Orbit related issues of the spin tune control at RHIC

V.Ptitsyn, M.Bai, W.MacKay, T.Roser

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STAR rotators

PHENIX rotators

Siberian Snakes

1zn

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1zn0zn

1zn

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sp dsnw

21 - spin tune shift in first order on perturbations

z-verticaly-longitudinal coordinate

n - periodical spin solution on the design orbit (stable spin direction)

Calculation in first order perturbation theory

Effects of horizontal orbit

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Siberian Snakes

1zn

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1zn0zn

1zn

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-two parts of periodical orbit

distortion: closed orbit and averagemomentum error (non-zero mean orbit)

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For closed orbit:

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0

For momentum error:

measured in Q3-Q4 sections measured in Q7-Q8 sections

Full solution was found:(CA/AP Note 334, M.Bai,V.Ptitsyn, T.Roser)

integrates to 0

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

Snakes 0.1 15.4 0.042

Rotator 0.1 7.7 0.234

Closed orbit error:

Design D’, mrad sp, 10-3

Snakes -53.6 -4.2

Rotator 5.3 0.2

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 offsetwas (Run-8) less than 0.2mm in both rings. The same number

characterizes tune spread.May be largest factor contributing tothe spin tune spread.

Correction atemptIn last day of the pp run-8 the attempt was made to correct the snake anglesat 3 o’clock area with local orbit bumps. The correction was made on thewhole ramp as well as in the store. However, the correction led to considerable orbit excursion at neighboring BPMs.

In Blue requiredcorrection varied:0.06-0.34mradin different stones

Snake orbital angle during ramp in BlueM.Bai

Snake orbital angle during ramp in Yellow

M.Bai

Inside of rotator insertions: longitudinal field

dsnKGKzKG yC

pp

zyzsp )(1 021

Siberian Snakes

1zn

1zn

1zn0zn

1zn

0znI

III

IV

II

sn2

sn1

rt1

rt2

Integrates to 0due to the symmetry

STAR solenoidDX-D0edge fields

510sp

2.1 Tm

3102.4 sp

Noticeable effect only if the rotators are turned onat low energies. For the RHIC injection energyand longitudinal polarization at IP8:

Vertical orbit effects

21

00

21

21

rtx

rtx

Cxsp dsnzdsnzdsnz

Siberian Snakes

1zn

1zn

1zn0zn

1zn

0znI

III

IV

II

cozz -closed orbit distortion only (no dispersion)

inoutsp zz

21 0

Maximum tune shift (assuming nx=1 in the IR triplets) from each rotator:

sn2

sn1

rt1

rt2measured in Q3-Q4 sections

sp, 10-3

Orbit angle error 0.1 mrad 7.7

Design bump (IR separation)

3 mm 12.8

Per rotator at 250 GeV (assuming nx=1)

Bumps are presenton the rotator ramp

nx should be taken in the IR triplets. It depends on the beam energy androtator settings

IR6 and IR8 bumps has to beof opposite sign to cancel this tune shift

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

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.MacKaySimulation results

Third order effect: ~ xz2

Becomes important for bump amplitudes larger than 5mm

zbump, mm

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.