Aperture Measurements and Implications

Aperture Measurements and Implications H. Burkhardt, SL Division, CERN, Geneva, Switzerland Abstract Within short time, the 2/90 optics allowed to reach similar luminosity performance as the 90/60 optics, that has been used for years in LEP. The higher phase advance in the horizontal plane allows smaller emittances with the potential for higher luminosities and at the same time higher beam-energies for a given maximum RF-voltage. There is however one point of concern in using optics with a higher phase advance: The maximum stable emittance was found to be less than in the 90/60 optics due to the presence of enhanced non-ian tails. This presentation summarizes the results of recent maximum emittance and tail scan measurements and analyzes the implications for the physical and dynamic aperture needed for stable physics operation. DEFINITION AND UNITS OF APERTURE The same units can be used to define a physical or dynamic aperture. As example we will consider a solid physical aperture, like the beam-pipe or a collimator at a given distance from the beam axis, say at r =35mm (the smallest radius of the LEP beam pipe). The rms-beamsize without dispersion is σ = ɛβ (for regions with non-negligible dispersion D the beamsize is σ = ɛβ + D 2 σe 2 ). The relative energy spread in the beam is called σ E. The aperture can be given in the number of σ that can be accommodated: n σ = r σ = r ɛβ Numerical example: For an emittance ɛ =30nm a physical limit of r =35mm at a β = 50 m allows for 6.5 σ. As emittance independent measure of aperture one can define: r β The quantity A gives the linear dimensions normalized by / β and has units of m. In the case of non-negligible dispersion the aperture is: r β + D2 σ 2 E ɛβ The use of m units can be avoided by using: r2 β which has units of meter but the disadvantage of scaling as r 2. Here we will mainly use A and it will be sufficient to consider the case without dispersion. Using again as example r =35mm at β = 50 m one obtains numerically: 35 mm 50 m =2.86 3 m =2.86 µm or (35 mm)2 50 m =8.7µm The two measures of aperture are related as: n σ = r σ = A ɛ According to Sands[], the lifetime for a ian beam andanapertureofn σ is or numerically: τ = τ dam n 2 σ exp ( ) n 2 σ 2 τ dam n σ for n σ for msec h h LEP 64 5.4 5.8 LEP2 8 5.8 6.2 2 MAXIMUM EMITTANCE MEASUREMENTS 2. Horizontal Plane Studies of dynamic aperture using large kicks[2] leading to about 50 % beam loss have not systematically been done in 997. The measurements described here use emittance increase involving a change of the horizontal damping partition number J x. Aperture studies using both methods have been discussed in the previous Chamonix workshop[3]. The maximum aperture measurements were performed as follows: The starting point is a well corrected machine, using low chromaticity (Q =.5) in both planes and physics tunes. The RF-frequency is then reduced up to the point were the lifetime drops down to a level of hour. For the data presented here, emittances were calculated using the MAD program[4]. The nominal emittance on the design orbit ɛ n and the actual horizontal emittance as function of the damping partition number ɛ x are related by ɛ x = ɛ n J x J x can be written in terms of the standard radiation integrals I 4 and I 2, or in excellent approximation, as function () 80

of the RF-frequency change f RF with respect to the central frequency. J x = I 4 =+ f RF dj x I 2 α c f RF dp/p A numerical example for the determination of the maximum stable emittance as calculated with the RF-frequency change in the 90/60 lattice is sketched below: Measured frequency for zero tide : 352 254 54 Hz Tide correction: +4.3 Hz Central frequency (tide corrected): 352 254 58.3 Hz Using the nominal f RF = 352 254 70.0 Hz corresponds to a frequency shift with respect to the central orbit of f RF =.7 Hz. The lifetime dropped to hour for a trim of -75 Hz corresponding to f RF = -63.3 Hz / With α c =.855 4 and dj x dp/p = 275.35 we get J x =0.32. With ɛ n = 35.25 nm this implies ɛ h x = 3 nm. It is reasonable to assume that the beam occupied at least 5.5 σ from which we can obtain a lower limit on the dynamic aperture: A x 5.5 ɛ h =.8 µm. Date optics βy E b f trim ɛ h cm GeV Hz nm 5.5 ɛ h µm 3/9 8/90 2 45.6 80 4. 2/ 8/90 2 90 70 48.2 4/9 2/90 27 45.6 30 7.5 2/ 2/90 27 90 85 58.3 9/ 2/90 5 9.5 95 68.4 / 90/90 2 45.6 35 99.7 / 90/90 2 85 95 75.5 2/9 90/60 5 45.6 75 3.8 Table : Summary of the maximum emittance measurements performed in 997 The largest stable emittance was obtained with the 90/60 lattice. Whenever time and equipment allowed, the emittances were checked using the BEUV and tail scans were done at the nominal frequency and for a frequency shift resulting in about h lifetime. Figure shows the result of a tail scan in the 2/90 lattice at 90 GeV[5]. The measured tail distribution is much larger than expected from a ian distribution for an emittance of ɛ x = 53nm. The lifetime starts to be reduced by a physical aperture limit, the collimator COLH.IP5, at a setting of about 3 mm. The horizontal β function at this collimator is β x =25.25 m. The tail scan Measured by Jörg Wenninger inverse lifetime (/h) from scraping at aperture limit n σ using ε x = 5 nm 0 2 4 6 8 2 - -2 53 nm 5.5σ -2 collimator reducing lifetime to h - external jaw internal jaw 5 nm (just to guide the eye) tail scan by I.Reichel -3 3 0 2 4 6 8 2 4 6 8 20 COLH.IP5 setting in mm Figure : Tail scan in the 2/90 lattice at 90 GeV. The nominal frequency shift of 75 Hz corresponds to f RF = 57 Hz and J x =0.68 leading to a predicted (core) emittance of ɛ x =53nm. shows that the aperture needed for the beam with tails is Ax =3mm/ β x =2.6 µm. Similar measurements were also done for the other lattices in 997. The results are summarized in table 2. optics E b COLH.IP5 Ax ɛ h GeV mm µm nm n σ 8/90 90.5 2. 48 9.6 2/90 90 3 2.6 68 90/90 85 2.5 2.5 75 8. 90/60 45 9.5.9 3 5.7 Table 2: Summary of results from tail scans in 997. Horizontal aperture were COLH.IP5 starts to limit the lifetime. From the collimator setting, normalized by / β x and the maximum stable emittance one can calculate the number of sigmas occupied by the blown up beam at h lifetime according to: n σ = Ax ɛ h The results in table 2 show, that only in the case of the 90/60 optics, the number of sigmas needed is still compatible with a ian shape even at maximum emittance. In the other optics, more than 5.5 σ is needed for big beams (this was observed previously, for a discussion and qualitative explanation see [6]). It can be concluded that: τ (h) 2 It is mainly the appearance of non ian tails which reduces the maximum stable emittance. 8

Collimators should not be set tighter for the low emittance optics, rather be opened further to allow for enhanced tails. 2.2 Vertical Plane There were also attempts, to measure the maximum stable vertical emittance. The method used was: Increase the horizontal emittance using damping partition (and emittance wiggler at 45.6 GeV) as for the measurement of the maximum horizontal emittance. Introduce some coupling (for example by removing the machine coupling compensation). move on coupling resonance, q x = q y. In the best case, one obtains about round beams with ɛ x ɛ y. Very strong frequency shifts are needed. In the 90/60 optics for example, lifetimes started only dropping at 270 Hz frequency shift or for J x close to zero. At this level, the energy changes already significantly: f RF f RF = η p p α E x E here E =+0.4% Date optics E b f trim ɛ h GeV Hz nm 5.5 ɛ h µm 23//96 8/90 45.6 0 8 0.74 6/8/97 90/60 45.6 270 3 0.62 9//97 2/90 9.5 45 30 0.95 Table 3: Summary of attempts to measure the maximum stable vertical emittance, β y =5cm. Table 3 summarizes the results. The emittance is based on beam size measurements using the BEUV. There are some doubts on the precision of these measurements, particularly for the one done on the 6/8/97 were 3 nm emittance seems far too little for a frequency shift of 270 Hz. There is also some knowledge on the space needed in the vertical plane for good lifetime: 90/60 optics, 45.6 GeV, fill 39 on 28/7/97 and MD on 6/8/97. Lifetime was effected by cutting at to 2 mm at a β y =60.2m implying A y.5 µm 2/90 optics, 9.5 GeV, fill 443, moving COLV2.QL8.R5 from 2 to mm reduced the lifetime from 7 to 2.7 h so that A y.4 µm The case of fill 39 is illustrated in Figure 2. The collimator settings used in fill 39 are given below. For the out or ramp&squeeze settings: hor.: 2.7 σ of 48. nm A x =2.8 µm ver.: 57.8 σ of 2.4 nm A y =2.8 µm For the in or physics settings: hor.: 2.0 σ of 35.0 nm A x =2.2 µm ver.: 25.0 σ of 3.5 nm A y =.5 µm Ie-, ma.495.490.485.480.475.470.465 τ = 25 h H,V collimators in τ = 3h out τ = 30 h Q v trim H in V in τ = 8h Fill parameters: 4 2+4 2 bunches ξ y = 0.02 I e + = 260µA /bunch I e - = 85µA /bunch out tune trims, orbit corr. τ = 25 h physics 5 6 7 8 9 20 2 22 23 24 25 26 27 28 29 30 time in minutes from 9:00 Figure 2: Electron beam current in the 30 minutes from colliding to stable physics in fill 39, at 45.6 GeV on the 28/7/997 The lifetime was reduced by the vertical collimator settings. Only after some tune adjustments and orbit corrections, it was possible to run with the physics settings and good lifetimes. 3 WHAT IS NEEDED? We know [7, 8, 9] that non-ian beam tails can be substantial, in particular for high beam beam tune shifts high chromaticity as can be seen in Fig. 3. Losses from Scraping in /hours nσ using the measured emittance 0 20 40 60 80 0 20 - -2-3 -4 gaussian core Q'=7 separated beams, Q'=7 45.6 GeV, ε y 0.4 nm /6/95 using scint., Q'=, ξ y 0.03 Q'=, ξ y 0.04 Lifetime poor - -5 5 0 0.25 0.5 0.75.25.5.75 2 2.25 2.5 collimator setting / ß, in -3 m Figure 3: Measured beam tails in the vertical plane. 90/60 lattice at 45.6 GeV. 2 3 4 Lifetime from Scraping in hours 82

The number of σ of the core emittance is not a good measure of the aperture needed. Smaller emittances in collision lead to higher beam-beam tune shifts and more tails. To be sure that collimators do not limit the aperture one should aim for A y =2 µm(or32 σ of ɛ nom =4nm). inverse lifetime (/h) from scraping at aperture limit nσ for ε = 25 nm 0 2.5 5 7.5 2.5 5 7.5 20 - -2-3 -4 tailscan by I.Reichel Fill 38 3..95 :05 50µA ξy =.05 ξx =.0 29 nm collimator physics setting Fill 327 9..95 20:42 500µA / bunch ξy =.046 ξx =.04 like tail ~95 nm 2 3 4 0 0.5.5 2 2.5 3 3.5 collimator position / ß, in µm Figure 4: Observed horizontal beam tails at 65 GeV for low and high horizontal beam-beam tune shift. Figure 4 shows horizontal tail scans done at 65 GeV. A strong tail at about 2 σ x from the core emittance was observed for high horizontal beam-beam tune shift. The collimator physics settings were at A x =2.54 µm. This was in fact about what was needed. The main collimator settings used in 997 are listed below in number of sigma for the nominal emittance 2 and the equivalent in terms of A. For the 90/60 optics, 45.6 GeV: 2 σ of 35 nm A x =2.25 µm 25 σ of 3.5 nm A y =.48 µm The setting in the vertical plane is tight and resulted in lifetime reduction as observed in fill 39. 90/60 optics, 9.5 GeV: 2 σ of 48. nm A x =2.4 µm 25 σ of 2.4 nm A y =.22 µm The vertical settings reduce the aperture but lifetimes were ok for present bunch currents and beam-beam tune shift. 2/90 optics, 9.5 GeV: 2 σ of 38 nm A x =2.35 µm 25 σ of.9 nm A y =.09 µm The vertical settings reduced the aperture and lifetime optimization was necessary to allow stable running as is discussed below. 2 as used by Georg von Holtey τ (h) 4 APERTURE NEEDS IN THE 2/90 LATTICE IN PHYSICS There is some first experience on the aperture needs from the last week of 2/90 operation in 997. First attempts to push the luminosity up using frequency shifts of more than +50 Hz resulted in poor lifetimes. The chromaticity settings used in physics were Q x =5and Q y =4,which is not particularly high. Higher chromaticities have frequently been used in the 90/60 optics to suppress coherent beam-beam oscillations. Moreover measurements showed, that the horizontal chromaticity was nearly 4 units lower then the setting (the measured Q y instead agreed with the setting). Losses from Scraping in /hours nσ using the measured emittance 0 20 40 60 80 0 20 ε x = 23 nm (b.b. scan and calculated) ξ x = 0.028 ε y = 0.36 nm, ξ y = 0.035 Q x '= 4 Q - y '= 4 Q x '= 7 Q y '= 3-2 -3-4 gaussian core Q x '= 4 Q y '= 3 aperture from collimator physics settings n σ = 25, ε nom =.9 nm A y =.09 µm - -5 5 0 0.25 0.5 0.75.25.5.75 2 2.25 2.5 collimator setting / ß, in -3 m Figure 5: Vertical beam tails observed in physics operation at 9.5 GeV in the 2/90 optics for three different chromaticity settings. Figure 5 shows vertical tails, measured towards the end of fill 4430 (the last day of 997 operation) in physics. The beam currents were I e + =.7mA and I e =.9mA (or on average 460 µa/bunch). The nominal RF-frequency shift was 0 Hz. Strong tails were measured for Q y = 4. They were substantially reduced when the vertical chromaticity was decreased by one unit. A change of the horizontal chromaticity of three units also had a significant effect on the vertical tails. There were no problems with coherent beam-beam oscillations and it was possible to reduce the vertical chromaticiy to Q y =2. This was applied in the last days of 997 operation and allowed frequency shifts beyond +50 Hz. Fill 443 (9.5 GeV, 2/90 optics) on the 9//997 was operated under these conditions. The lifetime throughout the fill is shown in Figure 6. A single beam lifetime of 40 h is well compatible with the expectation from Compton and Beam Gas scattering. For a beam-beam tune shift of 0.05, we expect 8.5 h lifetime in collisions adding up (inversely) with the single beam lifetime to a total of 6.8 h. 2 3 4 Lifetime from Scraping in hours 83

lifetime in hours 60 50 40 30 20 0 3 a 22.4 GeV cm a 87.00 GeV 5 cm e+ e- a 9.50 GeV 5 cm p 9.50 GeV 5 cm colliding 4 5 6 7 8 9 daytime in hours a 9.50 GeV 5 cm separated aperture meas. Figure 6: Beam Lifetime for fill 443. The observed single beam lifetimes of about 40 h and the lifetimes in collision of about 7 h at the beginning of the fill are as expected. There is no indication of significant extra losses by scraping into tails. The beam-beam tune shifts in this fill are showninfigure7. tune shift parameter ξ.06.04.02 Fill 443, 2/90 9.5 GeV, ßx* = 2 m κ = % ε x = 23 nm (J x =.6) 0 0 0.2 0.4 0.6 Bunch current in ma ξ y ξ x from ε x = 23 nm and current Figure 7: Beam-Beam tune shift parameters as function of the bunch current in fill 443. The vertical beam-beam tune shift is calculated from the observed luminosities of the four LEP experiments. The horizontal beam-beam tune shift is calculated from the expected horizontal emittance assuming no emittance increase in collision. The increase of the vertical beam-beam tune shift for high currents coincides with the frequency shift in steps to +0 Hz. The decrease at lower currents is compatible with an emittance ratio of %. At the end of the fill beam-beam deflection scans were done. 5 SUMMARY, CONCLUSION Aperture is important in the horizontal and vertical plane. The space is needed for extended non-ian tails. It should be avoided to reduce the aperture by collimator settings unless absolutely needed for background. The 2/90 (and also the 90/90) optics need already more than 5.5 σ even for single beams when the emittance is large. The aperture needed depends on the amount of non- ian tails and parameters like ξ, Q, J x and the working point and can therefore to some extend be optimized. The available aperture has limited the performance at 45 GeV and was just enough at 65 GeV and in the recent 2/90 operation. The 2/90 looks promising for high luminosities at high energy but tends to have more non-ian tails than the 90/60 optics. In future it will be attempted to collide higher bunch currents. Aperture and non-ian tails are a potential limitation. 6 REFERENCES [] M. Sands. The Physics of Electron Storage Rings. SLAC REPORT 2, SLAC, 970. [2] J. Jowett. Non-linear Resonances: Predictions, Effects and Measurements. In J. Poole, editor, Proceedings of the 7th Workshop on LEP Performance, pages 76 88, 997. [3] I. Reichel. Dynamic Aperture and Tail Scans. In J. Poole, editor, Proceedings of the 7th Workshop on LEP Performance, pages 67 7, 997. [4] H. Grote and F. C. Iselin. The MAD Program, User s Reference Manual. SL Note 90-3 (AP) (Rev. 4), CERN, March 995. [5] D. Brandt et al. Test of the 2 /90 optics at high energy. SL-MD Note 244, CERN, October 997. [6] J. Gareyte. LEP2 Optics: Options and Implications. In J. Poole, editor, Proceedings of the 7th Workshop on LEP Performance, pages 89 90, 997. [7] H.Burkhardt et al. Beam Tails in LEP. In V. Suller and Ch. Petit-Jean-Genaz, editors, Proceedings of the 5th European Particle Accelerator Conference, volume 2, pages 52 54, 996. [8] I. Reichel. Studies of the Transverse Beam Profile in LEP. PhD thesis, RWTH Aachen, work still in progress. [9] H. Burkhardt. Beam-Beam Interaction and Beam Lifetime in LEP. Proceedings of the 4th Advanced ICFA Beam Dynamics Workshop on Beam Dynamics Issues for e + e Factories, Frascati 20-25 October 997. 84