1. Orbit related issues of the spin tune control at RHIC V.Ptitsyn, M.Bai, W.MacKay, T.Roser

2. STAR rotators PHENIX rotators Siberian Snakes - spin tune shift in first order on perturbations z-vertical y-longitudinal coordinate - periodical spin solution on the design orbit (stable spin direction) Calculation in first order perturbation theory

3. Effects of horizontal orbit Siberian Snakes I III IV II -two parts of periodical orbit distortion: closed orbit and average momentum error (non-zero mean orbit) For closed orbit: sn2 sn1 rt1 rt2 For momentum error: measured in Q3-Q4 sectionsmeasured in Q7-Q8 sections Full solution was found: (CA/AP Note 334, M.Bai,V.Ptitsyn, T.Roser) integrates to 0

4. Typical scales for horizontal orbit effects Orbit angle error, mrad  sp, 10 -3 Tolerance (in mm) on BPMs to achieve 1e-3 spin tune shift Snakes0.115.40.042 Rotator0.17.70.234 Closed orbit error: Design  D’, mrad  sp, 10 -3 Snakes-53.6-4.2 Rotator5.30.2 Momentum error dp/p = 5e-4 (~0.8mm radius offset): All calculations are done for 250 GeV energy At store (after ramping RF to target frequency) the radius offset was (Run-8) less than 0.2mm in both rings. The same number characterizes tune spread. May be largest factor contributing to the spin tune spread.

5. Correction atempt In last day of the pp run-8 the attempt was made to correct the snake angles at 3 o’clock area with local orbit bumps. The correction was made on the whole ramp as well as in the store. However, the correction led to considerable orbit excursion at neighboring BPMs. In Blue required correction varied: 0.06-0.34mrad in different stones

6. Snake orbital angle during ramp in Blue M.Bai

7. Snake orbital angle during ramp in Yellow M.Bai

8. Inside of rotator insertions: longitudinal field Siberian Snakes I III IV II sn2 sn1 rt1 rt2 Integrates to 0 due to the symmetry STAR solenoidDX-D0 edge fields 2.1 Tm Noticeable effect only if the rotators are turned on at low energies. For the RHIC injection energy and longitudinal polarization at IP8:

9. Vertical orbit effects Siberian Snakes I III IV II -closed orbit distortion only (no dispersion) Maximum tune shift (assuming n x =1 in the IR triplets) from each rotator: sn2 sn1 rt1 rt2 measured in Q3-Q4 sections  sp, 10 -3 Orbit angle error0.1 mrad7.7 Design bump (IR separation) 3 mm12.8 Per rotator at 250 GeV (assuming n x =1) Bumps are present on the rotator ramp n x should be taken in the IR triplets. It depends on the beam energy and rotator settings IR6 and IR8 bumps has to be of opposite sign to cancel this tune shift

10. For better precision (~10 -3 ) of the spin tune shift calculation orbit kick produced by the rotators should be included into the consideration W.MacKay

11. Higher-order orbit effects Considerable spin tune shift from combined horizontal and vertical separation bumps at IR12. Combined bumps are used to manage the beams around and through the H-jet. W.MacKay Simulation results Third order effect: ~ xz 2 Becomes important for bump amplitudes larger than 5mm zbump, mm

12. Conclusions Several effects related with the closed orbit can lead to the spin tune shifts at 10 -2 -10 -3 level: –Horizontal orbit angles at Snakes –Horizontal orbit angles at Rotators –Vertical orbit angles at Rotators –Combined orbit bumps at IR12 –Mean horizontal orbit (radius) offsets During the operation the orbit should be controlled at the snake locations at least with 200 mm accuracy level (for  sp < 0.005): –Realignment of the magnets around the snake regions done in the shutdown. –Beam-based alignment measurements to reveal BPM-to-quad center misalignments are planned. –Yellow snake area BPM repaired –Special orbit 4-bumps are prepared to simplify the orbit angle control at the snake areas Other orbit control issues: –Control of the horizontal and vertical orbit at the rotators –Application of IR6 and IR8 vertical separation bumps of opposite sign –More careful arrangement of IR12 bumps –Orbit radius control on the ramp to less than 1mm Dedicated beam studies are planned to measure the orbit effects on the spin tune shift.