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
1/06/07 Liverpool Christmas meeting
The University of Liverpool/Cockcroft Institute L I Malysheva
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
1/06/07 Liverpool Christmas meeting
The University of Liverpool/Cockcroft Institute L I Malysheva
,dS
Sds
( 2)
2spin orbit
g
SPIN PRECESSION ( THOMAS-BARGMANN-MICHEL-TELEGDI)
( 2)
2
ga
a Spin-tune
whereNote
1/06/07 Liverpool Christmas meeting
The University of Liverpool/Cockcroft Institute L I Malysheva
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
1/06/07 Liverpool Christmas meeting
The University of Liverpool/Cockcroft Institute L I Malysheva
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
1/06/07 Liverpool Christmas meeting
The University of Liverpool/Cockcroft Institute L I Malysheva
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
1/06/07 Liverpool Christmas meeting
The University of Liverpool/Cockcroft Institute L I Malysheva
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
1/06/07 Liverpool Christmas meeting
The University of Liverpool/Cockcroft Institute L I Malysheva
INVARIANT SPIN FIELD COMPONENTS: RF Dipole only
1/06/07 Liverpool Christmas meeting
The University of Liverpool/Cockcroft Institute L I Malysheva
INVARIANT SPIN FIELD COMPONENTS in the presence of betatron motion
1/06/07 Liverpool Christmas meeting
The University of Liverpool/Cockcroft Institute L I Malysheva
Frequency scansVertical component of ISF
QRF QyQy-QRF
2QRF
1/06/07 Liverpool Christmas meeting
The University of Liverpool/Cockcroft Institute L I Malysheva
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”