More on MEIC Beam Synchronization Yuhong Zhang MEIC Accelerator R&D Meeting August 6, 2015

Facts about Path Length Adjustment for Achieving Beam Synchronization Nominal bunch spacing (for electrons and ions): 63 cm @ 476 MHz rep rate Range of path length adjustment: 63 cm (1 IP with harmonic number change) 18 to 100 GeV up to 254 cm (without harmonic number change) 12 to 100 GeV up to 555 cm (without harmonic number change) Consider the case with harmonic number change, path-length adjustment +/-31.5 cm Due to symmetry, each half ring is responsible for +/- 15.75 cm (still big!) (CEBAF path length correction +/-1 cm, Rublin) Needs three chicane (Morozov) of 66 to 110 m length to cover +/- 31.5 cm (requiring to move up to 24 dipoles and 27 quads, and other elements) Present design, one arc is 755 m in e-ring, 3 chicane is up to 22% of the two arc We are effectively moving up to 1/5 of the arc! # of FODO cells # of magnet moved Path length change Radial movement range Maximum change in magnet spacing 3 4 dipoles, 5 quads 10 cm +52 / -69 cm 20 mm 4 6 dipoles, 7 quads +36 / -39 cm 14 mm 5 8 dipoles, 9 quads +28 / -29 cm 11 mm 66 m 88 m 110 m

Fixed Bypass Beam Line for Reducing the Range of Magnet Moving We introduce a set of fixed bypass beam lines for discrete increments of path length for assisting the (large) path length adjustment The movable chicanes will be required to cover much smaller ranges of path length adjustment. We hope these chicanes are not much more than the CEBAF chicanes (15 m long for +/- 1 cm) A switch yard will direct electrons to different orbit which is most closed to the required path length. There is an extra cost for these additional bypass beam lines, but it may make the problem less harder. And it is better done at the e-ring for cost effectiveness. These bypass beam lines can be staged Switch yard merger

An Economy Way of Using Bypass Beam Lines Add multiple (>2) bypass beam lines at one location prevents simultaneously use of them. We propose only two beam lines at one location. It can be called “path length jump”. The electrons will go either one of two beam lines. We distribute several “jumps” in the ring (left and right symmetrically), then the increments of the path length can be added up to produce a much large amount of increase. If the jumps are chosen properly, any path length adjustment should be covered Switch merger Units Path length adjustment Sum of Chicanes cm (+/-1)x2 ==> 4 4.5 5 6 Jump 1 4 Jump 2 8 9 10 Jump 3 13.5 12 Jump 4 Total 32 31.5 Building blocks Path length (cm) Chicanes 0 to 4.5 Chicanes + Jump 1 4.5 to 9 Chicanes + Jump 2 9 to 13.5 Chicanes + Jump 3 18 to 22.5 Chicanes + Jump 2&3 22.5 to 27 Chicanes + ump 1&2&3 27 to 31.5

An Illustration in Electron Collider Ring Present CEBAF path length chicane: +/-1 cm chicane “Path length jump” e- R=155m RF Spin rotator CCB Arc, 261.7 81.7 IP Tune trombone & Straight FODOs Future 2nd IP variable +/-1 cm Fixed +4 cm Fixed +8 cm Fixed +8 cm Fixed +8 cm Variable +/-1 cm Electron collider ring w/ major machine components

Harmonic Number Change Without Gear Change (A Backup Plan) Still allow change of harmonic number in the ion ring Change the harmonic number in the electron ring to match the harmonic number in the ion ring (both rings always have the same number of bunches) Change electron ring path length to accommodate additional bunches Advantage: no gear change, restoring one-to-one collision pattern Advantage: gaps will be synchronized, no extra luminosity loss Have multiple by-pass beam lines (jumps) to absorb large path length change Have 2 or 4 chicanes to adjust +/- half bunch spacing (for one IP) for covering energies between harmonic energies. Why change harmonic numbers in the ion ring? Making the RF frequency change not too large Why change harmonic numbers in the electron ring? Have the same bunch numbers in two collider rings

Change of Electron Path Length for No-Gear Change Scheme From 18 to 100 GeV, there are 4 harmonic numbers The electron ring needs to cover 4x63=252 cm  3x63 cm + +/-31.5 cm Each arc: 1.5x63 cm + +/-15.75 cm Add two large “path-length jumps” in each arc 0.5x63 cm = 31.5 cm 1 x63 cm = 63 cm Ion Energy Bunches GeV/u 47.25 3416 29.28 3417 22.91 3418 19.38 3419 Units Path length adjustment Sum of Chicanes cm 31.5 4 4.5 6 Jump 1 Jump 2 8 9 10 Jump 3 13.5 Jump 4 Large jump 1 Large jump 2 63 Total 242

What is the Impact on the Ring Design? Issues Space and location for large by-pass beam lines Cost of additional beam lines (magnet power supplies may be shared within a jump) Optics (nonlinear beam dynamics) Magnet field strength Synchrotron radiation and its impact on the emittance and spin From Vasily Morozov’s email “Looks very good. Of course, engineering issues especially near the spreader and recombiner points need to be checked. My only potential concern is about how this may affect the chromaticity compensation scheme. That is if we place sextupoles in the arcs we will need to make sure that the bypasses do not affect the phase advance between the sextupoles, etc. We should also take a quick look at the optics of the bypass sections to make sure there is no significant impact on the emittance, spin, etc.”

Harmonic Numbers with 1 IP (J. Guo) Energy(GeV/u) max dfe (kHz) 139.42 max dfi (kHz) 278.83 62.93 ions γ β Ne Np fe (MHz) dfe (kHz) fp (MHz) dfp (kHz) Le (m) dLe (cm) 100 107.5789 0.999957 3416 476.388 69.719 952.776 139.437 2149.700 -31.465 90 96.92101 0.999947 476.383 64.943 952.766 129.886 2149.721 -29.310 80 86.26312 0.999933 476.376 58.289 952.753 116.579 2149.752 -26.308 70 75.60523 0.999913 476.367 48.628 952.734 97.255 2149.795 -21.947 60 64.94734 0.999881 476.352 33.827 952.704 67.654 2149.862 -15.268 50 54.28945 0.99983 476.328 9.475 952.655 18.949 2149.972 -4.277 47.25391 51.3627 0.99981 476.318 0.000 952.636 2150.015 40 43.63156 0.999737 476.283 -34.841 952.567 -69.682 2150.172 15.728 35.2677 38.58793 0.999664 476.248 -69.698 952.497 -139.397 2150.329 31.465 3417 32 35.10525 0.999594 476.355 36.381 952.709 72.763 2149.850 -16.421 29.28052 32.20686 0.999518 28 30.84209 0.999474 476.297 -20.790 952.595 -41.579 2150.108 9.384 25.5341 28.21396 0.999372 476.249 -69.658 -139.315 31.447 3418 22.90505 25.41195 0.999225 20.93303 23.31019 0.999079 -69.617 -139.233 31.428 3419 19.37978 21.65476 0.998933 18.11901 20.31104 0.998787 -69.576 -139.152 31.410 3420 17.06557 19.1883 0.998641 16.17181 18.23573 0.998495 -69.535 -139.071 2150.328 31.392

Fitting the Physics Operation Scenario A possible operation scenario (P. Nadel-Turonski) 100 GeV proton 66.7 GeV proton and Helium-3 50 GeV all A/Z = 0.5 nuclei including d, p 40 GeV all stripped Pb ions, protons 20-30 GeV (?) low-energy setting A better choice of 1st harmonic number is 52.7 GeV  reducing path-length adjustment to +/-23.6 cm (25% reduction) for 40 to 100 GeV Low energy (20 to 30 GeV) be curved by three harmonic energies Ion energy (GeV/u) Harmonic number 30.5 +1 23.5 +2 19.71 +3 17.30 +4 15.57 +5 14.25 +6 13.22 +7 12.36 +8 Ion energy (GeV) Path length adjustment per arc (cm) Chicanes (+/-1 cm) per arc 5 cm Jumps per arc 100 11.8 1 2 66.7 6.1 50 1.8 - 40 -11.8 Even number for two IPs! Are these discrete energies are good enough? This works for two IPs!

What is a New (Ugly) Baseline for MEIC Beam Synchronization? Do not change the ion ring circumference, but do allow change of its harmonic number (ion bunch number) Allow adjusting the electron ring circumference up to +/-0.5 bunch spacing for one IP (and up to +/-1 bunch spacing for two IPs) Allow adjusting the RF frequency in both collider rings Set the 1st harmonic number to 47.3 GeV, thus, no harmonic number change from 35.3 to 100 GeV Electron ring circumference will be adjusted by multiple chicanes. Optionally using the path-length jump If “gear-change” must be avoid, increase harmonic number in the electron collider ring to make same bunch numbers in both rings (“harmonic number jump without gear change”); Increase electron ring circumference to accommodate extra electron bunches; add large “path-length-jumps”