The status of longitudinal and transverse Schottky observation systems for the synchrotron light source ANKA is presented. ANKA regularly operates in a dedicated low alpha mode with short bunches for the generation of coherent THz radiation. The Schottky measurement results are shown and compared with theoretical predictions for the regular as well as the different stages of the low alpha mode of operation. Special care had to be taken to control and mitigate the impact from strong coherent lines of the short bunches on the signal processing chain. The system setup is shown, expected and unexpected observations as well as applications are discussed

Birkel, I

Casalbuoni, S

Caspers, Friedhelm

Hiller, N

Huttel, E

Müller, A S

Smale, N J

Sonnad, K G

Weigel, R

CERN Document Server

STATUS OF SCHOTTKY DIAGNOSTICS IN THE ANKA STORAGE RING∗K. G. Sonnad, N. Hiller, Universita¨t Karlsruhe (TH), GermanyF. Caspers, CERN, Geneva, Switzerland,I. Birkel, S. Casalbuoni, E. Huttel, A.-S. Mu¨ller, N. Smale, FZK, Karlsruhe, GermanyR. Weigel, MPI-MF, Stuttgart, GermanyAbstractThe status of observations of longitudinal Schottky sig-nals at the ANKA storage ring is presented. After a shortreview of the theory, experimental setup and results are dis-cussed. Special care had to be taken to control and mitigatethe impact from strong coherent lines of the short buncheson the signal processing chain. Evidence for Schottky-likesignals was observed.INTRODUCTIONOver the years, it has been widely regarded that Schot-tky signals cannot be observed in electron rings because thecoherent signal dominates over the incoherent one. This islargely because (1) shorter bunches lead to a strong coher-ent signal, (2) synchrotron radiation contributes to back-ground noise. However, one should note that signals ob-tained from pick-ups always contain a mixture of coherentand incoherent lines for bunched beams. [1]. For examplethe coherent signal problem was overcome at the SPS at therevolution harmonic after careful filtering of unwanted fre-quencies [2]. In this paper, we discuss that it may be pos-sible to observe Schottky-like signals in an electron stor-age ring with appropriate signal processing and frequencyband selection. In fact the first detection of these signalsin a d.c. electron beam was done in 1918 [3]. As an in-teresting point in the context of optical stochastic cooling(THz range), which requires the availability of incoherentsignals in order to identify individual particels, demonstra-tion experimetns using electron beams have been proposedand discussed [4].ANKA is an electron storage ring used as a synchrotronradiation source operating in the energy range from 0.5 to2.5 GeV. The revolution frequency is about 2.7 MHz. In ad-dition to the regular 2.5 GeV mode of operation, the storagering is periodically operated in a ”low-αc mode” at ener-gies of 1.3 or 1.6 GeV for the generation of coherent THzradiation from short bunches. The study of the longitudinalspectrum will help to understand the complex dynamics inthis operation mode.THEORETICAL CONSIDERATIONSA charged particle bunch can be viewed, e.g., as a rigidbody or a large number of discrete particles. The “rigid∗This work has partly been supported by the Initiative and NetworkingFund of the Helmholtz Association under contract number VH-NG-320body” model can be generally associated with global quan-tities such as total charge, etc. Effects arising form thediscrete particles are referred to as Schottky noise. Thespectrum produced by the “rigid bunch” is referred to asthe coherent signal, while the incoherent signal arises fromrandom phases of the individual particles. The amplitude ofthe coherent signal would be proportional to N2 while thatof the incoherent one would be proportional to the numberof particles N .Bunch with Fixed Density ProfileFollowing [5], we start with the analysis for a bunch witha fixed profile given by g(t). In this case, the beam currentI(t) can be expressed asI(t) = eN∞∑n=−∞g(t− nT0) (1)where, e is the fundamental charge, N is the number ofparticles, T0 is the beam revolution period. This could beexpressed as a Fourier sum given byI(t) =∞∑n=−∞In exp(−inω0t)g(t) (2)where ω0 is the angular revolution frequency andIn = I0g˜(nω0) (3)is the nth Fourier component of the bunch profile and g˜ isthe Fourier transform of g. This may be expressed asIn =1T0∫ T00dtI(t) exp(−inω0t) (4)The average current is given by I0 = Ne/T0, and we em-ploy the normalization g˜(0) = 1Bunch with Individual ParticlesThe current contributed by a single particle can be rep-resented asI(t) = e∞∑n=1δ(t− nT0) (5)Employing the same procedure of Fourier decomposition,we getI(t) = ef0∞∑n=−∞exp(inω0t) (6)For a sum of N particles, this could be expressed asI(t) = ef0N∑p=1∞∑n=−∞exp(inω(p)0 t) (7)TH6PFP076 Proceedings of PAC09, Vancouver, BC, Canada3880Beam Dynamics and Electromagnetic FieldsD02 - Non-Linear Dynamics - Resonances, Tracking, Higher Orderwhere (p) is the index of the specific particle. In this expan-sion, we assume that each particle has a different revolutionfrequency ω0. The spread in the revolution frequency is as-sociated with the energy spread of the particles through theslippage term η, As a result, we getΔEE0= −1ηΔ(ωn)nω0(8)where the observed frequency ωn = nω0. Thus the ob-served spread is amplified by a factor of n the revolutionharmonic.Synchrotron Oscillations w. Fixed Bunch ProfileWith synchrotron oscillations, the current for a bunchprofile g(t) is given by,I(t) = eN∞∑n=−∞g[t− nT0 + A cos(ωst + φ)] (9)where ωs is the synchrotron frequency, φ is an arbitraryphase, and A is an oscillation amplitude. For synchrotronfrequencies much smaller than the revolution frequency, wecan make a Fourier decomposition of the current as follows.I(t) =∞∑n=−∞In exp{inω0[t + A cos(ωst + φ)]} (10)Here, In has the same expression as in the coast-ing beam case. Using the identity exp[iz cos(θ)] =∑∞k=−∞ ikJk(z) exp(ikθ), we can further expand theabove expression as follows,I(t) =∑n,kInk exp[i(nω0 + kωs)t] (11)with the coefficient Ink given by,Ink = I0g˜(nω0)Jk(nω0A) exp(ikφ)ik (12)Synchrotron Oscillations w. Individual ParticlesThe current due to a bunch with individual particles ex-ecuting synchrotron oscillations may now be expressed asI(t) = e∞∑n=−∞N∑p=1δ[t− nT (p)0 + A(p) cos(ω(p)s t + φ(p))](13)Using Eq (12) this can be expanded as follows,I(t) =∑p∑n,kI(p)nk exp[i(nω(p)0 + kω(p)s )t] (14)This equation indicates that, for ω0  ωs, and n  k, thespread in the peak is dominated by the contribution fromthe revolution frequency spread Δω0 while the contributionfrom Δωs is insignificant. In electron storage rings, theconditions are such that the synchrotron side bands are usu-ally separated from the revolution harmonic band, whichtranslates to ωs ≥ nΔω0. This condition would hold trueeven for n ≈ 1000. On the other hand, with hadron storagerings, one could expect that the synchrotron side bands areburied in the revolution harmonic spread, so ωs ≤ nΔω0.In the above equation, the coefficient I(p)nk is given byI(p)nk =eT0Jk(nω(p)0 A(p)) exp(ikφ(p))ik (15)Here, the phase φ(p) for the individual particle is random.As a result of this, for k ≥ 0, the power of the signal isproportional to N , the number of particles, correspond-ing to an incoherent signal. It is easy to see that this isnot true when k = 0, the revolution harmonic, becauseof the absence of the factor exp(ikφ(p)) in In0. Thus,while electron storage rings suffer from the disadvantageof a high coherent to incoherent signal ratio at the revolu-tion harmonic, they also offer the advantage that the syn-chrotron side bands are separated from the revolution har-monic spread, where this ratio is much smaller. The co-herent signal in the side band is a result of the longitudinaloscillation of the beam centroid and is given by Eq (11).EXPERIMENTAL RESULTSFor the measurements, the signal of an annular electrode(AE) installed in the ANKA storage ring was subjected toa band pass filter around the RF harmonic. This helps toreduce the amount of signal that could otherwise affect ad-versely the spectrum analysis. The filtered signal is thenamplified to bring the rather small synchrotron sidebandsout of the noise level. A sketch of the setup is shown inFig. 1. The spectrum analyzer used was a HP 8562E (rangeof 30 Hz to 13.2 GHz). The AE used for the measurementsdescribed in the following is a narrow ring-like pick-upwith a single feed-through. In order to determine the fre-quency response of the system consisting of the AE andthe total cable length (about 20 m) the signal amplitude ofthe RF harmonics was measured as a function of frequency.The result is displayed in Fig. 2. Up to about 3 GHz the am-plitudes only show a small decay. The total phase noise ofRF system and klystron measured directly (without ampli-fier or filter) at a wave guide pick-up is shown together withan AE signal recorded with identical settings in Fig. 3. Theshape of the total phase noise clearly dominates the shapeof the revolution peak’s base.The noise floor of the setup was determined to be−105 dBm at a central frequency of 2.7 GHz for a 500 kHzspan and a resolution bandwidth of 1 kHz. Two frequencybands were studied: one close to the 500 MHz RF har-monic at 465 MHz and one at 2732 MHz (that is close tothe vacuum chamber cut-off of ≈ 2600 MHz). The higherfrequency range sees slightly less signal from the AE andthe filter with 1.65 MHz bandwidth has a loss of 5 dB. Theamplifier for this range operates with a gain of 32 dB. Themeasurement is shown in Fig. 4. For this dataset the noiseFigure 1: Sketch of the measurement setup for the annularelectrode (AE). The amplifier and filter for each frequencyband under study were matched. The spectrum analyzerused was a HP 8562E.Proceedings of PAC09, Vancouver, BC, Canada TH6PFP076Beam Dynamics and Electromagnetic FieldsD02 - Non-Linear Dynamics - Resonances, Tracking, Higher Order 38810.5 1 1.5 2 2.5 3 3.5 4 4.5-50-40-30-20-100Frequency / GHzAmplitude/dBmFigure 2: Amplitude of an RF harmonic as a function offrequency. This measurement represents the characteristicsw.r.t. frequency of the annular electrode (including cablesetc.) used in the studies presented here. Up to about 3 GHzthe curve is reasonably flat.level measurement translates to a floor of−115 dBm. FromFig. 2 we see that the lower frequency range experiences aslightly higher signal level from the AE. The band pass fil-ter used here had 2 dB loss and a bandwidth of 0.643 MHz.The amplifier has a gain of 40.1 dB. The result is displayedin Fig. 5. In this case the noise floor is roughly−110 dBm.Both Fig. 4 and Fig. 5 show clearly the first synchrotronsideband. For the higher frequency band, even the secondharmonic is just visible. Although the expected total sig-nal level should be lower, the base seems to be elevated incomparison to the lower frequency band. One possible ex-planation could be an influence from a detection of coher-ent synchrotron radiation from the short bunches (<50 ps).It seems safer, therefore, to measure far away from thewaveguide cut-off. This is the case for Fig. 5. A closer lookreveals an asymmetric (triangular) shape of the synchrotronsidebands, an effect that has been described for the caseof peak detected Schottky signals in a proton machine [1].The ratio between the coherent central peak and incoherentsidebands is expected to be proportional to the number of-50 -40 -30 -20 -10 0 10 20 30 40 50-140-120-100-80-60-40-200-- signal from AE at 500 MHz-- signal from wave guide pick-up f / kHzΔAmplitude/dBmFigure 3: Spectrum of the AE at the 500 MHz revolutionharmonic showing the upper and lower first synchrotronsideband and the signal obtained from a wave guide pick-up. The total phase noise of RF system and klystron clearlydominates the shape of the central peak’s base.-100 -80 -60 -40 -20 0 20 40 60 80 100-100-80-60-40-200-- singal of AE at 2732 MHz f / kHzΔAmplitude/dBmFigure 4: Spectrum of the AE at the 2732 MHz revolutionharmonic showing the upper and lower first synchrotronsideband. The second sideband is just visible. The spec-trum was recorded with a resolution bandwidth of 100 Hzand for a span of 200 kHz.-100 -80 -60 -40 -20 0 20 40 60 80 100-100-80-60-40-200-- signal of AE at 465 MHz f / kHzΔAmplitude/dBmFigure 5: Spectrum of the AE at the 465 MHz revolutionharmonic showing the upper and lower first synchrotronsideband. The second sideband is not visible. The spec-trum was recorded with a resolution bandwidth of 300 Hzand for a span of 200 kHz with video averaging turned on.particles, that is to be about 90 dB. Figure 5 shows a ratioof roughly 80 dB, which could be an indication that we ob-serve a mixture of coherent and incoherent (Schottky-like)signals. The fact that the width of the sidebands is largerthan the one of the revolution harmonic points in the samedirection.REFERENCES[1] E. Shaposhnikova, CERN-BE-2009-010[2] D. Boussard, T. Linnecar, W. Scandale, IEEE Trans. Nucl.Science. Vol. NS-32, No. 5, 1985[3] S. Chattopadhyay, CERN-84-11[4] W. A. Franklin, PAC07, p. 1904, 2007[5] S. Krinsky, Measurement of the longitudinal parameters of anelectron beam in a storage ring. Frontiers of Particle Beams;Observation, Diagnosis and Correction. Springer Berlin /Heidelberg, Volume 343/1989, pp 150-166[6] T. Linnecar, W. Scandale, IEEE Trans. Nucl. Science, Vol.NS-28, No. 3.TH6PFP076 Proceedings of PAC09, Vancouver, BC, Canada3882Beam Dynamics and Electromagnetic FieldsD02 - Non-Linear Dynamics - Resonances, Tracking, Higher Order

Status of Schottky Diagnostics in the ANKA Storage Ring

Status of Schottky Diagnostics in the ANKA Storage Ring

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