LER Beam-Beam Collimation. Studies Using TURTLE

Transcription

1 LER Beam-Beam Collimation Studies Using TURTLE Stephanie Majewski, Witold Kozanecki October 21, 2004 Abstract We report the results of a TURTLE study designed to explore the use of collimation to minimize background due to beam-beam effects in the LER. We have found that background from horizontal beam-beam tails can be reduced by tighter collimation in PEP Region 4 in conjunction with the relocation of an existing collimator to a location 25 m downstream of the detector.

2 Contents 1 Overview 3 2 TURTLE 4 3 Beam-Beam Tails in the Horizontal Plane Consistency Checks Effectiveness of Proposed Downstream Collimators Beam-Beam Tails in the Vertical Plane 18 5 Recommendations and Summary 20 References 21 Appendix: Comparison to Previous Durin Study 22

3 1 Overview The primary motivation for this study is to reduce background due to LER tails produced by beam-beam effects through more effective collimation. Certain key LER collimators should guard against backgrounds from the particles in these tails. In particular, four collimators in PEP Region 4 (PR04) and two movable jaw collimators in PEP Region 2 (PR02) have the greatest impact on these tails. The PEP region map is shown in Figure 1, pinpointing the approximate locations of these six collimators upstream of the IP in the LER. Also shown on this map are the mirrored locations of the PR02 collimators. This study hopes to detail the effects of tightening the PR04 collimators and to explore the possible relocation of the PR02 collimators, all with the aim of reducing background in the detector. In particular, the position of the PR02 collimators (as of January 2004) projects electromagnetic shower debris into the detector. These collimators also generate very significant HOM-induced heating, resulting in unacceptable thermal outgassing in the incoming LEB straight. Both problems will hopefully be avoided by collimating downstream of the detector, so that shower products or beam-gas secondaries travel harmlessly down the beamline and mostly hit the beam pipe long before completing a full turn around the ring. This study does not attempt a full simulation of the complicated physics of beambeam tail production. Instead, we perform a worst-case scenario analysis by producing a large-emittance particle beam that samples all betatron phases in one turn rather than consecutive turns. One can mimic the turn-to-turn betatron phase shift experienced by a particle on consecutive turns by using thousands of particles scattered throughout 3

4 Figure 1: PEP-II Region Map showing collimator locations. The positrons travel in the counterclockwise direction. phase space that only traverse one turn. Consequently, the results of this study provide a collimation strategy that is independent of the actual shape of the beam-beam tails. 2 TURTLE Trace Unlimited Rays Through Lumped Elements, or TURTLE, is a single-pass charged particle beam transport program. The version of TURTLE used, called Lost-Particle TURTLE, or LPTURTLE [1], is a modified version of DecayTURTLE [2]. The elements in the beamline (magnets, apertures, etc.) were taken from a MAD input and converted into a TURTLE deck. A beam was then generated at the IP and propagated throughout the LER until passing the IP once more and going 25 m beyond it. In TURTLE coordinates, m is at the first IP (the beam starting point), and the second 4

5 Table 1: Collimator Locations and Apertures. PEP Region Collimator Name z Location May 2004 Aperture Setting PR04 Primary Y 365 m y 10.5 mm 3014 PR04 Primary X 345 m x 11.8 mm 2082 PR04 Secondary X 320 m x 8.4 mm 2042 PR04 Secondary Y 313 m y 6.3 mm 2032 PR02 Movable Jaw 25 m x 19.5 mm STEP 3077/3076 x 22.0 mm PR02 Movable Jaw 12 m x 27.5 mm STEP 3044/3043 x 26.0 mm IP is at 0 m along the z-direction. x and x describe the horizontal plane 1 and y and y describe the vertical plane for the physical beamline. Using these conventions, the collimator locations and aperture settings are listed in Table 1. The deck used in this study was l turtle, a deck prepared in 1998 by Ted Fieguth. The tune is therefore slightly outdated, with a value of 0.57 instead of the May 2004 value of The nominal IP beam size is mm in x, mrad in x, mm in y, and mrad in y. These values correspond to a nominal emittance of 22 nm-rad in x and 1.49 nm-rad in y. The x and y dimensions in the beam optics are for the most part decoupled, so this analysis treated them independently. Therefore, to 1 Note: The TURTLE convention is that in the LER, the positive x-direction is toward the center of the PEP ring 5

6 cover all of phase space, the y-emittance was increased 10,000-fold, while the x-emittance remained nominal, and conversely the x-emittance was increased (although only 900-fold) while the y-emittance was held to nominal 2. This effectively divided the analysis into two sections. 3 Beam-Beam Tails in the Horizontal Plane In order to study the effects of beam-beam tails in the horizontal plane, the x and x 1σ values were each increased by a factor of 30. A plot of the phase space distribution is shown in Figure 2(a). The beam initially generated uniformly filled this entire region of phase space. The PR04 and PR02 Collimators were left completely open for this run. The central envelope is empty because TURTLE plots only particles that hit apertures, and these central particles passed through the beamline unscathed. Figure 2(b) shows the positions along the beamline where the corresponding particles were lost. In Figure 3, the trajectories of particles lost near the IP are plotted. These are representative of the areas of phase space that need to be collimated in order to reduce background in the detector. 2 For the TURTLE expert, the particles generated were actually Coulomb-scattered over a region of essentially zero length at the beginning of the deck. This was because LPTURTLE only plots lost particles that are also scattered. 6

7 Figure 2: (a) Plot of the IP coordinates x /σ x vs. x/σ x, where σ x = mm and σ x = mrad (the nominal values). This includes only the particles that strike an aperture in the single turn. (b) This plot shows the z-locations where the colorcorresponding particles in (a) were eventually lost along the beamline. 785 particles were lost out of

8 Figure 3: Trajectories of particles lost near the IP for large x-emittance. 3.1 Consistency Checks Various consistency checks were performed to verify the current results. The results from the first of these checks, a comparison with a study conducted in 2000, can be found in the Appendix. This comparison showed adequate agreement between the two studies. Another check involved performing a first-order R-matrix calculation based on parameters from the MAD deck. We first generated a large x-emittance beam and transported it with Turtle to the location of the possible future collimator, +25 m downstream of the IP (Fig. 1). The phase space of all 1000 generated particles at that location is illustrated in Figure 4. The slight curvature of the x-x correlation is presumably caused by the S2 sextupoles. Also, note the absence of any significant x-y or x-y correlation, reflecting the fact that the LER deck contains neither the BaBar solenoid, nor any of the compensating 8

9 Table 2: MAD Beam Optics Parameters. α x β x [m] µ x [2π] +25 m m (+1 turn) m (+1 turn) skew quadrupoles. Starting from this location (IP+25 m), each particle is transported down the beam line, to first order only, by taking its initial displacement and angle, and multiplying it by a matrix (R) whose elements are calculated from beam optics parameters at the initial and final locations. These parameters, α, β, and µ, are listed in Table 2 for the starting point and locations one turn down the beamline. Only a 2 2 matrix is needed because of the inherently uncoupled character of our beamline model (Fig. 4). The first-order transport equation is: x x b R 11 R 12 x = R 21 R 22 x a. (1) Equations 2 and 3 show the relationships between the matrix elements and the optics parameters. R 11 = β b β a (cos µ + α a sin µ) (2) R 12 = β a β b sin µ (3) After inputting the parameters from Table 2, the first-order equations for each final 9

10 Figure 4: Snapshot of positions and angles of particles after propagating 25 m in TUR- TLE. One can see that only x and x are correlated. 10

11 location are: x 25m (+1 turn) = 9.6x +25m x +25m, and x +25m (+1 turn) = 4.9x +25m 23.1x +25m. The TURTLE-generated histograms for x and x at 25 m can then be plugged into this equation. The resulting histograms should roughly agree with the histograms that TURTLE generates at locations further downstream. Figure 5 shows the initial phase space projections at the starting point (IP+25 m), and the corresponding distributions, calculated either by TURTLE or using the first-order R-matrix formalism, at two locations: the present 25 m collimator and the +25 m collimator after one full turn. A direct comparison of particle positions computed by the two methods (Figure 6) suggests the actual optics contain significant higher order terms. This becomes fully apparent when plotting the difference in calculated x positions at the 25 m collimator vs. the x-angle at the starting location (Figure 7). 3.2 Effectiveness of Proposed Downstream Collimators This section presents x-position histograms of particles that would strike within ±25 m of the IP. This region of interest was chosen so that it generously included the region in which particles would cause backgrounds in the detector. Histograms are recorded at the z-positions of the actual adjustable collimators (PR02 STEP 3077/3076, 3044/3043), and at the possible downstream locations (PR02 STEP 2172/2172, 2142/2141); the adjustable jaws are left fully open in this simulation. In this way, one can see how effective 11

12 Figure 5: A comparison between TURTLE-generated histograms and histograms calculated using first-order beam optics. The first row is the starting x and x generated by TURTLE after the particles travel 25 m downstream. The second row is at the location of the 25 m collimator upstream of the IP, and the third row is exactly one full turn after the starting point. The two sets of histograms are roughly consistent considering no nonlinearities are taken into account in the R-matrix calculation. 12

13 Figure 6: These two plots show the particle positions calculated using first-order optics versus the particle positions as transported by TURTLE (which models up to at least third order) at the same location. The nonlinearities are especially evident after one full turn (right plot). The straight line is a visual reference showing an ideal first-order result. The fact that the full ray-tracing yields positions systematically above (left plot) or below (right plot) the first-order calculation indicates the presence of significant second- and possibly higher-order terms in the LER. 13

14 Figure 7: The correlation between the difference in calculated x positions (R-matrix calculation TURTLE) at the 25 m collimator and the x-angle at the starting location (+25 m). 14

15 Table 3: PR04 Collimator 8, 10, and 12σ settings, assuming fully-coupled emittances (ɛ x = 48 nm-rad and ɛ y = 24 nm-rad). Collimator z location 8σ [mm] 10σ [mm] 12σ [mm] m y 6.8 y 8.5 y m x 8.9 x 11.1 x m x 6.5 x 8.1 x m y 5.5 y 6.9 y 8.3 a collimator in each of the four locations would be in reducing detector background. Figures 8 and 9 show these results. In each subfigure, the top plot shows, in red, the locations of each particle that would hit near the IP. The green vertical lines show the May 2004 collimator setting, the outer black vertical lines show the 10σ setting, and the innermost black vertical lines show the physical minimum aperture of the collimators. The second, third, and bottom plots in each subfigure show a progressive tightening of the PR04 collimators to their 12σ, 10σ, and 8σ settings, respectively. These settings are listed in Table 3. From these plots, one can see that closing the PR04 collimators more tightly does indeed reduce the number of particles that strike apertures near the detector, as expected. The PR04 collimators seem to collimate most of these troublesome particles. However, there is a small subset of particles that cannot be collimated in PR04 and yet still strike near the IP. The existing PR02 collimators would be able to collimate them, but this solution is not currently practical due to secondaries that hit the detector and HOM heating. Figures 8 and 9 show that particles that would hit near the IP are located farther out in x at the downstream collimator locations. Therefore, in principle, 15

16 16 Figure 8: The x distributions of particles hitting the beam pipe in the vicinity of the IP, plotted at the present 25 m collimator (left), and at a possible new collimator located +25 m downstream of the IP (right). The green vertical lines show the current 25 m collimator setting (as of May 2004), the outer black vertical lines show the 10σ setting, and the innermost black vertical lines show the minimum aperture. From top to bottom, these plots show PR04 collimators completely open and then the effects of tightening the PR04 collimator apertures to their 12σ, 10σ, and 8σ settings (see Table 3).

17 17 Figure 9: The x distributions of particles hitting the beam pipe in the vicinity of the IP, plotted at the present 12 m collimator (left), and at a possible new collimator located +12 m downstream of the IP (right). The green vertical lines show the current 12 m collimator setting (as of May 2004), the outer black vertical lines show the 10σ setting, and the innermost black vertical lines show the minimum aperture. From top to bottom, these plots show PR04 collimators completely open and then the effects of tightening the PR04 collimator apertures to their 12σ, 10σ, and 8σ settings (see Table 3).

18 the same collimators moved downstream can have wider apertures than at the upstream locations and yet collimate more particles. This is especially advantageous from a beam lifetime perspective since tightening collimators has an adverse effect on the beam lifetime. Therefore it appears that the alternate, mirrored locations downstream of the IP at +12 and +25 m would make collimation even easier in addition to the benefit that this collimation would occur nearly an entire turn before the detector. 4 Beam-Beam Tails in the Vertical Plane In a similar manner to the horizontal beam-beam study, tails in the vertical plane were created by generating a uniform distribution in which the y-emittance increased by a factor of 10,000 and the x-emittance remained at its nominal value. Figure 10(a) shows the phase space in y, while Figure 10(b) is a histogram of the locations along the beamline where these particles collided with apertures. It is particularly worthwhile to note that none of these particles strike an aperture within ±25 m of the IP. Therefore, these plots demonstrate that even at extremely large vertical amplitudes, beam-beam tails in the vertical plane will not cause increased backgrounds in the detector. The loss points in Figure 10(b) correspond to high-β points in the beam optics. Figure 11 shows the β-functions in x and y for the entire ring. As a consistency check, TURTLE was forced to keep track of all the particles it produced, rather than only the particles lost in a certain region 3. Figure 12 shows the 3 This is technically accomplished by placing a false wall (an aperture card with a large offset and an extremely small slit) at the end of the deck. 18

19 Figure 10: (a) Plot of y /σ y vs. y/σ y at the particles initial locations, where σ y = mm and σ y = mrad (the nominal values). Only particles that hit an aperture somewhere in the single turn are shown. (b) Plot of the z-locations along the beamline where these particles are lost. The plots are color-coded so that one can see which sections of initial phase space are lost at various locations. The peaks are also numbered to show that they correspond to peaks in the β-functions in Figure 11. The number in the upper right corner is the number of particles lost, 453, out of the 1000 particles generated. Note that no particles are lost within 50 m of the IP. 19

20 Figure 11: β versus z. One would expect particles to get lost at peaks in the β-function. Note that the z-axis is NOT in TURTLE coordinates; the IP is located at the center of the plot. For comparison, the numbered peaks in the green, dashed β y correspond to the loss points in Figure 10(b). trajectories of the particles that pass through the ±5 m region around the IP. These particles correspond to those in the empty envelope in Figure 10(a) because they did not strike a physical aperture. 5 Recommendations and Summary In summary, vertical beam-beam tails do not contribute to detector background in the LER. Horizontal beam-beam tails can be successfully collimated downstream of the detector at +25 m, in conjunction with the PR04 collimators, assuming there is no grave impact on the lifetime of the LEB. A slight drawback is that a downstream collimator would not protect the detector against particles that are Coulomb-scattered between 20

21 Figure 12: Plot of particle trajectories for particles that do not strike apertures anywhere along the beamline. The IP is located at 0 m. The initial y-emittance was 10,000 times the nominal emittance. PR04 and 25 m. The original recommendation is that the 12 m collimator be moved to the +25 m location, and that the 25 m collimator remain in place. In practice, both the 12 m and 25 m collimators had to be removed during the shutdown in August 2004 to alleviate HOM heating. One of these collimators will be moved to the +25 m location during a subsequent shutdown. References [1] W. Kozanecki and J. Matthews, Addendum to Decay TURTLE Manual. witold/turtle/tur107 manual.turdoc [2] D. Carey, K. Brown, and C. Iselin, Decay Turtle Manual, SLAC-246 (1982). 21

22 [3] W. Kozanecki and S. Majewski, Beam-Beam Collimation Study. Talk given on 7 July 2004 at the BaBar Collaboration Meeting, MDI Parallel Session II. detjul04/wed4f/kozanecki1.ppt Appendix: Comparison to Previous Durin Study In 2000, Bruno Durin completed Background Studies in PEP II with TURTLE. LP- TURTLE allows for beam-gas interactions in the form of beam-gas bremsstrahlung and multiple Coulomb scattering. Durin plotted Coulomb scattering histograms in the LER of the z locations of where the particles were scattered and the z locations where particles struck apertures. In doing so, Durin only allowed scattering in the range z 62 m. Figure 13 shows the replication of that study 4. Through visual inspection, since Durin s results are not electronically available, it appears that the only discrepancy is a loss peak at 3 m in his study that disappears in Figure 13 after closing the PR02 collimators. 4 Parameter 6 of the Coulomb decay card was set to GeV 2 /m. 22

23 Figure 13: Coulomb-scattered particles in the LER, replicating the Durin study. Scattering was allowed in the region z 62 m. The histograms in the left-hand column depicts where the particles were scattered, and the right-hand column shows histograms of where particles were lost. In the first row, all PR04 and PR02 collimators are completely open. In the second row, all of the PR04 collimators are closed to 10σ. The third row additionally closes the 25 m collimator to its 10σ aperture setting, and in the bottom row all six apertures are closed to 10σ (see Table 3). 23