Funakoshi, Y

Kawamoto, T

Kikutani, E

Koiso, H

Nakayama, H

Ozaki, H

Sugahara, R

Urakawa, J

CERN Document Server

Particle Accelerators, 1990, Vol. 27, pp. 83-88Reprints available directly from the publisherPhotocopying permitted by license only© 1990 Gordon and Breach, Science Publishers, Inc.Printed in the United States of AmericaMEASUREMENT OF THE COHERENT BEAM-BEAM TUNE SHIFT IN THE TRISTANACCUMULATION RINGHARUYO KOISO, YOSHIHIRO FUNAKOSHI, TAKASHI KAWAMOTO,EIJI KIKUTANI, HISAYOSHI NAKAYAMA, HITOSHI OZAKI,RYUHEI SUGAHARA and JUNJI URAKAWANational Laboratory for High Energy Physics1-1 Oho, Tsukuba-shi, Ibaraki-ken, 305 JapanAbstract In the TRISTAN accumulation ring, the coherent beam-beam tune shift was measured at 5.0 GeV in various optics. Theemittance and the luminosity were derived from the observed tuneshifts. They were compared with the design value of theemittance and with the measured value of the luminosity obtainedby a luminosity monitor,respectively. Based on thesecomparisons, the relation between the incoherent beam-beamparameter and the coherent beam-beam tune shift is discussed.INTRODUCTIONIt is well known that the beam-beam interaction is one of the mostimportant factors that limit the luminosity of a colliding machine.The effect of the interaction is expressed by the beam-beam parameter~ = r I {3 / 21fe f-ya (a +a ), (1)x,y e x,y x,y x ywhere reis the classical electron radius, I the bunch current, (3x,ythe beta function, e the elementary charge, f the revolutionfrequency, 'Y the beam energy in units of the electron rest mass andax, y the r.m.s. beam size. The beam-beam parameter is not able to bemeasured directly. What we can observe is the tune differencebetween the coherent O-mode and 1f-mode oscillations, ~v.Before our colliding experiment, there had been provided a fewformulae which relate ~v to~. The typical ones are;cos21f{vo+~v) = COS21fVo-41f~sin21fVo (by Piwinski1 ) (2)cos21f{vo+~v) = COS21fVo-21f~sin21fVo (by Hirata2 ), (3)where V o is the unperturbed tune between collision points. For small~v and ~, these formulae are reduced to~v = 2~ (4)[329]/8384/[330]~v = ~,H. KOISO ET AL.respectively. The latter was believed to be more reliable andactually gave acceptable estimation in the measurement of the tuneshift in the TRISTAN main ring.3 The estimated value of the emittanceusing Hirata's formula agreed with its design value within 15 %accuracy. However, in' our measurements in the TRISTAN accumulationring (AR) , the discrepancy amounted to larger than 30 %. In orderto settle the problem, more elaborated formula was devised by Yokoya.4The relation between ~ and ~v is given as~v /~ A(r) = 1.330-0.370r+0.279r2 (6)x <;x~vy / ~y A(1-r) , (7 )where r is a /(a +a). In the following sections, we describe resultsy x ythe measurement of the coherent beam-beam tune shift and compare theexperimental results with theoretical estimation by the above formulaeand with luminosity measurements. Based on this comparison, therelation between ~ and ~v is discussed.EXPERIMENTAL CONDITIONSAR is a single ring collider with two interaction regions (IR's), thenorth IR and the south. A pair of electro-static separators areinstalled in each IR in order to separate electron and positron beamsduring injection at 2.5 GeV and acceleration up to the collidingenergy. The locations of quadrupole magnets in the IR's are differentfrom each other so that the beta function at the south interactionpoint (IP) can be squeezed to 3 cm or less. A luminosity monitor whichcounts Bhabha events is placed only at the south IP.5The colliding experiment was performed at 5.0 GeV with a singlebunch per beam. The coherent beam-beam tune shift and the luminositywere measured under five optics whose parameters are summarized inTable 1.Four of the optics listed in Table 1 were designed for thedouble-IP operation and had the same P /P ratio at the both IP's.y xThe optic D was used for single-IP operation where two beams wereseparated vertically at the north IP. To localize a bump orbit madeby the separators, the vertical phase advance between the separatorswas adjusted to TI. The distance between the beams was 3.4 mm at5.0 GeV at the north IP and the long-range beam-beam tune shift wasBEAM-BEAM TUNE SHIffestimated to be less than .001 in the vertical direction.[331]/8511x11yPxs (m)~s (m)p" {m}pXN (m)yN 7€xo (10- m rad)# of IP'sParameters of experiment.TABLE 1OPTICS A10.1710.252.00.15.00.251.662optics usedB10.139.241.50.0312.50.252.242in theC9.159.251.50.0310.00.202.652D10.1310.271.40.03(8.9)(1.5)1·711E10.8710.782.00.112.50.251.642HORIZONTAL TUNE SHIFTThe beam-beam parameter of very flat beams, ~x' is related to theemittance € asx~X === reI/21Tefl'€x' (8)and is independent of the beta function. We may normally expect thehorizontal emittance €x to be close to its design value. We can thenestimate ~x by this expression.The horizontal beam-beam tune shift per revolution was measuredwith the accuracy of 0.001 under the optics A, B, C and E in double-IPoperation. The tune shift per collision, ~vx' was obtained by dividingthe observed values by 2 since it was expected to be almost equal atthe both IP's. Results were plotted by full circles in Figure 1.Throughout the measurement, the currents of the electron and positronbeams were equal to each other within 5 % and the vertical-to-horizontal emittance ratio was ascertained to be less than .025 bymeasuring the vertical and·horizontal tune shifts simultaneously.As is evident in Figure 1, the horizontal tune shift percollision ~lIx is proportional to the beam current, which suggests thatthe value of the emittance is approximately constant for each optics.Three solid lines in the figure show the expected values of the tuneshift calculated by the three formulae (4), (5) and (6) with r=O,respectively, on the assumption that the emittance is kept to be itsdesign value. Among the three formulae, eq.(6) reproduces excellentlythe behavior of the horizontal tune shift for all the four optics. Inother words, estimated values of the emittance agrees very well withtheir design values using eq.(6), while they are smaller by more than30 % using eq.(5).86/[332] H. KOISO ET AL.0.04 0.04Optic A Optic Bi"'\.0.03• ~t/x 0.03~.;)• ~t/xo ot/x ?~\ o ot/x~ ~v'to-4:E(/)(J) 0.02 0.02~ ~~~~ t>"'~\' t>"'~~+»~V~~0.01 0.010.00 15 0.00 00 2.5 5 7.5 10 12.5 5 10 15 20 25lotal beam currenl (rnA) lotal beam current (rnA)0.04 0.04?~'Y...0.03 0.03 ~v~'to-4:E ~~~(/)0.02 0.02 t>V~\'(J)~ t>"'~~::s+»~V~~o 00.01 0.015 10 15 20lolal beam currenl (rnA)25 2.5 5 7.5 10lolal beam currenl (rnA)12.5 15FIGURE 1 Coherent beam-beam tune shift per collision vs. totalbeam current.Optic PI.t~~=~--:/I; "l7=1::2385t/ A=2~I10.0,-....0 5.0Q)(/)~80>C?0...... 1.0~~~'Y; 0.50~'E~.E0.1Op'tic (L ~t/F~"-~+/ _11F="2tIA /'TI5 10bunch current (rnA)50 10010.05.01.00.50.15 10bunch currenl (rnA)50 100FIGURE 2 Luminosi ty vs. bunch current.BEAM-BEAM TUNE SHIff [333]187Because the formulae (6) and (7) were obtained considering onlythe linear term in the beam-beam parameter, they are correct only forsmall !J.v and ~. However, our data suggests that the formula (6) isvalid up to the region where !J.vxis larger than 0.02.In Yokoya's theory, the beam-beam force has been averaged overthe ring. Accordingly, it has been ignored that the beam-beaminteraction occurs only at the interaction point. In his paper, it hasbeen suggested that the localization effects can be taken intoaccount to some extent by using the formula like eqs.(2) and(3).Then we have introduced a parameter, OV, defined ascos2n(vo+!J.v) = cos2nvo-2novsin2nvo• (9)If this method is adequate, the following equation is more accuratethan eq. (6);oVx/~x = A(r). (10)The calculated values of ov from the measured tune shift!J.v arex xplotted by open circles in Figure 1. Because V o was close to aninteger or a half-integer, the difference between !J.vxand oVxwasamount to more than 10 %in the higher current region. As seen in thefigure, oVxis systematically larger than ~vx under the optics A, B,and C, ;while it is smaller under the optic E, since the fractionalpart of V o is between 0.25 and 0.5 in the optic E. We may regard c5vxas depending linearly on the beam current. Thus we can estimate theemittance from c5vx• The estimated values using eq.(10) are differentfrom their design values by 7-10 %. However, at this stage, we cannotdetermine which is better between eqs.(6) and (10), considering theexpected accuracy of the measurements and the theory.VERTICAL TUNE SHIFTIn the vertical case, we compared the luminosity estimated from thevertical tune shift with the measured one by the luminosity monitor.In the case of very flat beams, the luminosity depends on the verticalbeam-beam parameter ~y asL ~ 7~yI/2erePy. (11)The vertical beam-beam tune shift and the luminosity were measuredin both single-IP and double-IP operation under the optics C and D.Results are shown in Figure 2. Three solid lines in the figurecorrespond to the estimated values from the tune shift measurement by88/[334] H. KOISO ET AL.correspond to the estimated values from the tune shift measurement bythe three formulae (4), (5) and (7) with r=O. The error of the tuneshift measurement is within ±5 %. The data obtained by the luminositymonitor is plotted with bars which show the statistical error only.The systematic error is estimated to be ±10 %.As shown in the figure, only the formula (7) agrees with theluminosity measurement within the errors. However, the superiority ofthe formula over the other two is not so clear as in the horizontalcase because of possible large errors in the luminosity measurement.SUMMARYThe coherent beam-beam tune shift was measured at 5.0 GeV in theTRISTAN accumulation ring. Yokoyats formula explains well theexperimental results. In the horizontal case, the estimated values ofthe emittance using eq.(6) agree very well with their design values infour different optics. In the vertical case, the estimated values ofthe luminosity using eq.(7) are also consistent with those obtained bythe luminosity monitor within the errors.REFERENCES1. A. Piwinski, IEEE Trans. Nucl. Sci. 26, p. 4268 (1979).2. K. Hirata, Nucl. Instr. Meth. A269 (1988) 7.3. T. Ieiri et al., Nucl. Instr. Meth. A265 (1988) 364.4. K. Yokoya, these proceedings.K. Yokoya et al., to be published in Particle Accelerators.5. E. Kikutani et al., these proceedings.

Measurement Of The Coherent Beam-beam Tune Shift In The tristan accumulation Ring

Measurement Of The Coherent Beam-beam Tune Shift In The tristan accumulation Ring

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