AN INSTRUMENT FOR MEASURING BETATRON RESONANT FREQUENCIES,

C. W. PottsArgonne National La.boratory

Argonne, Illinois

Summary Previous Techniques

An instrument has been developed to measure beta-tron tunes with a minimum of disturbance to normaloperation. In one mode of operation, the beam isdriven by a frequency sweeping voltage controlled os-cillator (VCO). The output of this VCO is comparedto (1-v) feedback from the beam in a phase-sensitivedemodulator. The dc output of this demodulator helpsto control the frequency of the VCO, thus closing aloop around the beam. At frequency coincidence be-tween the (1-v) feedback and the VCO, a pulse is gen-erated which stops the VCO frequency sweep andallows phase lock on the beam if desired. This pulsealso activa.tes measuring and digitizing circuitry torecord pertinent data at the instant of frequency co-incidence. Other modes of operation permit mea.sure-ment of, and phase lock to, unexcited or "na.tural"resonances.

Introduction

Knowledge of the a.ccelerator tunes and how theyvary with beam energy, beam position, dB/dt, etc.,is a powerful diagnostic tool in the hands of an a.ccel-erator physicist. Perha.ps more than any other accel-erator in the world, the Zero Gradient Synchrotron(ZGS) has be.nefited from the utilization of tune meas-urements as a guide to successful modifications.Vital focusing coils, called "end guards" were anafterthought whose design parameters were estab-lished by tune measurements. The radial and verti-call damping systems operate with time delayed beamfeedback to help control the size of the beam. One ofthe determining factors of these time delays is thechanging value of the tune during the accelerationcycle.

Any disturbance of the beam which is strongenough or reinforced often enough can cause a largeportion of the beam to exhibit a "coherent betatron'"oscillation. A sensing device, such as a radial dif-ference induction electrode2, can be used to senseradial coherent betatron oscillations. The signalsobserved are the proton bunch signals, which areamplitude modulated at a rate which is the differencebetween the betatron resonant frequency and the rota-tion frequency. This frequency is sometimes calledthe (1-v) frequency. As might be expected, if onedrives the beam radially at this frequency, large co-herent oscillations will result. These oscillationsmay grow until the beam is "knocked-out" of theaccelerator, therefore, the (1-v) frequency is alsocalled the "knockout" frequency and the symbol Fkois used.

'Work performed under the auspices of the U. S.Atomic Energy Commission.

While some accelerators use the main RF sys-tems3 to excite betatron oscillations, the designers ofthe ZGS had the foresight to install a large poweramplifier which could either be co.nnected to a ferritecore for radial beam excitation or to a set of deflect-i.ng plates for vertical excitation. This power ampli-fier and ferrite core is the heart of the horizontalbeam damper at the present time.

In the past, a gated signal generator has been usedin conjunction with this power amplifier and core.The gate would be open for a. few milliseconds whenthe beam was at the energy and position to be studied.The operator would then ma.nually vary the input fre-quency from pulse to pulse until some evidence of co-herent betatron activity was noted on the electrodesignals. The frequency to which the beam was mostse.nsitive was the Fko. While the accuracybf thismethod was not questioned, it was felt that automatingthis procedure might make measurements faster,less dependent on operator judgement, and in somecases compatible with normal high energy physics(HEP) operatio.n.

Concept

The electrode signals used for evidence of betatronactivity are heavily filtered to suppress beam bu.nchsignals, synchrotron oscillations, ring magnet rippleeffects, etc. The bandwidth of interest, 100 to350 kHz, is still wide enough so that noise makesvisual judgement highly subjective. A device such asa phase-sensitive demodulator, however, is ideal forlocating the fundamental frequency of a noisy signal.A phase-sensitive demodulator puts out dc voltagewhen its two ac inputs are of the same frequency.The magnitude of this dc voltage is proportional to themagnitudes and the phase differe.nce of the ac inputs.

The instrument bei.ng described in this paper,called the Tune Detector, employs a VCO and a de-modulator in a closed loop which includes the beamitself. The output of the VCO is one i.nput to the de-modulator a.nd the sig.nal from the beam is the other.The logic circuitry in the Tune Detector generates avoltage ramp on command. The voltage ramp is fedinto the VCO, thus causing it to sweep in frequency.When the VCO sweeps through the Fko being generatedby the betatron oscillations of the beam, the demodu-lator puts out a dc voltage. This dc voltage triggers a.compara.tor whose output pulse stops the frequencysweep. It is possible, of course, to let both demodu-lator voltage and the ramp volta.ge control the VCOoutput frequency. Then when the trigger pulse stopsthe ramp, the demodulator voltage controls the VCO.Since the demodulator voltage depends on the betatronoscillations of the beam, we now have closed the loop.If the necessary servo stability criterions a-re now

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met, the VCO will track the betatron oscillations ofthe bea.m and we ha.ve in communication's parlance a"phase-locked loop. " We also may use the frequencycoincidence pulse to start an instantaneous collectionof a.ll pertinent tune data..

The Tune Detector

The circuitry in the Tune Detector is so arrangedthat four different operating modes a-re possible. TheMode III operation will be explained in some detail.The differences in the other modes will be pointed outlater.

Mode III

Figure 1 is a. block diagram of the Mode III logic.The following describes the operating sequence. Theopera.tor selects the timing of the set pulse. The setpulse to FF1 starts the 50 ms timing period of M1.This starts the voltage ramp by the unclamping actionof CL1 and CL2 on integra.tor II. The voltage rampin turn starts the frequency sweep of the VCO. TheM1 pulse also energizes R1 and G2, thus switchingthe radial damper power amplifier from its normaldamping activity to that of a radial beta.tron exciter.By careful adjustment of P2, it is possible to createa measura.ble resonance without loss of a.cceleratedbeam. As the VCO a.pproaches the resonant fre-quency of the beam, the Fko feedback tends to slowdown the df/dt of the VCO. Diode D1 helps to keepthe demodulator feedback in the correct polarity toslow down the df/dt. D1 a.lso functions as a thresholdnoise gate on the signal into comparator C 1. If thefrequency coincidence between the VCO and Fko of thebeam lasts long enough, comparator C1 will be trig-gered and latched. The leading edge of the C1 pulsestarts the data collection sequence and also clampsCL1 through G1. Note that CL2 is not clamped at thistime so that the integrator is not reset to zero but isstopped at the point of frequency coincidence. TheVCO can now track the changing Fko in a phase-lockedloop since the beam oscillations control the VCO fre-quency. It is often possible to stay locked on thebeam for tens of milliseconds. The end of the Mtiming period restores the radia.l damper poweramplifier to its normal damping function.

The data collection sequence mentioned above con-sists of:

1. Counting the VCO for 1 ms.

2. Counting the master oscillator frequency for1 ms.

3. Stopping a gauss counter a.t the time of fre-quency coincidence to record the main ringguide field. This, of course, yields informa-tion on particle energy.

4. Sampling and holding the radial positioninformation.

The data storage circuitry involved will be discussedin more detail but the point to note here is that C1 hasbeen latched so that the stored data cannot be altered

by additional C1 pulses on later resonances. Unlessthe "Data Hold" button is pushed, the stored data willbe destroyed and the measurement circuitry reacti-vated by the reset pulse which comes some 3 s later.

Due to the finite driving capability of our poweramplifier and the inertia of the beam, it takes sometime for the bea.m to respond when excited at theproper Fko. Therefore, the sweep ra.te of the VCOmust not be too great.

Experiments have determined that a rate of changeof frequency (df/dt) of 1. 33 MHz/s allows the beamsufficient time to respond in most cases. However,the approximate rate of change of the Fko frequency(dFko/dt) is +1. 33 MHz ± 8 kHz/s for a particleenergy range of 250 MeV to 1. 5 GeV. We don't knowmuch about the frequency selectivity of the protonbeam (the Q in electronic terms). It seems probablethat exciting the beam for a 50 ms period with a fre-quency just a few kHz away from the Fko frequencymight force a. response from the beam at some otherfrequency than tha.t of the VCO. By sweeping the VCOfrom a high frequency to a low frequency (df/dt =

-1. 33 MHz) , we can still allow the beam time to re-spond while suppressing any possible tracking of thetune until phase lock occurs. For somewhat similarreasons, the Excitation Gai.n Pot, P2, should be setto generate the minimum beam disturbance.

It should be noted that as the betatron oscillationsgrow in size, the Tune Detector error signal is i.nsuch a direction as to force the VCO to be more out ofphase with the beam oscillations, so that our rate ofadding energy to the beam decreases. This ha.s atendency to be a stabilizing factor which prevents lossof beam.

Mode IV

This mode of operation is only an a.utomation of theold measuring technique mentioned in an earlier para.-graph. This is most useful when one wants to studythe magnetic gradients by studying the tunes at con-stant energy as a function of beam radial position.

The operator manually changes the frequency inresponse to signals from the electrodes. The TuneDetector does the gating of the power amplifier(usually less tha.n 5 ms), looks at the signals from theexcited beam to decide whe.n a tune has been found,and records the pertinent data. Like Mode III, thismode time shares the radial damper power amplifierand is partially compatible with normal HEP opera.-tion, but is most often used during a machine re-search period.

Mode I and Mode II

These modes are strictly passive in tha.t they areused only to measure unexcited or 'natural" reso-nances. In Mode I the resonances are viewed by theoperator who then triggers the Tune Detector sweepat a time that allows the sweep frequency to i.nterceptthe resonance. The action of the demodulator stillallows phase lock and tracking of the Fko although thesystem now has no ability to sustain or enhance the

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beam oscillations. The measurement sequence is a.sbefore with the operator making the decision to holddata. when he desires. Mode II differs from Mode I inthat the Tune Detector itself looks at the electrodesigna.ls and automa.tically makes its own decisionabout when to start a. frequency sweep.

Since these two modes do not distur.b the beam,they are totally compatible with normal HEP. Onemust rea.lize, of course, that "natural" resonancesoccur only spora.dica.lly and, as such, do not provideenough da.ta. for a. tune map. They do, however, pro-vide data about specific blowups which may help usretune the accelerator.

We do not have a. problem of bea.m response timein these modes so we may sweep the VCO muchfaster. We use a. sweep rate of about 20 MHz/s for a.20-ms period. This gives a, frequency window of400 kHz which is grea.ter than the Fko range. Asnoted before, the fa.stest df/dt of the Fko is1. 33 MHz/s. We obviously have a good probability offrequency coincidence since one changes slowly withrespect to the other.

In Modes I and II we can measure vertical tunesmerely by connecting the Tune Detector to a verticaldifference sensing electrode. Modes III and IV re-quire, in addition to vertical Fko signals, somedevice to exert vertical forces on the beam. Ourpower amplifier can be connected to vertical deflec-tion plates which a-re loca.ted near the radial forcingferrite. However, when this is done, we no longerha.ve drive to the ferrite so we have no radial dampingaction and such operation is, of course, not compat-ible with HEP operation. We do have a. high frequencydistributed power amplifier for our vertical dampingsystem. Its lower corner frequency is about 50 kHz.Some thought has been given to using the Tune Detec-tor in a time-sharing mode with this distributed a-m-plifier for vertical measurements.

The old procedure for detailed tune mapping hasbeen to measure vy a.nd compute vx from the equationv + v2 k . The va.lue of k has been found to bex y

anywhere from 1. 31 to 1. 36. Ta.king the extremevalues of k, in conjunction with certain existing datacan lead one to think there are Vx = vy resonances.Operating experience tells us otherwise. The point wea-re trying to make here is that there is real value inseparately measuring Vx and v rather than ma.kingquestionable assumptions abou the value of k.

Data Storage Circuitry

Block diagrams of the data. storage circuitry maybe seen in Fig. 2. The data. is stored in an 8-4-2-1BCD form. The outputs are ''wire-ored'' togetherinto one set of nixie rea.douts. Since this data. is all instandard digital form, computer collection and utili-zation of this data is merely a matter of ca.bling andprogramming.

The sections of Fig. 2 labeled Fko and Fmo a-remerely gated integrated circuit counters used to count

the VCO frequency and the master oscillator fre-quency at frequency coincidence. The inputs to the"and" gate are the respective signals and a 1 ms'read" pulse which comes at frequency coincidence.The Fko ranges from about 100 kHz to 350 kHz creat-ing a. quantizing error of a. maximum of 1%. Since thetune is a ratio of Fko to FMO, the 1 ms 'read' pulsewidth does not ha.ve to be accurately controlled. How-ever, if one hopes to also use the master oscillatorfrequency for position information, accurate countingis required.

The e.nergy of the beam for tune measuring pur-poses is obtained by counting the same magnetic clockpulses supplied to the HEP experimenters. The partof Fig. 2 labeled "B" shows the circuitry of a counterwhich presets itself to 500 (the starting point) bycounting clock C1, then switches to the experi-menters' clock. The leading edge of the "read" pulseresets the flip-flop, thus stopping the count at thepoint of frequency coincidence. This count is a.ccu-rate to ±2 G out of 20, 000 G.

The beam radial position is uniquely known oncethe magnetic field and the master oscillator frequencyare recorded a.t any one time. To supplement thisinformation, the Tune Detector records the positionsignal from a. radial induction electrode. The leadingedge of "read" pulses causes a. "sample and hold"circuit to take a sample of this analog position voltage.Other circuitry then digitizes this sample. This cir-cuitry acts very much like a. simple ramp and com-parator type of digita.l voltmeter. The output iscalibrated to readout in the units and polarities em-ployed in the ZGS coordinate system.

Accuracy

The Fko at low beam energies is near 100 kHz.Since we only count this for 1 ms, we obviously havea. 1% a.ccuracy limitation. To complicate matters, themaster oscillator frequency is changing rapidly insome nonlinear way in this same I-ms period. If wehave achieved phase lock, we then have an averagetune over this 1-ms measuring period. At high ener-gies, our error decreases to 0. 3% since Fko is 300 kcand master oscillator frequency change is less.

We recently have purchased a Hewlett-PackardModel No. 5360 computing counter which, on com-mand, will measure the master oscillator frequencyto 0. 1% while using only a 1 lis measuring time. TheTune Detector is being modified to allow the VCOfrequency to be mea.sured over an accurate 10-msperiod when it is in its nonsweeping mode--Mode IV.In this condition, the tune a.ccura.cy should approach0. 27%. The shorter resolution time of the masteroscilla.tor frequency combined with the already goodmagnetic resolution should make dv/dB mea.surementsbetter.

Like any other servo system, too much ga.in ma.kesthe pha.se-lock loop oscillate. This frequency modu-lates the VCO which in turn can cause errors duringmeasureme nt.

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Acknowledgements

While we have spoken of compatibility of tunemeasurements with HEP operation, it is only fair topoint out that detailed tune mapping of the type re-quired to accurately determine magnet gra.dients re-quires very narrow beams and, therefore, lessintense beams. In weak focusing machines, such as

12nthe ZGS, the normal 2. 5 x 1012 proton beam is about3-in wide at high energy and much, much widershortly after injection. In a wide beam, one probablycannot resonate the entire beam at one frequency un-less there are no gradients. Any resonance of onlypart of the beam that is measured leads to confusionin the computation of dv/dB. The proper trade-off isthe smallest beam that gives adequate betatron sig-nals. This is about 2-to-3 x 1011 with our instrumen-tation. Of course, space-charge effects on the tunemust be considered at higher intensities also.

If one is to judge the performance of the TuneDetector on the agreement with old tune data, it hasto be judged successful. While the criterions formeasuring tunes used by this instrument are differentfrom those used by the operators over the years, thedisagreements in the results are in the third decimalplace. The hoped-for improvements i.n tune measur-ing speed have not manifested themselves yet; mainlybecause not enough time ha.s been spent using thisinstrument.

Much credit is due to W. Chyna and R. Zolecki fortheir hard work and useful suggestions. My gratitudealso goes to J. Bogaty and R. Trendler for providingme with information concerning previous tune meas-uring techniques.

References

1. R. C. Trendler and J. M. Bogaty, ArgonneNa.tional La.boratory, The Horizontal and VerticalDamper Systems at the Zero Gradient Synchro-tron (ZGS) and Their Performance Characteris-tics, 1971 Particle Accelerator Conference,Chicago, Illinois, Ma.rch 1 - 3, 1971.

2. C. W. Potts and F. R. Brumwell, ArgonneNa.tional Laboratory, The Zero Gradient Synchro-tron (ZGS) Closed Orbit Position MonitoringSystem, 1971 Particle Accelerator Conference,Chicago, Illinois, Ma.rch 1 - 3, 1971.

3. K. C. Crebbin and F. H. Lothrop, La.wrenceRadiation Laboratory, Stimulation and Measure-ment of Radial Betatron Oscillations in the Beva-tron Using the RF Accelerating System, 1969Particle Accelerator Conference, Wa.shington,D. C., March 5 - 7, 1969, IEEE Transactions onNuclear Science, Vol. NS-16, No. 3, June 1969,p. 855.

Figure 1. Mode III Logic.

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C onc lusion

READ

Figure 2. Data Storage Logic.

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