Design and Test of a Prototype Cavity for a
Stern-Gerlach Polarimeter
Peter Cameron - BNL
Design and Test of a Prototype Cavity for a
Stern-Gerlach Polarimeter
P. Cameron1, M. Conte4, N. D’Imperio1, W. Franklin6,
D.A.Goldberg3, A. Luccio1, M. Palazzi4, M. Pusterla5,
R. Rossmanith2, W. MacKay1, T. Zwart6
1Brookhaven
National Laboratory, Upton, NY 11973, USA
2Forschungszentrum Karlsruhe GmbH, D-76021 Karlsruhe, Germany
3Lawrence Berkeley National Laboratory, Berkeley, CA 94720 USA
4Universita and Sezione INFN di Genova, 16146 Genova, Italy
5Universita and Sezione INFN di Padova, 35131 Padova, Italy
6MIT-Bates Laboratory, Boston MA 01949 USA
2
Outline
• What this is about
• Stern-Gerlach History
• Derbenev and the transverse pickup
• Conte et al and the longitudinal kicker
• Conte et al and the transverse kicker
• The Bates polarimeter
• The RHIC polarimeter
• What next?
3
What this is about
• Polarization measurement as beam instrumentation
rather than a scattering experiment
• The essence of the problem
•
•
Enhance interaction of m with pickup
Dynamic range – accomplish the measurement in the presence
of the electric charge background
• The approach
• Resonant pickup
• Magnetic dipole has geometry – take advantage of relativity
• Mode suppression and filtering
• First electrons, then protons
4
Brief History
1896
1922
1927
1983
1985
1993
Zeeman splitting - fine structure dE = hdn = mB
Stern/Gerlach splitting - ‘space quantization’ F = grad(mB)
kicker
Pauli proposes spin S = sqrt(s(s+1)) = 1.732/2 s = 1/2 observable
Barber & Cabrera and Michigan/AGS - Squid
pickup
Niinikoski and Rossmanith- transverse splitting in a synchrotron kicker
Derbenev - RF Resonance Polarimeter - transverse moment
pickup
1995 Conte et al - longitudinal spin splitting
g? 1/g?
kicker
1996 Argonne BIW Cameron et al - Squid Polarimeter - longitudinal
1998 RHIC Note Cameron et al - MIT-Bates Cavity - longitudinal
2000 LANL preprint server - Conte et al - transverse
2001 PAC - poster and paper based on MIT-Bates meeting
2002 September - Spin 2002 MIT-Bates, RHIC, LHC,…
g2
pickup
pickup
pickup
pickup
pickup, kicker
5
Derbenev - Transverse
• Hamiltonian approach with spin motion as described
•
•
•
•
•
by BMT.
Potential confusion - BMT lives in more than one
reference frame
Requires TM cavity mode, which couples strongly to
beam charge.
Excitation to move spin away from stable spin
direction (spectral separation) also drives the cavity
No gamma dependence - small signals, no advantage
to working at high energy
Requires extremely high-Q (~1010) resonant cavity
6
Conte et al - Longitudinal
• Longitudinal magnetic moment transforms as g –
•
•
•
•
Jackson, Hagedorn,…
First proposal for a longitudinal spin splitter
Proposal for polarimeter at MIT-Bates
Nature conspires against observation - contribution
due to space and time gradients of magnetic field
cancel to order 1/ g
Squid polarimeter should still work for electrons
(non-linear device, energy comes not from beam but
rather from junction bias) but if it doesn’t work for
protons, why bother?
7
Outline
• What this is about
• Stern-Gerlach History
• Derbenev and the transverse pickup
• Conte et al and the longitudinal kicker
• Conte et al and the transverse kicker
• The Bates polarimeter
• The RHIC polarimeter
• Conclusions
8
Conte et al - Transverse
• Reference – LANL preprint 0003069
• Transverse magnetic moment is invariant
• BUT - interaction of moment with appropriate TE cavity
mode goes as g2
•
analogous to inverse Compton scattering, FELs,???…
• Second proposal for a longitudinal spin splitter – kick ~ g2
• Second proposal for polarimeter at MIT-Bates - signal ~ g4
• Cheap, fast, accurate, non-destructive polarimeter
• Possibility of calibration from first principles (straightforward
EM calculations, comparison with signal from charge)
• We learn a lesson - the Italians (Waldo MacKay is an
honorary Genoese) are both smart and tenacious
9
TE011 on-axis Fields
B
E
10
TE011 Fields
0
0
0
1
1
bkg problem
1
0
0
0
m=0 n=1 p=1
11
SG Force in lab frame
also Heinemann
12
Bates S/N
• TE011 mode
• Signal strength is good
• Schottky ~ -150dBm
-50dBm
Bates
• Charge background
requires alignment at the
level of a few mrad
• First choice is motion
control, cheapest is
beam steering
signal -60dBm
bkg
-80dBm
0
mrad
25
13
Prototype Cavity
• Refine frequency calculations to include beampipe perturbation
• Determine probe length for optimal coupling
• Determine optimal coupling for TM mode dampers
• Investigate need for tuners
14
S21 – Closed and
Beampipe
TE011
2.735GHz
TM121
TM111
4.348GHz
3.211GHz
new modes
with beampipe?
TE031
5.496GHz
TM131
5.762GHz
blue – closed box
red – with beampipe
15
S21 – with and w/o short
TE011
TM111
TM121
modes attenuated
by short
TM131
blue – with beampipe
red – with short
16
Mode Strengths
17
Ratio of m to q Power
100dB - Bates
200dB - RHIC
18
More Mode Strengths
Contamination by finite Q – TM mode damper?
• TM111 mode ~ 500MHz away
• Lorentzian lineshape down by ~ 120dB at this distance
• Ratio - amplitude ~ 100dB above TE011 signal (g4 helps)!
• 20dB margin is not comfortable, argues for damper
Beam Stability – TM mode damper?
Conclusion – effect of TM damper on TE modes is weak,
to be conservative we will add damper to next iteration.
19
Block Diagram
Cavity
beam
TM Mode
Coupler
FFT Box
Mix
D
Filter
Filter
20
What about RHIC?
• Ideally one would avoid a superconducting cavity.
Signal strengths appear to permit this.
• Signal power can be enhanced by high frequency,
stimulating coherence with longitudinal kicker.
• Problem is charge background (foreground?).
•
•
Impossible alignment tolerances? Signal mode
Contamination due to finite Q – TM modes
• Measure only when spin is away from stable spin
direction? Dynamic range (excitation of TM)
• Another is implementation of the 1/g2 suppression
of charge interaction. Careful study is necessary.
21
RHIC S/N
• Bates cavity in RHIC
• 1% longitudinal bunching at
2.7GHz to provide coherence
• Signal strength is adequate
• Charge background requires
alignment at sub-nanoradian level -110
• We need (at least) one more
good idea
• free precession?
• 1/g2 suppression of charge?
• else?
-145
RHIC
signal -130dBm
bkg
0
mrad x 104
25
22
What next?
• Add mode dampers to prototype cavity
• Cut to frequency and measure
• Decide whether or not to add tuners
• Design filter
• Design Review – at Bates? November?
• Build vacuum compatible cavity and measure
• Follow on with 1/g2 suppression?
• RHIC polarimeter
• Polarization at full energy – LHC?
23
TE201 Fields
Advantages
• longitudinal moment
transforms as g – Jackson,…
• 2nd order (position and angle)
cancellation of electric charge
interaction due to geometry
BUT
• contribution due to space and
time gradients of magnetic
field cancel to order 1/ g
24
TE201 Fields
1
0
0
No bkg
problem
0
0
1
0
0
1
m=2 n=0 p=1
25