Racetrack Booster Option & Initial Spin Tracking Results A.M. Kondratenko, M.A. Kondratenko, and Yu.N. Filatov presented by V.S. Morozov MEIC Weekly R&D Meeting September 10, 2015 F. Lin

Racetrack Booster Motivation to consider racetrack booster Shorter circumference better for space charge Lower cost

Racetrack Booster Motivation Booster lattice Reduction of space charge tune shift due to shorter circumference Cost optimization Convenient simplified model to benchmark theory and simulations Booster lattice Modified figure-8 lattice with arc sections removed Injection in a straight, which should be okay for transverse phase-space painting

Ring Length Same straights Figure-8 Racetrack BL, Tm Ldip, m 267 89 188 63

Spin Resonances in Racetrack Particles Number of spin resonances integer  = k intrinsic  = k N  y coupling  = k N  x non-superperiodic  = k  y (k  mN) protons 16 32 deuterons 1

Polarized Protons About 80 resonances for protons Siberian snake Solenoidal snake ~34 Tm at 9 GeV/c: 2  4.6 m with Bmax = 3.7 T Inserted in a straight Ramped with energy Optical effects Compensate betatron tune shift adjusting two quadrupole families in triplets Leave transverse coupling uncompensated as in Nuclotron

Optics with Siberian Snake

Polarized Deuterons Snake not practical (~100 Tm, ~30 m long) Resonance crossing more adequate Characteristic ramp time giving full depolarization For Taccel = 0.01 T *, resonance w crossed fast with 1% depolarization For Taccel = 100 T *, resonance w crossed adiabatically with 1% depolarization (not really practical due to weaker resonances) For typical parameters  fast crossing requires ~4 s ramp time (demonstrated in Nuclotron)  at slower rates, easier to use figure-8

Tracking: Longitudinal Phase Space Crossing of  = y – 5 resonance at 1 T/s B from 5.3 to 5.53 Tm in 3104 turns Benchmarking Zgoubi Longitudinal phase space: Option Integration steps inside body (cm) CPU time, total (s) Quad Bend A 1/10 = 0.1 1/8 = 0.125 1750 B 1/6 = 0.167 1/4 = 0.25 1200 C 1/3 = 0.333 1/2 = 0.5 500 D 1 2 160 A B C D

Tracking: Vertical Phase Space B C D

Tracking: Spin  = y – 5 resonance induced by offsetting strength of one of the quads A B C D

Tracking: Slower Ramp Rate Ramp rate of 510-3 T/s, largest integration step size (D) ~150 times greater polarization loss consistent with expectation

Summary & Conclusions Racetrack shortens the circumference reducing space charge effect and potentially saves the cost Acceleration of polarized protons in a racetrack requires Siberian snake Polarized deuterons feasible with quickly-rampable Nuclotron-style magnets Additional benefit of faster booster cycle Simulations underway in Zgoubi, results consistent with expectations Zgoubi convenient for testing, validation and optimization, longer-term simulations may need to be done with something else, e.g. GPU Spink Next steps Tracking proton polarization in racetrack booster with Siberian snake Validating statistical model Moving on to collider ring Results with exception of spin tracking will be presented at DSPIN