Update on MEIC Nonlinear Dynamics Work V.S. Morozov Teleconference on Nonlinear Dynamics July 7, 2015 F. Lin

Complete Ring Lattice Two identical CCBs, one upstream and the other one downstream of the IP Optimal phase advances first obtained using thin trombones then implemented by adjusting phase advances of dispersion-free quadrupole sections Betatron tunes: x = 25.22, y = 23.16 IP

MAD-X vs Elegant vs LEGO Betatron tunes: x = 25.22, y = 23.16 No synchrotron motion x = 23.4 m, y = 4.7 m, p/p = 310-4 @ 60 GeV/c p/p = 0 p/p = ~3p/p p/p = 10p/p

Tracking in Elegant Betatron tunes: x = 25.22, y = 23.16 No synchrotron motion x = 23.4 m, y = 4.7 m, p/p = 310-4 @ 60 GeV/c No issue with thin trombones in Elegant, ok to use for optimization Thick trombones Thin trombones

Frequency Map in x-p Elegant, 1000 turns, no synchrotron motion, thick trombone case x y dr x y dr

Frequency Map in y-p Elegant, 1000 turns, no synchrotron motion, thick trombone case x y dr x y dr

RF Parameters Proton Lead ion Energy 20 30 40 50 60 70 80 90 100 GeV/u Rev Frequency 0.139 MHz gamma 22.3 33.0 43.6 54.3 64.9 75.6 86.3 96.9 107.6 44.1 RF frequency 952.6 Current 0.50 A Harmonic Number 6832 Circumference 2147.94 2149.11 2149.53 2149.73 2149.84 2149.91 2149.95 2149.98 2150.00 2149.54 m Momentum Compaction 6.413E-03 Energy Spread 2.00E-04 Bunch Length 12 mm Phase Slip Factor 4.40E-03 5.49E-03 5.89E-03 6.07E-03 6.18E-03 6.24E-03 6.28E-03 6.31E-03 6.33E-03 5.90E-03 CavityActiveLength 0.157 Vpeak 2.64 4.93 7.05 9.08 11.09 13.06 15.03 16.9793 18.93 17.90 MV Cavity Insertion Length 1.91 Syn. Phase 0.00 degree temperature 2 K Vgap 0.88 1.23 1.17 1.14 1.19 1.25 1.21 1.18 BCS Resistance 8.91 nΩ Gradient 5.58 7.83 7.46 7.22 7.55 7.96 7.71 7.52 7.59 MV/m Residual Resistance 4.39 Syn. Tune 0.025 0.031 0.034 0.035 0.036 Surface Resistance 13.3 Forward Power 25.28 49.77 45.17 42.25 49.70 46.20 51.37 48.19 45.84 46.68 kW Geometric Factor 217.01 Cavity Power 0.4 0.9 0.8 0.7 W R/Q 105.687 Reflected Power Qzero 1.63E+10 Coupling Beta 2.26E+05 Shunt Impedance 1.72E+06 MΩ δf -28.7 -20.4 -21.4 -22.2 -21.2 -20.1 -20.8 -21.3 -21.1 kHz Qext 7.22E+04 Qloaded Active Cavity Number 3 4 6 8 9 11 14 16 15 Total RF Power 75.9 199.1 271.0 338.0 447.3 508.2 616.4 674.7 733.4 700.2

Tracking in MAD-X with Synchrotron Motion Thick trombone case Betatron tunes: x = 25.22, y = 23.16 Thin RF cavity, h = 6832, V = 11.09 MV, s = 0.0367 @ 60 GeV/c x = 23.4 m, y = 4.7 m, p/p = 310-4 @ 60 GeV/c p/p = 0 p/p = 3p/p p/p = 10p/p

Conclusions & Outlook LEGO, MAD-X PTC and Elegant all give very consistent results Started analyzing non-linear behavior of the CCB scheme RF parameters straightened out Understand RF settings in both MAD-X and Elegant, currently running tracking with synchrotron motion in Elegant Further work Would like to understand what limits the CCB scheme: check resonance driving terms, play with phase advances, etc. Betatron tune scan