# Presentation: 756535

## Depolarization along the RHIC ramp

- Copyright, 1996 © Dale Carnegie & Associates, Inc.

## Overview

- Review Spin Resonance
- Consider relevant snakes Resonance during 2002 run
- Examine Imperfection, Intrinsic and Coupled spin resonance in RHIC
- A Case for 3/14th coupled snake resonance
- Fitting a simple coupled snake spin Resonance model

## Review of Spin Resonance

- 	With out snakes the spin precesses Gg times each period.  Depolarization occurs when:
- Gg = integer                Imperfection
- Gg = N±Qy                  Intrinsic
- Gg = N±Qx                  Coupled

## Imperfection Resonance strength depend:
Y closed orbit distortions
Lattice periodicity
Acceleration rate, vertical emittance
Intrinsic Resonance strength depend:
 Lattice periodicity 
 Vertical and Horizontal tune
Acceleration rate, vertical emittance

- Y closed orbit distortions
- Lattice periodicity
- Acceleration rate, vertical emittance
- Intrinsic Resonance strength depend:
-  Lattice periodicity
-  Vertical and Horizontal tune
- Acceleration rate, vertical emittance

## Coupled Spin Resonance depend on:
Lattice periodicity
Strength of global coupling
		- skew and solenoidal fields
		- |Qx-Qy|
Acceleration rate, Horizontal emittance

- Lattice periodicity
- Strength of global coupling
- 		- skew and solenoidal fields
- 		- |Qx-Qy|
- Acceleration rate, Horizontal emittance

## The introduction of a snake forces the spin tune to be 1/2 and thus energy independent. In this way the imperfection, intrinsic and coupled spin resonance condition can be avoided. However this introduces a new “snake” resonance condition given by:				δQy =  (Qs±k)/lwhere l= order of resonance

## l=odd                   Odd Snake Resonance
Associated intrinsic or coupled spin resonance strength, acceleration rate
l=even                 Even Snake Resonance
Associated intrinsic or coupled spin resonance strength, acceleration rate
Imperfection resonance strength
        -Splits resonance by

- Associated intrinsic or coupled spin resonance strength, acceleration rate
**l**=even                 Even Snake Resonance
- Associated intrinsic or coupled spin resonance strength, acceleration rate
- Imperfection resonance strength
-         -Splits resonance by

## Relevant Snake Resonance During the 2002 run

- Tune
- Box

## Imperfection, Intrinsic and coupled spin resonance in RHIC

- From recent survey Data we can see that
- Y(co) max < 5 mm
- In the Energy range of the ramp this places
- |є|max < 0.2
- Which for the even snake resonance:
- 1/4 - 0.0076=0.242
- 3/16 +0.0019= 0.189

## Slide 10

## Slide 11

## 3/16

- res. split

- 1/4
- res. split

## Slide 13

## A Case for the 3/14 and 1/4 Snake Resonance

- Since our vertical tune was kept well above 3/14 depolarization could only come from 1/4 resonance
- However our Horizontal tune did cross the 3/14 tune and Strong coupling known to exist
- Since intrinsic Resonance < 0.2 numerical simulations in the past rule out the effect of higher order resonance

## Fitting a simple coupled snake spin Resonance model

- Data Sorting:
- For 3/14 snake resonance fit we excluded any fills with Qy > 0.245
- From these collected tune and orbit data for the three major intrinsic resonance locations along the ramp
- From these Picked the Resonance with min |Qx-3/14| value.

## Slide 16

## Slide 17

## To understand the variability of these coefficients versus Blue Rsq=0.724 and Yellow Rsq=0.663 
Swapping term by term in Blue for Yellow
		-  0.715,0.676,0.597,0.724
Swapping term by term in Yellow for Blue
		-  0.663,0.643,0.426,0.663
Largest variability due to the Yrms term 
			-could be due to old orbit data

- Swapping term by term in Blue for Yellow
- 		-  0.715,0.676,0.597,0.724
- Swapping term by term in Yellow for Blue
- 		-  0.663,0.643,0.426,0.663
- Largest variability due to the Yrms term
- 			-could be due to old orbit data

## Blue 1/4 snake Resonance

## Yellow 1/4 snake resonance

## Conclusion

- To avoid Depolarization we suggest
- Correction of vertical closed orbit
- Better tune control to avoid 3/14 and keep tune separated
- Try to better De-couple machine