

246 Fig. 3 Schematic of the hydrogen storage system with detection of atomic hydrogen.

Fig. 6 Hydrogen dispersion signal as measured at the output of the phase-detector (open-loop operation). No beammodulation. Recording time constant: S. Sweep speed: 5.6 Hz/s.

10kHz

Fig. 4 Hydrogen hyperfine resonance in a free hydrogen beam; obtained by hydrogen atom detection. Post- detectionbandwidth: 1 Hz.

Fig. 7 Hydrogendispersion signal as measured at the output of the synchronous detector (open-loop operation). Beam modulated at 1 Hz. Recording time constant: 10 S. Sweep speed: 0.022 Hz/s. c

t CORRECIIWG I YOLILGE

120 *HIv Fig. 8 Frequencystability of thedevice of Fig. 5 meas- ured against a crystal oscillator (triangles) and a cesium beam frequency standard (circles). The square root of the Allan variance 02(N, T, 7,B) is plotted where: Fig. 5 Block diagram of the atomic hydrogen storage number of samples fi = 2, deadtime T - 7 = 0, and beam frequency standard. Phase- shifters and isolation bandwidth B = 30 Hz. Thesampling time 7 is the devices not shown. variable, and y denotes fractional frequency fluctuations.

247