Dynamic Aperture for LEP 2 with Various Optics and Tunes

Transcription

1 Dnamic Aperture for LEP with Various Optics and Tunes Francesco Ruggiero SL Division Abstract We present latest simulation results and discuss dnamic aperture measurements performed in 995 on various LEP optics. After recalling the protocol proposed for these measurements and the outcome of several related MD s, we compare the 9 =6,the8 =6 and the 8 =9 lattices and tr to draw some conclusion for the performance of LEP above 9 GeV. INTRODUCTION As discussed in Refs. [], the measured aperture until the end of 993 was nearl a half of the dnamic aperture predicted b tracking and most likel due to a phsical obstacle in the beam pipe. After November 993 both Q-meter and single-kick measurements gave larger results and, in particular, during an eperiment at 45.6 GeV with damping and emittance wigglers turned on to simulate LEP conditions, horizontal measurements using the injection kicker IK3E were in ecellent agreement with MAD simulations for the 9 =6 squeezed optics g5p46. The measured horizontal aperture, corresponding to a kicker voltage of 6 kv for a bunch current loss of 5%, was A meas =: 3p mto be compared to A MAD :4 3 p m with wigglers off and to A MAD : 3 p m with wigglers on. It should be mentioned that there is some discrepanc between the horizontal emittance computed b MAD with wigglers on and the predictionsof the program WIGWAM, which makes use of a better interpolation algorithm to evaluate radiation integrals. Therefore MAD tracking results with wigglers on ma have to be taken with some care. Also the dnamic aperture for electrons and positrons, having different tunes, can be significantl different and a more sstematic tracking campaign is still required. The single-kick method is now preferred over the method based on resonant ecitation b the Q-metre, since it gives more reproducible results. The analsis of these results is particularl simple for a kicker voltage corresponding to a bunch current loss of 5%, since in this case the dnamic aperture is given b the product of the kick angle b the square root of the betatron function at the kicker centre: it is independent of the beam emittance, but an additional measurement b the -turn technique is required in case of significant beta-beating. Although a pencil beam would be better suited for a sstematic eploration of the stabilit region in the si-dimensional phase space, for practical reasons a fat beam with emittance and damping wigglers at their maimum level is recommended during dnamic aperture measurements. The reason is that usuall the betatron phase of the kicks is never varied, since we alwas use the same kicker, nor do we eplore different momentum deviations of the bunch. Therefore the results obtained with wigglers on are more conservative and reliable; the can be considered as a survival test under conditions as close as possible to LEP conditions. Moreover, it is much easier to find the kicker voltage corresponding to 5% current loss using a fat beam rather than a pencil beam. In the net two sections, we discuss the results of several related MD s at 45.6 and at 65 GeV, respectivel, where the dnamic aperture was measured or inferred for the 8 =6 and the 8 =9 optics. Recent tracking results are presented in the last section, together with some perspective for the performance of LEP above 9 GeV. MEASUREMENTS AT 45.6 GEV. Dnamic aperture for the 8 =6 optics The measurements at 45.6 GeV on the 8 =6 squeezed optics e5r46 are discussed in Ref. []. After commissioning the ramp and squeeze, the aperture was first measured on a positron beam with Q = :76, Q = :7, Q =3:8 and Q =:9. The damping and emittance wigglers were switched on at their maimum value and the measured emittances were " =nm, " =nm. For a voltage of 3 kv on the injection kicker IKP3, where = 5 m, the bunch current was reduced b 5% (down to 8 A). Therefore, using the kicker calibration =:73 mrad kv GeV E ; the corresponding kick angle was =:96 mrad and the dnamic aperture for positrons A e+ =p =: 3 p m. This measured value is considerabl smaller than the value obtained b tracking (without wigglers), namel A MAD =:65 3 p m. It should be mentioned that the kicker timing was first set to an old 9 value of 76:6 s (recommended in the standard protocol) and then to the correct 95 value of 64:7 s. The positron beam was dumped and the aperture measurement was then repeated with electrons, having Q = :7, Q = :59 and Q = Q = 3:8. Alwas with wigglers on, this time the 5% bunch current loss occurred for a voltage of 4:5 kv on the injection kicker IK3E (the bunch current being reduced from down to 59 A). The

2 corresponding kick angle was =:36 mrad and the dnamic aperture for electrons A e =:5 3 p m, in fairl close agreement with tracking predictions.. Dnamic aperture for the 8 =9 optics The measurements at 45.6 GeV on the 8 =9 optics are discussed in Ref. [3]. An electron beam was kicked with the kicker IK3E, where = 6 m, under different conditions: the resulting bunch current losses are reported in Fig.. I I b b 3 V kick [kv] Figure : Relative bunch current loss vs. IK3E kicker voltage under different conditions for the 8 =9 optics at 45.6 GeV (from Ref. [3]): ) = 9 cm and no wigglers, ) =9cmandemittance plus damping wigglers switched on, 3) =5cm and no wigglers. With wigglers switched off, the losses reached about 4% for a kicker voltage of 6:6 kv when = 9 cm and for a kicker voltage of 6: kv when = 5cm. The corresponding dnamic aperture was therefore A meas =(: :4) 3 p m, in agreement at the % level with the simulation value A MAD =:5 3 p m. When damping and emittance wigglers were switched on, with = 9 cm, significant losses appeared alread at a kicker voltage around 4: kv (see curve in Fig. ): the corresponding emittance and relative energ spread were " =4nm and =:4 3, respectivel. With wigglers on and =5cm, the electron beam had a poor lifetime. This can be partl eplained b the limited energ acceptance of the squeezed optics 5e46, of about 8 3, without setupole re-cabling. The observed losses for the 9 cm optics with wigglers off (see curve in Fig. ) show a local maimum for a kicker voltage around 4:6 kv. This has been tentativel associated with particle trapping in the third order resonance and subsequent escape to larger amplitudes due to quantum fluctuations [3]. However, accepting such a mechanism as a possible eplanation, the conclusion would be that the effective horizontal beam size is bigger than the nominal and the usual criterion adopted for the required dnamic aperture (at the beam beam limit) should then be revised. 3 MEASUREMENTS AT 65 GEV 3. Increasing the beam emittance with the 8 =6 optics The measurements at 65 GeV on the 8 =6 optics are discussed in Ref. [4]: there was no time to kick the beam, but the dnamic aperture was estimated b increasing the horizontal emittance using the wigglers and then changing the damping partition numbers b a reduction of the RF frequenc. A single positron beam (with I b A) was first ramped to 45:6 GeV, then squeezed to = 5 cm and ramped up to 65 GeV. The emittance measured at the BEUV without wigglers was " BEUV =6nm (while the nominal value is " nom = 6 nm). With the emittance wigglers at their maimum value (:84 Tm), the measured emittance became " BEUV = 35 nm (while the value computed b WIGWAM is " nom = 3 nm). At this point the RF frequenc was reduced b 5 Hz, corresponding to a partition number J = :76 and to an emittance " nom = 39 nm: the measured emittance became " BEUV = 45nm and the beam lifetime was stillver good. The vertical emittance remained around " BEUV =:5nm. A further reduction of the RF frequenc b 5 Hz led to an emittance " BEUV =6nm accompanied b poor beam lifetime. The (BEUV) emittance corresponding to a beam lifetime still around 4 hours was estimated to 55 nm. Meanwhile the horizontal betatron function was measured b the -turn technique and the corresponding beta-beating at the BEUV was found to be 4%. Before discussing the conclusions that can be drawn from these measurements, it is worth mentioning that the horizontal emittance computed b MAD after the first 5 Hz reduction of RF frequenc (with emittance wigglers on) is " MAD =43nm instead of the WIGWAM value of 39 nm. The emittance computed b MAD after the second 5 Hz step is " MAD =69nm, i.e., even larger than the value measured b the BEUV. This results correspond to a wiggler strength adjusted in MAD such as to reproduce the nominal WIGWAM emittance of 3 nm before the first frequenc step (however, the MAD value of J is :7 instead of ). The simulation results corresponding to MD conditions after the first 5 Hz reduction of RF frequenc are shown in Figs. and 3: the (; ; 7) beam ellipsoid refers to the nominal horizontal emittance " = 39 nm and to the measured vertical emittance " = :5 nm. The three-dimensional plot in Fig. indicates that the available dnamic aperture is not sufficient to accommodate the (; ; 7) beam ellipsoid. This is even more clear from the two-dimensional cut shown in Fig. 3, where the beam ellipse crosses the dnamic aperture in the (A ;A )plane at A =:75 3 p m. Since the measured beam lifetime under these condition was still ver good, one could be tempted to conclude that the simulation results must be wrong. To be fair, let us trust the BEUV and assume that a beam

3 .8 e5r46 65GeV MD condition E=39nm,E=nm on the measured horizontal dnamic aperture: A meas 7 q " BEUV ' :65 3 p m: Therefore the eperiment with the 8 =6 optics at 65 GeV is compatible with MAD predictions..6 Sqrt[At/%].4. ˆ3Sqrt[A/m].5 Second surface is {,, 7}sigma ellipsoid.5 ˆ3Sqrt[A/m] Figure : Dnamic aperture computed b MAD tracking for the 8 =6 optics e5r46 using MD conditions at 65 GeV (V RF = 6 MV): three-dimensional plot and beam ellipsoid corresponding to " = 39 nm and " = :5 nm. The and -ais denote normalised apertures (but the smbols A and A appearing in the figure labels are the square of those discussed in the tet), while the vertical ais can be identified with the relative energ deviation p=p in per cent. Sqrt[A/m].5 ˆ3Sqrt[A/m].5 Figure 3: Dnamic aperture in the (A ;A ) plane for the optics e5r46 at 65 GeV: two-dimensional cut of picture in Fig. for p =. The dashed line corresponds to the (; ) beam ellipse with " =39nm and " =:5nm. with horizontal emittance " BEUV = 55 nm (i.e., almost twice the nominal emittance at 9 GeV) had still a lifetime of 4 hours. The point is, however, that a single beam has a good lifetime provided the available aperture is about 7 in all three planes (remember that the criterion applies to beams in collision) and this sets the following lower bound 3. Negative chromaticit tests The LEP dnamic aperture scales roughl as the inverse of the setupole strengths. A straightforward wa to increase the aperture is thus to weaken the chromaticit correction, working with transverse feedback and negative chromaticities. A first test with a low intensit beam (I b =A) using the 8 =6 squeezed optics at 65 GeV showed that, in the absence of feedback, the chromaticities could be lowered down to Q = 7 and Q = 6 before having lifetime problems. With the 9 =6 squeezed optics still at 65 GeV, two beams were put in collision (at a beam-beam tune shift bb :3) with the vertical feedback on (the horizontal feedback did not work properl). Then the vertical chromaticit was progressivel lowered and for Q = 7 the beams were lost, probabl because of an RF trip. We repeated the test with two separated beams (I b = 5 A), stopping the ramp at 45:6 GeV. The vertical chromaticit could be reduced down to Q = 5 with good lifetime, but the beams were lost when the vertical feedback was switched off. During a final test with colliding beams at 45:6 GeV (with a beam-beam tune shift bb :7)the chromaticit could be lowered down to Q = with 5 hours beam lifetime and vertical feedback on. 4 TRACKING RESULTS AT 9 GEV At LEP energies, the dnamic aperture of the 8 =9 optics 5e46 (with odd tunes Q = 3:68, Q = 97:93) is mainl limited b Radiative Beta-Snchrotron Coupling [5]. As shown in Figs. 4 and 5 it is largel sufficient in the (A ;A )plane, but is marginal in the (A ;A t = p=p) plane. On the contrar, the main problem of the 8 =6 optics is the large =@A, leading to an insufficient dnamic aperture in the (A ;A )plane. This is shown in Fig. 6, where the aperture is normalised to the beam dimensions at 9 GeV. This plot has been obtained b a modified version of MAD (available as rgomad in the director hpariel:/users/rgo/rgomad) with new features such as the automatic search and optimisation of dnamic aperture. A comparison of the dnamic aperture in the (A ;A ) plane for different optics at 9 GeV, including also the effect of quadrupole misalignments and closed orbit, is shown in Fig Perspectives The dnamic aperture of low-emittance lattices has been measured for the first time in 995: the agreement with

4 Sqrt[A/m].5.5 DYNAPY DYNAP WITH RADIATION DAMPING: DELTAP=, E=E/ C5R46 (8/6): E=9 GeV, Vrf=8 MV, Qs=., E=3 nm HP/UX version 8.8/ 7// ˆ3Sqrt[A/m]. 8. Figure 4: Dnamic aperture in the (A ;A ) plane for the 8 =9 optics 5e46 at 9 GeV: V RF = 464 MV, Q s = :6 and (; ) beam ellipse corresponding to " = " =. Sqrt[At]/% DYNAPX Table name = SPECIAL.5 Figure 6: Dnamic aperture in the (A ;A ) plane for the 8 =6 optics c5r46 at 9 GeV: the scale on the two aes is the number of beam s..5 ˆ3Sqrt[A/m] data and rgomad, are now available for more sstematic studies and for a pragmatic approach to the optimisation of the LEP dnamic aperture. Figure 5: Dnamic aperture in the (A ;A t =p=p) plane for the 8 =9 optics 5e46 at 9 GeV: same conditions as in Fig. 4. MAD predictions at 45:5 GeV is at the % level, although with the 8 =6 lattice the aperture for positronswas considerabl lower than that for electrons (possibl as a consequence of the kicker timing), while the 8 =9 lattice with = 5cm had poor lifetime with wigglers on. The measurements at 65 GeV with the 8 =6 lattice are compatible with MAD predictions. Above 9 GeV, the aperture is marginal for the 8 =9 lattice and probabl insufficient for 8 =6 lattice. However: octupoles can be used to improve the aperture of the 8 =6 lattice and larger values of Q are beneficial to that of the 9 =6 lattice [3]. further improvements for all lattices (at the 5% level) are possible b means of a reliable transverse feedback sstem, working at negative chromaticities Q 5. 5 ACKNOWLEDGEMENTS I would like to thank J. Jowett and S. Tredwell for their tracking results, shown in Figs., 3, 4 and 5. 6 REFERENCES [] F. Ruggiero, in Proceedings of the Fourth Workshop on LEP Performance,Chamoni, 994, Ed. J. Poole, CERN SL/94-6 (DI), pp (994) and ProceedingsoftheFifth Workshop on LEP Performance, Chamoni, 995, Ed. J. Poole, CERN SL/95-8 (DI), pp (995). [] D. Brandt, A. Hofmann, G. von Holte, M. Lamont, M. Meddahi, G. Ro, Ramp, squeeze and collide with the 8 =6 lattice for bunch train operation, SL-MD Note 89 (995). [3] Y. Aleahin, Improving the dnamic aperture of LEP, CERN SL-95- (AP) (995). [4] C. Arimatea, D. Brandt, A. Hofmann, G. von Holte, R. Yung, M. Lamont, M. Meddahi, G. Morpurgo and F. Ruggiero, Dnamic aperture with the 8 =6, SL-MD Note 99 (995). [5] J. Jowett, in Proceedingsof the Fourth Workshopon LEP Performance, Chamoni, 994, Ed. J. Poole, CERN SL/94-6 (DI), pp (994). new tools, namel post-processing of MAD tracking

5 Figure 7: Dnamic aperture in the (A ;A )plane at 9 GeV for different optics (from Ref. [3]). The solid lines refer to the perfect machines with V RF = 5 MV, the dotted lines are the ellipses and the dashed lines represent the average aperture over man seeds (dots) for quadrupole misalignments, closed orbit correction and V RF = 37 MV.