Design and Test of a Prototype Cavity for a Stern-Gerlach Polarimeter

Peter Cameron - BNL

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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, USA2Forschungszentrum Karlsruhe GmbH, D-76021 Karlsruhe, Germany

3Lawrence Berkeley National Laboratory, Berkeley, CA 94720 USA4Universita and Sezione INFN di Genova, 16146 Genova, Italy5Universita and Sezione INFN di Padova, 35131 Padova, Italy

6MIT-Bates Laboratory, Boston MA 01949 USA

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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?

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What this is about

• Polarization measurement as beam instrumentation rather than a scattering experiment

• The essence of the problem• Enhance interaction of 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

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Brief History

1896 Zeeman splitting - fine structure E = h = B

1922 Stern/Gerlach splitting - ‘space quantization’ F = grad(B) kicker

1927 Pauli proposes spin S = sqrt(s(s+1)) = 1.732/2 s = 1/2 observable

1983 Barber & Cabrera and Michigan/AGS - Squid pickup

1985 Niinikoski and Rossmanith- transverse splitting in a synchrotron kicker

1993 Derbenev - RF Resonance Polarimeter - transverse moment pickup

1995 Conte et al - longitudinal spin splitting kicker

1996 Argonne BIW Cameron et al - Squid Polarimeter - longitudinal pickup

1998 RHIC Note Cameron et al - MIT-Bates Cavity - longitudinal pickup

2000 LANL preprint server - Conte et al - transverse 2 pickup

2001 PAC - poster and paper based on MIT-Bates meeting pickup

2002 September - Spin 2002 MIT-Bates, RHIC, LHC,… pickup, kicker

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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

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Conte et al - Longitudinal

• Longitudinal magnetic moment transforms as – 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/

• 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?

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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

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Conte et al - Transverse

• Reference – LANL preprint 0003069• Transverse magnetic moment is invariant• BUT - interaction of moment with appropriate TE cavity mode

goes as 2

• analogous to inverse Compton scattering, FELs,???…

• Second proposal for a longitudinal spin splitter – kick ~ 2

• Second proposal for polarimeter at MIT-Bates - signal ~ 4

• 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

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TE011 on-axis Fields

E

B

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TE011 Fields0

00

0

1

1

1

0

bkg problem

0

m=0 n=1 p=1

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SG Force in lab frame

also Heinemann

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Bates S/N

Bates

rad

bkg

signal -60dBm

dBm

dBm

• TE011 mode• Signal strength is good

• Schottky ~ -150dBm• Charge background requires alignment at the level of a few rad• First choice is motion control, cheapest is beam steering

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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

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S21 – Closed and Beampipe

blue – closed boxred – with beampipe

TE0112.735GHz

TM1113.211GHz

TM1214.348GHz

TE0315.496GHz

TM1315.762GHz

new modes with beampipe?

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S21 – with and w/o short

blue – with beampipered – with short

TE011TM111 TM121

TM131

modes attenuatedby short

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Mode Strengths

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Ratio of to q Power

100dB - Bates

200dB - RHIC

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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 (4 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.

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Block Diagram

TM Mode Coupler

beam

Cavity FFT Box

Mix

Filter Filter

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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 1/2 suppression of charge interaction. Careful study is necessary.

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RHIC S/N

RHIC

rad x 104

bkg

signal -130dBm

• 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• We need (at least) one more good idea

• free precession?• 1/ suppression of charge?

• else?

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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 1/2 suppression?• RHIC polarimeter• Polarization at full energy – LHC?

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TE201 Fields

Advantages• longitudinal moment transforms as –Jackson,…• 2nd order (position and angle) cancellation of electric charge interaction due to geometryBUT

• contribution due to space and time gradients of magnetic field cancel to order 1/

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TE201 Fields

0

00

0

1

1

1

0

No bkg problem 0

m=2 n=0 p=1