Status of Proton Deuteron Spin Tracking in Racetrack

Status of Proton & Deuteron Spin Tracking in Racetrack Booster A. M. Kondratenko, M. A. Kondratenko, and Yu. N. Filatov presented by V. S. Morozov MEIC Weekly R&D Meeting December 17, 2015

Model Racetrack Booster Same straights as in figure-8, arcs based on the smaller arc of figure-8 Fractional betatron tunes x / y = 0. 947 / 0. 836 MEIC Weekly R&D Meeting 12/17/15 2

Error Effect Quadrupole strength error = k/k = 10 -3 ( x / y = 4 / -2 10 -3) symmetry breaking “non-super-periodic” intrinsic resonances Misalignment and roll errors currently being studied MEIC Weekly R&D Meeting 12/17/15 3

Transverse Motion (Zgoubi) Vertical Horizontal Transverse phase-space dynamics in a ring with quadrupole strength errors during acceleration to kinetic energy T of ~3. 7 Ge. V for protons and 6. 5 Ge. V for deuterons with a field ramp rate of 1 T/s showing adiabatic damping deuterons protons MEIC Weekly R&D Meeting 12/17/15 4

Longitudinal Motion (Zgoubi) Approaching transition energy deuterons p/p vs. T protons MEIC Weekly R&D Meeting 12/17/15 5

Proton Polarization (Zgoubi) Vertical proton polarization vs. G Perfect lattice Synchronous particle Lattice with k/k errors Synchronous particle “Super-periodic” intrinsic spin resonances … Non-super-periodic intrinsic spin resonances … transition energy MEIC Weekly R&D Meeting 12/17/15 6 Lattice with k/k errors 3 particles on ellipse with p/p = 5 10 -4 Synchrotron side-band spin resonances

Deuteron Polarization (Zgoubi) Longitudinal deuteron polarization vs. T (hard to see any effect for vertical polarization) Perfect lattice Synchronous particle Lattice with k/k errors Synchronous particle No spin resonances due to the choice of y Non-super-periodic intrinsic spin resonances … MEIC Weekly R&D Meeting 12/17/15 7 Lattice with k/k errors 3 particles on ellipse with p/p = 5 10 -4 Synchrotron side-band spin resonances

Summary Started tracking spins of protons and deuterons in a racetrack booster Studied effect of quadrupole strength errors Working on misalignment and roll errors Results exactly as expected: racetrack is okay at 1 T/s field ramp rate Experiencing issues with solenoid in Zgoubi (need to talk to F. Meot) May need to compensate chromaticity to avoid coupling resonances in the presence of coupling (roll errors and Siberian snake) Other than that almost done with a racetrack, will then move on to figure-8 MEIC Weekly R&D Meeting 12/17/15 8