Flipping proton and deuteron spins in storage rings L.I. Malysheva.

Flipping proton and deuteron spins in storage rings

L.I. Malysheva

1/06/07 Liverpool Christmas meeting

The University of Liverpool/Cockcroft Institute L I Malysheva

Motivation

A high intensity polarised beams are an essential tool Past: VEPP, HERA, LEP, AmPS… NOW: COSY , RHIC Future: LHeC, FAIR, eRHIC , JPARC, Super-B, ( ILC? ) Radio-frequency (RF) methods for spin manipulation: a) Spin-flipping technique: Stable and fast b) Beam Energy Calibration using resonance depolarisation c) Polarimeter calibration

Use of RF dipoles or Solenoids



Polarisation for spin-1/2 and spin-1 particles

SPIN-1/2 density matrix

11

N

ii

SP

NS

2 2

1

2I P

1 2 3, ,P P P P

SPIN-1 density matrix 3 3

1 3 3

3 2 2 ij i j j iI P P

ijPare tensor polarisation components. ( Irreducible tensor of rank 2 )

( )P Tr



,dS

Sds

( 2)

2spin orbit

g

SPIN PRECESSION ( THOMAS-BARGMANN-MICHEL-TELEGDI)

( 2)

2

ga

a Spin-tune

whereNote



Single Resonance Model (SRM) and spin-flipping

B Analogous to NMR

RF transverse field

Froissart –Stora formula

2

22 1f

i

Se

S

where

is the rate of resonance crossing

is “resonance strength” : The value can be extracted from experiments data. Unexpected or misinterpreted??

If 0 RFk Q SRM expected

RFdQ

dt



COSY is a cooler synchrotron and storage ring

Length: 180 m closed loop vacuum tube.

momentum range: 600 ---3700 MeV/c ( 175 -- 2880 MeV).

"internal experiments“ : experiments with the circulating beam

"external experiments": experiments with the extracted beam

"COoler SYnchrotron"

Tests ongoing to evaluate the technique of spin-flipping



ISF as a new tool for evaluation of spin-flipping technique Froissart-Stora formula is based on SRM If the ‘naive’ SRM does not provide a sufficient

description, then expect some unexpected behaviour ! Two views to follow: 1) Using Froissart-Stora formulae and DEPOL program…2) DESY expertise based on application of Invariant Spin

Field (ISF) concept: If ISF exists (all parameters fixed) then

(A.I.)The SRM can be solved exactly analytically or numericallyThe “stroboscopic averaging” algorithm provides a reliable

tool for calculating ISF in the presence of RF dipoles.Investigate static spin configuration for fixed frequencies

ˆ( , )n z

ˆJ S n const



Simple Model

To test concept: simplified model of COSY Ring was used: only dipoles and quadrupoles.

Real parameters There are 2 effects associated with

presence of RF dipole in the lattice: Direct effect on spin motion Contribution to the resonance strength

due to forced betatron oscillation

, , , ,RF betQ Q E



INVARIANT SPIN FIELD COMPONENTS: RF Dipole only



INVARIANT SPIN FIELD COMPONENTS in the presence of betatron motion



Frequency scansVertical component of ISF

QRF QyQy-QRF

2QRF



Status and Future plans Go beyond the usual superficial view on

the topic: various diagnostics is build in dedicated code

Simulations for protons confirm strong enhancement in resonance strength vs. “nominal” RF dipole strength.

Now: check against Froissart-Stora simulation on ISF – ongoing

Next: proton and deuteron simulation on the real ring (Using SPRINT) to try to disentangle COSY’s spin-flip “mysteries”

Flipping proton and deuteron spins in storage rings L.I. Malysheva.

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