1. 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
F. Lin

2. Model Racetrack Booster
Same straights as in figure-8, arcs based on the smaller arc of figure-8
Fractional betatron tunes x / y = / 0.836

3. 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

4. Transverse Motion (Zgoubi)
Transverse phase-space dynamics in a ring with quadrupole strength errors during acceleration to kinetic energy T of ~3.7 GeV for protons and 6.5 GeV for deuterons with a field ramp rate of 1 T/s showing adiabatic damping
protons
deuterons
Horizontal
Vertical

5. Longitudinal Motion (Zgoubi)
Approaching transition energy
protons
deuterons
p/p vs. T
p/p vs. s

6. Proton Polarization (Zgoubi)
Vertical proton polarization vs. G
Perfect lattice
Synchronous particle
“Super-periodic” intrinsic
spin resonances …
Lattice with k/k errors
Synchronous particle
Non-super-periodic intrinsic
spin resonances …
Lattice with k/k errors
3 particles on ellipse with p/p = 510-4
Synchrotron side-band
spin resonances
transition energy

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

8. 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