Hara, M

Nakamura, T

Ohshima, T

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Particle Accelerators, Vol. 59, pp. 143-156Reprints available directly from the publisherPhotocopying permitted by license only© 1998 OPA (Overseas Publishers Association) N.V.Published by license underthe Gordon and Breach SciencePublishers imprint.Printed in India.A RIPPLE EFFECT OF A KLYSTRONPOWER SUPPLY ON SYNCHROTRONOSCILLATIONM. HARA*, T. NAKAMURA and T. OHSHIMASPring-8, JASRI, Kamigori, Ako-gun, Hyogo-ken 678-12, Japan(Received 6 August 1997; In final form 17 November 1997)Coherent synchrotron oscillation was observed in the SPring-8 storage ring as side-bands at the harmonics of the accelerating frequency, which is independent of beamcurrent. This is explained using a forced oscillation model of the synchrotron oscilla-tion affected by the disturbance of accelerating voltage. The RF disturbance is inducedby the ripple noise in the klystron power supply at the harmonics of the frequency ofthe AC power supply.Keywords: Ripple; Coherent synchrotron oscillation; Forced oscillation;RF phase noise1 INTRODUCTIONHigh voltage DC power supplies are an integral part of most particleaccelerators. However, they tend to produce ripple noise thatdetracts from the accelerator's overall performance. If a klystronpower supply has excessive ripple noise, electron beams acceleratedby a cathode voltage in the klystron suffer from ripple effects thatmodulate their velocities, and, as a consequence, amplified RF ismodulated. If one of the frequency components is close to the syn-chrotron oscillation frequency, the ripple noise induces a coherentsynchrotron oscillation.*Corresponding author. Tel.: 81-7915-8-0863. Fax: 81-7915-8-0850.E-mail: hara@sp8sun.spring8.or.jp.143144 M. HARA et al.The ripple noise effects in the SPring-8 storage ring were measuredby varying the effective accelerating voltage. These effects were foundto be a sideband signal of the accelerating frequency (508.58 MHz);and the sideband signal frequency was a higher harmonic of the ACpower supply (i.e., integral multiples of 360 Hz).Experimental evidence indicates that the design of a low-level RFsystem should pay special attention to the relationship between theripple frequency of the klystron power supply and the synchrotronoscillation frequency.l The effect of RF phase noises on the electronbeam were recently investigated theoretically.2 In the SPring-8 stor-age ring, coherent synchrotron oscillation caused by high voltage rip-ples in the klystron was found to be a sideband peak of theacceleration frequency; and the strength of the sideband can beexplained by a simple forced oscillation model.2 KLYSTRON PHASE DELAYA schematic diagram of a klystron is shown in Figure 1. Electronsare emitted from a cathode and accelerated by a cathode-collectorvoltage and captured by a collector that is usually connected to theearth. Input, output, and other cavities are installed between theanode and collector. Electrons are velocity-modulated by the inputcavity, which is excited at RF frequency, and pass through driftspace. On the way to the collector, the electrons are bunched byvelocity modulation; and the bunched electrons induce the RF volt-age in the output cavity.Slight changes in the cathode voltage affect the electron travel timeT, causing a phase delay in the RF output voltage. The phase delay~()D can be calculated from the following relations:(1)(2)(3)(4)A RIPPLE EFFECT OF A KLYSTRON POWER SUPPLY 145CollectorDrift Tube --+----+-......- ......Input CavityAnodeCathode ---11---.......HeaterFoucusing CoilUE:;;;;::~- RF InputFIGURE 1 Schematic diagram of a klystron.where: fRF is the RF frequency; L the length between the input cavityand the output cavity; (3 the dimensionless velocity of the electronbeam; c the velocity of light; ~ the dimensionless energy of the electronbeam; - Vk the cathode voltage; e electron charge; and mc2 the elec-tron rest mass energy.Voltage fluctuation (~VklVk) coefficient D for the phase delay iscalculated from Eq. (1),(5)This can be rewritten as(6)146 M. HARA et al.To get the physical image, the coefficient D is estimated numericallyand shown in Figure 2, where L == 2.5 m, andfRP == 508.58 MHz. If theklystron is operated at a cathode voltage of 80 kV, a ripple noise of~VI V == 10-3 induces a phase difference of 1.2°. This is comparable tothe bunch length O"e == 2.44° in the SPring-8 storage ring.The phase delay induces a phase modulation in the RF frequencyin an acceleration cavity. If the cathode voltage of the klystron has aripple component of ~Vk sin wt, the output signal of the klystronA sin(wRPt + ¢) is phase-modulated and can be expressed asA . ( ~Vk.)SIn WRFt + D--sInwtVk== A sin(wRFt + asinwt)== A(sinwRFtcos(asinwt) + coswRFtsin(asinwt))= A sin(wRFt) (Jo(a) + 2~ hn(a) cos 2nwt)+ A COS(WRFt) (2~hn~l(a) sin((2n - l)Wt))00== AJo(a) sinwRFt + AI: J2n(a) (sin(wRF + 2nw)t + sin(wRF - 2nw)t)n=l00+ A I: J2n-l (a) (sin(wRF + (2n - 1)w)t - sin(wRF - (2n - 1)w)t),n=l (7)1450Q) 1400~C)CD 1350~';1 1300C 1250CD·u 1200;:CD0 11500110055 60 65 70Cathode75 80 85 90 95Voltage (kV)FIGURE 2 Coefficient D to estimate phase delay for a given ~VIV. In this graph,- D is displayed because D is negative.A RIPPLE EFFECT OF A KLYSTRON POWER SUPPLY 147where Dti. Vkl Vk is replaced by a. From the equation, phase modula-tion effects appear as a sideband signals at WRF ± wand the amplitudeisti.Vkfor D Vk «1. (8)3 BUNCH RESPONSEThe equation for small phase oscillations T in a bunch is given by3where a E is damping coefficient given by(9)__1 (dUrad)a E - 2~ dE 'o Eo(10)Urad is a radiation energy loss per turn of an electron with an energyE, and n is the synchrotron oscillation (angular) frequency given by(11 )where a, To, Eo, and VRF are the momentum compaction factor, therevolution time, the electron energy, and the accelerating voltage,respectively. For a sinusoidal accelerating voltage,VRF == Vo sin(wRFt + cPs),n2 == aew RF Vo cos cPsTo Eo '(12)(13)where WRF and cPs are the acceleration angular frequency and thesynchronous phase.The phase modulation or amplitude modulation affects n2 throughVRF . This modulation can be treated as an external force in a simpleforced oscillation model.(14)148orM. HARA et at.d2T 2 dT n2 _ [22 ~V jwtd 2 + Q f d + ~ G T - V e .t t WRF(15)Solution of Eq. (14) can be expressed as([22 /WRF )~(}DejwtT == --;::============================V(D,2 - w 2)2 + 4a~D,2 (16)Equations (14) and (15) are equivalent and the solution of Eq. (15)can be expressed as Eq. (16) if ~(}D is replaced with ~VIV.A ripple of angular frequency W in a klystron power supply in-duces synchrotron oscillation with amplitude expressed by Eq. (16).If the accelerating voltage is changed for a fixed w, the amplitude ismaximum at n == wand the width is given by Q e If there is more thanone value for wand the coherent synchrotron oscillation is measured,the peak amplitude is larger for a smaller w.From Eqs. (14) and (15), the accelerating voltage modulation andphase modulation give the same results, and the mechanism is deter-mined by the magnitude of ~()D and ~VI V. If ~()D is larger than~VI V, the forced oscillation will be induced by phase modulation.The phase detector signal and klystron forward power were mea-sured in the SPring-8 storage ring RF system and it was confirmedthat ~(}D was larger than ~VIVas is shown in Figure 10 later.4 SYNCHROTRON OSCILLATION AMPLITUDEThe quantitative amplitude from the measured synchrotron oscilla-tion power spectrum can be obtained from the equations below.Cited from Ref. [4], a single particle longitudinal signal at time t andangular azimuth position () can be described as~ ( () 2n1f)slI(t,(}) ==e 8 t-T---- ,n=-oo WQ WQ(17)where: 8 is the Dirac function; T the time interval between the refer-ence particle passing and test particle passing; and WQ the angularA RIPPLE EFFECT OF A KLYSTRON POWER SUPPLY 149revolution frequency. Fourier transform of Eq. (17) gives a line spec-trum at frequencies wpm == pWo +mws:00SII(w,B) = e2:o 2..= rmJm(pwof)ej(plJ-m'l/Jo)8(w-wpm), (18)p,m=-oowhere lm(x) is a Bessel function; f the synchrotron oscillation ampli-tude; and Ws the synchrotron oscillation angular frequency. The spec-trum amplitude at the revolution frequency and the first sideband aredescribed asSOs(p) == Ilo(pwof),Sls(p) == III (pwof),(19)(20)where I is the electron current and p is an integer. Power spectrum isthe square of the amplitude, and the power spectrum ratio is given as(21 )Above is the single particle model, which is illustrated in Figure 3.Using this model, excited synchrotron oscillation amplitude can beestimated.FIGURE 3 Synchrotron oscillation in single particle model.1505 MEASUREMENTM. HARA et at.The SPring-8 storage ring has four RF stations. Each station has 8single-cell cavities which are powered by 1MW klystron. At the com-missioning stage three RF stations (B, C, and D) are installed. Thespecification of the klystron and power supply is listed in Table I.The power supply is thyristor regulated and has no crowbar circuitand no large capacitor bank.5 Each power supply is basically a six-phase rectifier circuit (with ripple noises occurring in integral multi-ples of 360 Hz): and the klystron power supplies in the three stationsare phase shifted by 20° from each other at their input transformer.Therefore, if each station is finely tuned and three stations arebalanced, equivalent 18-phase rectifier could be expected (with ripplenoises in integral multiples of 1080 Hz). In fact, there are some causesthat disturb the balances, so that the extra harmonic components areexcited in the power supply. An example of the ripple measurementsof the power supply using an FFT analyzer is shown in Figure 4.TABLE I Specification of klystron and power supplyKlystronFrequencyOutput powerPower supplyMaximum voltageMaximum currentsAC power line frequencyVoltage rippleE3786 (Toshiba)508.58 MHz1MW (CW)Thyristor regulated with sixphase-90kV20A60Hz0.5% p-p (at 360 Hz)360HzI720 HzI1080 HzI1440 HzI--34tillMAGdBV20d8/-94o PWR SP A han LINX. 50.00Hz Y -70.62d8V2kHzFIGURE 4 An example of the power supply ripple noise spectrum below 2kHz forD station. Vcathode = 60 kV. Measured by CF-360 portable dual channel FFT analyzer.A RIPPLE EFFECT OF A KLYSTRON POWER SUPPLY 151In this case, frequency components in integral multiples of 360 Hzcan be seen at the level ~V/V~ 10-3. Frequency components of60, 180, 540 Hz, etc., were also observed in the power supply output,which comes from the above stated unbalance. Low frequency com-ponents of less than 1kHz can be reduced by automatic level control(ALC) and phase lock loop (PLL) in the low power RF system.These are referred later.Sideband of coherent synchrotron oscillation is proportional toJl (p wof), therefore, it is necessary to measure at an appropriate fre-quency to observe the synchrotron oscillation (not too low pwof).The electron beam signal from a Beam Position Monitor (BPM) wasmeasured at the acceleration frequency (508.58 MHz, p = 2436).Cavity voltages (measured by the pickups attached to the cavitiesand vector summed) at three stations (B, C, and D) were keptconstant (set voltages were Vb == 5.13MV, Vc ==4.89MV andVd == 3.54 MV after calibration), and the phase of the B station (ob)was varied (Figure 5). Stored currents were about 200 J.lA.The power spectrum was measured using spectrum analyzer(HP8591E) and an example of the raw data is shown in Figure 6. Wecan see the sideband peaks of the coherent synchrotron oscillationaround the acceleration frequency. These peaks do not originate incollective phenomena because the current is very low. Sideband peakfrequencies are plotted for ob in Figure 7.Observed sideband peak frequencies were confined to the integralmultiples of 360 Hz (n x 360, n == 3,4, 5) near the synchrotron oscilla-tion frequency. The solid line in the figure represents the calculatedsynchrotron oscillation frequencies at ob, assuming a designedmomentum compaction factor of a == 1.46 x 10-4 .FIGURE 5 Voltage and phase relation of B, C, D stations and the effective voltage.152 M. HARA et al.FIGURE 6 An example of spectrum data taken at (}b = 18°. The large peak in thecenter is the accelerating frequency 508.589362 MHz; and the sideband peaks areobserved clearly at integral multiple of 360 Hz (1800 Hz). Synchrotron oscillationfrequency calculated from the design value of momentum compaction factor is1732Hz.2000..-.N:I: 1800"-'">auc: 1600CD::::J0"CD 1400...U.c: 12000;;.!!"u 1000tn0800- 2 0 0 20 40 60 80 100Phase B (degree)FIGURE 7 Frequencies of the sideband are plotted as a function of (}b. Circlesindicate the observed peak frequencies and the line is the calculated synchrotronoscillation frequency. Observed peaks are on the integral multiples of 360 Hz. A peakat 1620 Hz (180 x 9) is also seen.A RIPPLE EFFECT OF A KLYSTRON POWER SUPPLY 153The intensity of the sideband signals at 1080, 1440, and 1880 Hz,divided by that of the accelerating frequency, are plotted at the cor-responding synchrotron oscillation frequencies in Figure 8. The peakpower spectrum values on the accelerating frequency are propor-tional to the stored current. Therefore, the ratio of sideband intensityto the accelerating frequency is equal to the current normalizedintensity of the sideband signal. It is the ratio, not the sideband sig-nal itself, that determines the physical quantity. Sideband signals at1080 Hz peak at Is == 1150 Hz or less, while at 1440 Hz they peak atIs == 1400 Hz, and that at 1800 Hz have a rising shoulder around1700 Hz. The lines in the figure are calculated from the forced oscilla-tion model. Chain, dotted, and solid lines are calculated using w inEq. (16) set to 21f x 1080, 21f x 1440, and 21f x 1800, respectively. Thismodel reproduces these sideband amplitude fairly well.Figure 8 shows that maximum intensity ratio is measured to beabout 10-4 at 1080 Hz sideband. The single particle model in Section 3provides a basis for estimating the forced synchrotron oscillationamplitude: Ratio based on the single particle model is expressed byEq. (21); the calculated coherent synchrotron oscillation amplitude inlength is shown as a function ofpower spectrum ratio in Figure 9. Fromthis calculation, maximum forced coherent synchrotron oscillationo 0.001:;:asIX~ 0.0001·encQ).....:"ic:0)Cii"CCas.cQ)"CCii800 1000 1200 1400 1600 1800Synchrotron Frequency (Hz)2000FIGURE 8 Sideband signal intensities at 1080, 1440, and 1800 Hz divided by theaccelerating frequency signal of 508.58 MHz. The squares, circles and solid circlesrepresent data at 1080, 1440, and 1800 Hz, respectively. Three curves are calculatedusing the forced oscillation model Eq. (16).154 M. HARA et al.3~ 2.5::::J~C. 2Ecr:C 1.5o';C'CS(,)oo 0.5Intensity Ratioo..cCD"-CD.r:::.o(.)FIGURE 9 Coherent synchrotron oscillation amplitude based on a single particlemodel.amplitude is 1.5-2mm while the nominal bunch length is estimated tobe about 4 mm.6 DISCUSSIONThe performance of the RF low power system of the storage ringwas measured,6 which is equipped with an automatic level control(ALC) and phase lock loop (PLL). The klystron forward phase andRF voltage with ALC and PLL -off and -on in B station are shownin Figures 10(a) and (b). From the figures, you can see the amplitudefluctuation ~V/V was 1.5 x 10-2 and 3.7 x 10-3 with ALC -off and-on while the phase fluctuation ~()D was 3° and 1.4° with PLL -offand -on. As klystron power supply is based on thyristor control, thecorresponding ripple extends to several kHz. The feedback loops areeffective below 1kHz but not above 1kHz, where sharp spikesremain even with ALC and PLL -on. In order to reduce the rippleeffects, it is necessary to fine tune each power supply and balance thethree stations; and improve the feedback system so that it can adaptto a wider frequency range.A RIPPLE EFFECT OF A KLYSTRON POWER SUPPLY 155(a) (b)FIGURE 10 Raw data of phase and forward output voltage of the klystron withALC -off (a) and -on (b). The upper is the output signal of phase detector and thebottom is that of RF linear detector. The axis of abscissas is 50 ms/div, and that of theordinate is 50 mVIdiv. The scale of the phase is 10 /50 mV and the DC level of theoutput voltage is 2.7V for both (a) and (b).Sideband signals from the accelerating frequency were measured atlow current by varying the effective cavity voltage by means of a sta-tion phase. The measured sideband frequencies were integral multi-ples of 360 Hz. The characteristics of the signal are fairly wellexplained by a simple forced oscillation model. Though the peakposition of the sideband signal is a little bit different from the calcu-lated one, this comes from the errors in calibrating cavity voltage,phase, momentum compaction factor and so on. The origin of theforced oscillation is the phase modulation rather than amplitudemodulation, because the amplitude fluctuation ~V/V of 1.5 x 10-2and 3.7 x 10-3 is equivalent to the phase fluctuation ~()D of 0.85°and 0.2°, which is much smaller than the phase modulation itself.7 CONCLUSIONCoherent synchrotron oscillation is excited by the klystron phasenoise that comes from a ripple. The observed signal frequencies arein integral multiples of 360 Hz near synchrotron oscillation fre-quency. The excitation of coherent synchrotron oscillation is causedby power supply ripples through forced oscillation of a phase mod-ulation mechanism. The induced coherent oscillation amplitude isabout 2 mm in length, while the nominal bunch length due to the156 M. HARA et al.synchrotron oscillation is about al == 4 mm. In order to reduce thisripple effect, it is useful to balance the power supplies of the threestations and to improve the phase feedback system.A~knowledgementsThe authors wish to thank the members of the commissioning andoperation group of SPring-8 for the data taking, Dr. Y. Miyaharafor his helpful discussion and preparation for the manuscript, andthe member of RF group for useful discussion.References[1] E. Ezura, K. Arai, H. Hayano, M. Ono, M. Suetake and T. Takashima, Proc. 1987IEEE PAC, 1660 (1987).[2] Schin Date, Kouichi Soutome and Ainosuke Ando, NIM A 355 (1995) 199-207.[3] Mathew Sands, The Physics of Electron Storage Rings an Introduction.[4] J.L. Laclare, Bunched beam coherent instabilities, CERN 87-03, 21 April 1987.[5] N. Kumagai, C. Yamazaki and H. Kouzu, Star-point control for the klystronpower supply in the SPring-8 storage ring, Proc. Int. Power Electronics Con!,Yokohama, p. 1497 (1995).[6] Y. Ohashi, H. Ego, M. Hara, N. Hosoda, Y. Kawashima, T. Ohshima, H. Suzuki,T. Takashima and H. Yonehara, SPring-8 Annual Report, 161 (1996).

A Ripple Effect of A Klystron Power Supply on Synchrotron oscillation

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