Cavity tuning options for synchronization R. Rimmer, J. Guo H. Wang, S. Wang,

Synchronization options E-ring RF frequency fe0=1497MHz*7/22=476.318182MHz, harmonic Number=3416. Three basic synchronization schemes were put on the table: 1). Change e-ring path length to sync with β variation in i-ring, have to change RF frequency of both rings accordingly: The PEP-II RF cavities need to tune down by -0.504MHz in addition to detuning for beam The SRF cavities needs to double this due to they are 952.6 MHz, which is -1.007MHz Maximum e-ring path length change is +227.5cm. 2). Change e-ring path, change I-ring harmonic number from 3416 to 3424 for the ion energies of 100 to 12 GeV/u to reduce range of e-ring path. The maximum tuning of PEP-II cavity and SRF cavity is only 139 and 279KHz respectively maximum E-ring path length is 63cm only. No need to change the I-ring path length. If two fold symmetry is required, harmonic number must be even, max e-ring path length change is 126cm, RF frequency range will be 280kHz for e-ring, 560kHz for iring However, collision of electron bunch with different ion bunch in each turn. 3). Change the I-ring path length only No need to change both ring's harmonic numbers=3416 No need to tune both NCRF/SRF cavities No need to change E-ring's path length, but I-ring's. Maximum I-ring path length change is -227cm. With harmonic change, reduce range of path length change to 63cm or 126cm, same as in 2).

PEP-II cavity tuning range PEP-II cavities have one fixed and one movable tuner Each tuner has ~+- 500 kHz range Adequate for retuning to 476.3 MHz plus beam loading May be OK to tune over whole energy range. Moving plunger tuner Fixed tuner Moving tuner

JLab SRF cavity tuners Original CEBAF tuner Mechanism in LHe. Fairly large hysteresis. Warm motor (external). Rotary feedthroughs 10+ years service in CEBAF/FEL Upgrade Scissor-type tuner Very Low hysteresis. Warm motor (external). Linear feedthrough (Bellows) In service in CEBAF/FEL Upgrade zero length tuner Low hysteresis. Cold motor. Tested but not yet installed SNS-type tuner End mount Low hysteresis. Cold motor. In service in SNS

SRF cavity tuning range Typical JLab SRF cavity tuner +- 200 kHz at 1497 MHz, limited by switches. Could be +- 400 kHz? (Tom Powers). Where is the warm/cold elastic limit? Analysis needed. Scales to ~+- 250 kHz at 952.6 MHz. ±140kHz required for harmonic change of 1, ±280kHz for even harmonics Probably OK for tuning over even harmonics. Not sufficient for full energy range. Need to change the design to allow larger tuning range Decrease stiffness of cavity (in a controlled way) Longer stroke tuners Use plungers or external reactive tuners? Have some ideas…

Parameters: change harmonic by 1, change e-ring path and i-ring harmonic number, change frequency for both rings Energy(GeV/u) max dfe (kHz) 139.42 max dfi (kHz) 278.83 max(dLe) (cm) 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 3421 15.39758 17.41057 0.998349 14.7219 16.69044 0.998204 -69.495 -138.989 31.373 3422 14.12211 16.05119 0.998057 13.58834 15.4823 0.997912 -69.454 -138.908 31.355 3423 13.10604 14.96827 0.997766 12.67068 14.50427 0.99762 -69.413 952.498 -138.827 31.336 3424 12.27195 14.0793 0.997474 11.90811 13.69154 0.997329 -69.373 -138.745 31.318

Parameters: change harmonic by 1, change e-ring path and i-ring harmonic number, change frequency for both rings e-ring harmonic number: 3416 iring circumference 2149.607 optimized ion Energy: 47.252 GeV E-ring center circumference 2150.015 e-ring circumference(m) min 2149.70 Max 2150.33 Δ=0.63 i-ring Harmonic number i-ring Energy(GeV/u) γ β max 35.266 100.008 38.586 107.588 0.99966 0.99996 3417 25.531 35.268 28.211 38.588 0.99937 3418 20.931 25.534 23.308 28.214 0.99908 3419 18.117 20.933 20.309 23.310 0.99879 3420 16.170 18.119 18.233 20.311 0.99849 3421 14.720 16.172 16.688 18.236 0.99820 0.99850 3422 13.586 14.722 15.480 16.690 0.99791 3423 12.669 13.588 14.502 15.482 0.99762 3424 11.906 12.671 13.690 14.504 0.99733 E-ring Frequency(MHz) Δf(kHz) e-ring Δf(kHz) i-ring min max df min df max 476.25 476.39 -69.71 69.73 -139.42 139.46

Parameters: change harmonic by 2, change e-ring path and i-ring harmonic number, change frequency for both rings Energy(GeV/u) max dfe (kHz) 278.79 max dfi (kHz) 557.59 max(dLe) (cm) 125.84 ions γ β Ne Np fe (MHz) dfe (kHz) fp (MHz) dfp (kHz) Le (m) dLe (cm) 100.00 107.58 0.999957 3416 476.458 139.396 952.915 278.792 2150.644 62.921 90.00 95.92 0.999946 476.452 134.088 952.905 268.176 2150.620 60.525 80.00 85.26 0.999931 476.445 127.210 952.891 254.419 2150.589 57.420 70.00 74.61 0.99991 476.435 117.177 952.871 234.353 2150.543 52.891 60.00 63.95 0.999878 476.420 101.718 952.840 203.437 2150.474 45.914 50.00 53.29 0.999824 476.394 76.080 952.789 152.161 2150.358 34.341 40.00 43.63 0.999737 476.353 34.821 952.706 69.642 2150.172 15.717 35.27 38.59 0.999664 476.318 0.000 952.636 2150.015 30.00 32.97 0.99954 476.259 -59.187 952.518 -118.374 2149.747 -26.716 25.53 28.21 0.999372 476.179 -139.397 952.358 -278.795 2149.385 -62.921 3418 23.00 25.51 0.999232 476.391 72.592 952.782 145.184 2150.342 32.767 20.93 23.31 0.999079 0.040 0.080 0.018 20.00 22.32 0.998995 476.278 -39.968 952.556 -79.936 2149.834 -18.041 18.12 20.31 0.998787 -139.234 -278.469 2149.386 -62.848 3420 16.17 18.24 0.998495 0.122 952.637 0.243 0.055 14.72 16.69 0.998204 -139.071 -278.143 2149.387 -62.774 3422 13.59 15.48 0.997912 0.203 0.406 0.092 12.67 14.50 0.99762 -138.909 952.359 -277.818 2149.388 -62.701 3424 11.91 13.69 0.997329 0.284 0.568 2150.016 0.128 11.26 13.00 0.997038 -138.746 -277.493 -62.628

Parameters: change harmonic by 2, change e-ring path and i-ring harmonic number, change frequency for both rings e-ring harmonic number: 3416 iring Circumference 2149.293 optimized ion Energy: 35.2677 GeV center circumference 2150.015 e-ring Circumference(m) min 2149.39 Max 2150.64 Δ=1.26 i-ring Harmonic number Energy(GeV/u) γ β max 25.532 100.102 28.212 107.687 0.99937 0.99996 3418 18.116 25.536 20.307 28.216 0.99879 3420 14.719 18.120 16.687 20.312 0.99820 3422 12.667 14.722 14.501 16.691 0.99762 3424 11.258 12.671 12.999 14.505 0.99704 E-ring Frequency(MHz) Δf(kHz) e-ring Ion ring min max df min df max 476.18 476.46 -139.40 139.48 -278.79 278.96