We describe a system which is used operationally to measure the absolute intensity of single lepton bunches in a beam transfer line. It is based on the detailed knowledge of every single item of a complex measuring chain that comprises a beam coupler on one end and an acquisition system on the other end. This knowledge can be acquired by a well tested theoretical model and careful measurement of the transfer function of each processing module. A precision better than 3 % can be obtained and no external calibration is required. A value for the bunch length can be deduced from a spectral intensity measurement at two well chosen frequencies

Boccard, C

Bogey, T

Papis, J P

Vos, L

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Intensity and bunch length measurement for lepton beam in the injection lines of the SPS and LEP

INTENSITY AND BUNCH LENGTH MEASUREMENT FORLEPTON BEAMS IN THE INJECTION LINES OF THE SPS AND LEPC. Boccard, T. Bogey, J.-P. Papis, L. VosCERN, Geneva, SwitzerlandI. INTRODUCTIONAbsolute beam intensity measurements have beenthe privilege of beam transformers. When it wasconsidered convenient to turn to other instruments,transformers were still used for calibration purposes.The reason for this is the following. A simple,straightforward and reliable relation  exists betweenthe beam current (which can not be intercepted to bemeasured) and the response of the transformer, i.e.the turns ratio. The approach reported in this paper isthat the output of an electromagnetic monitor can beknown with the same confidence level as for atransformer. From then onwards it is sufficient toanalyse and measure the various signal processingbuilding blocks, including the acquisition system,that complete the measuring chain.The bunch intensity measurement chain containsthe following elements: an electro-magnetic coupler,summing hybrids, (long) signal transmission cables,signal filters, narrow band homodyne receivers,amplifiers and a peak signal detection system. Theperformance of the most important elements will bedescribed below. The layout of the monitors issketched in Figure 1. LEPSPSe- e+injection into SPSfrom PS at 3.5 GeV/cTT60TT10TI18 e +TI12 e-intensity monitorintensity monitor + bunch lengthLayout of intensity monitors in SPS/LEP transfer linesFIGURE 1II. TRANSFER IMPEDANCE OFCOUPLERIt may be interesting to note that the monitor wasdesigned and built to measure beam position. Itconsists of four 50 W  striplines shorted on one end. In[1] a formula was derived to compute the relevantproperties of a stripline. This formula was found to bereliable based on laboratory tests on several existingmonitors and on different prototypes developed forthe LHC. A typical monitor is sketched in Figure 2.hsignal out2r w  lElectromagnetic couplerFIGURE 2The maximum value of the transfer impedance ofa stripline electrode is :ˆZt =µ0 ε02piln rr − h  , (1)r=0.0665m is the outer radius of the monitor bodyand h  the height of the stripline. The striplineimpedance Z can be found with:Z =µ0 ε02pi2piΦln rr − h  (2)where f  is the total subtended angle which islarger than the mechanical subtended angle by anamount D f . The angles f  and  D f  are determinedby:Φ = ∆Φ + wr − h − t∆Φ = 2pi h2r − h(3)w =0.027m is the width of the line and itsthickness is t=0.0015m . The structural dimension h isnot always as well known as the other dimensionsr,w and t  since it is adjusted during mounting suchthat Z=50 W . However, an accurate value for h canbe derived from the set of equations (2),(3). Thisyields h=0.0067m and ˆZT = 6.37Ω .The actual value of the transfer impedancedepends upon the working frequency and the lengthof the stripline:  Zt = ˆZt sinωlc  . (4)The length   l of the stripline in a first type ofmonitor is 0.6m. An operating frequency of 50 MHzyields Zt = 3.75Ω . The length of a second type is0.34m. For an operating frequency of 50 MHz wefind Zt = 2.22Ω and for 200 MHz (specialapplication see below) Zt = 6.3Ω .III. THE RECEIVERSThe bunch signal can in general be written as :f t( ) = A ω ± δω( )e± j ω ±δω( )t , (5)where  A ω ± δω( ) is defined by the bunchspectrum and the characteristic of the filter. Thehomodyne receiver is a non linear system in whichthe input signal is shifted by its central frequency w .This yields a low frequency component at ±δω  anda component at twice the input frequency. The singlesideband low frequency demodulation product isthen:f dem t( ) = A ω ± δω( ) e± jδωt . (6)IV. THE FILTERSThe complete system contains two filters. Thefirst one is a bandpass filter which selects theoperating frequency (50 or 200MHz) of the receiver.The second one is a low pass filter which rejects thehigh frequency demodulation harmonics of thereceiver. The bandwidth of the second filter is thelargest one. The combined filter integration time∆t = 1 ∆f  is a result of the convolution of both filtersand can be derived rather accurately from themeasured transfer functions (amplitude and phase). Itshould be noted that the acquisition is based on thepeak detection of the signal impulse. The peak signalv  at the output of the filter of a single spectralsideband is:v = ZteNe2pih ω( )∫ dω = Zte Ne∆t (7)where N is the number of particles in the bunch, eis the electronic charge and Zte  is the e f f ec t i vetransfer impedance taking all gains and attenuationsinto account up to that point of the measuring chain.The bunch spectrum is h ω( ) . For the 50MHz filterswe found ∆t = 1 4.54MHz = 220ns  and for 200MHzthis was ∆t = 1 4.93MHz = 203ns .V. INFLUENCE OF BUNCH LENGTH ONMONITOR RESPONSEThe spectrum of a bunch with a Gaussian profileis:h ω( ) = Ne( )e−12ωσ t( )2 (8)where σ t  is the r.m.s. bunch length in time. It isoperationally advantageous to work with a smallvalue for ωσ t  so that h ω( ) ≅ Ne . The expectedbunch length of the leptons injected in the SPS isσ t ≤ 0.9 ns . The operational frequency is 50 MHz sothat ωσ t ≤ 0.28. Hence, the measurement is low by3.5% when the simplified formula is used. This canbe corrected as will be pointed out later. The error atthe SPS extraction is entirely negligible sinceσ t = 0.13ns  and ωσ t ≤ 0.04  for the sameoperational frequency.The spectral dependence on bunch length can beturned into an interesting application. Indeed, thesame bunch signal can be sampled atω1 2pi = 50MHz  and ω 2 2pi = 200MHz  which arethe frequencies for which receivers are available.The signal reduction factor computed with (8) can beapplied to (7) and the following signal ratio is found:v1v2= e12σ t2 ω 22−ω12( ). (9)The r.m.s. bunch length follows :σ t =2ω 22− ω12( ) lnv1v2 . (10)Putting in the numbers gives :σt ns( ) = 2pi10.3ln v50MHzv200MHz . (11)This measurement of s t  relies exclusively on therelative signals measured at 50 and 200 MHz. Henceit is in principle possible to correct the 50 MHzintensity value for bunch length. With the availablehardware it is not possible to make a useful bunchlength measurement on the beams extracted from theSPS since the expected signal difference between 50and 200 MHz is too small (1.26%!).VI. INFLUENCE OF BEAM POSITION ONINTENSITY SIGNALThe four electrodes cover somewhat less than20% of the full circumference of the monitor. Thesignal is enhanced when the beam approaches one ofthe electrodes and it is reduced when the beam israther in between two electrodes. This effect can andhas been computed. It is very non linear andincreases quickly with increasing distance from thecentre of the monitor. However, in practice it can beneglected. For example, the variation of the signalinduced by a beam circulating at a distance from thecentre equal to 1/3 of the aperture (20 mm) is lessthan 3%. Beams tend to be at less than 10mm fromthe centre. A dedicated monitor built especially forintensity would look like a coaxial line and cover thefull circumference so that the signal becomes totallyindependent from beam position.VII. OTHER ELEMENTSThe performance of all elements have to beaccurately measured in order to guarantee anintensity measurement of sufficient quality. The otherelements are cables, amplifiers, attenuators, hybrids.Their attenuation/gain has been determined withgreat precision such that the total error is estimatedat less than 5% (0.4 dB). A lot of care is required. Asan example it may be worth mentioning that there isa slight discrepancy in gain in the receiver unitsbetween pulsed mode operation and continuous waveoperation. Therefore it was necessary to do all themeasurements in pulsed mode, which is somewhatmore cumbersome. Figure 3 shows the schematicdiagram of the measuring chain.SSShyhr id cableat tenua torreceivercouplerampli ampli to peakdetectionacquisitionfilterFIGURE 3VIII. CONCLUSIONThe system has been operational for two years.One monitor is installed in each lepton injectionline(bunch length available for positrons only) of theSPS and two monitors (up- and downstream) in eachSPS extraction line. The intensity evolutionmeasured from injection, SPS circulating beam (DCmonitor), extraction are quite acceptable from aphysical point of view. Typically the loss at injectionis rather large (up to 50% due to high frequencytransverse mode coupling instability), some 10% lossin the SPS, 3 to 4% during extraction and a few % inthe transfer line.REFERENCES[1] J.-P: Papis, L. Vos, Design Basis for the LHCBeam Position Monitor, CERN SL/91-6(BI), 1991

Intensity and bunch length measurement for lepton beam in the injection lines of the SPS and LEP

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