Experiment Momentum W. Morse - BNL 1 Maxwells Equations Asymmetry - - PowerPoint PPT Presentation

Optimal Electron SR-EDM Experiment Momentum

• W. Morse - BNL

1

Maxwell’s Equations

• Asymmetry – electric charge exists, but not

magnetic charge.

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Moment Electric Magnetic Monopole Yes No? Dipole Violates T and P Yes Quadrupole Yes Violates T and P

E

E B     

Dipole Moments: MDM and EDM

• 1920s: Dirac equation: ge = 2, QED 2.00227……
• 1930s: Dirac finds that existence of a magnetic

monopole gives electric charge quantization.

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* * *

dS B d E dt     

2 2 2 geS g a m    

Spin Precession Due to MDM in SR

4

2

magic

g  

G = a = (g-2)/2

Spin Precession in SR Due to Electric Dipole Moment

• Spin precession due to EDM is in the vertical

plane (y = vertical) plane.

• Spin precession due to MDM is in the

horizontal (x = radial, z = longitudinal) plane.

5

   

y z z x z y x z y

dS dp d E v B e E v B dt dt       

EDM Measurement Statistical Error

• This talk covers the last factor.
• Need polarimeter:
• Need lattice:

2

2

d av TOT fill

h a g P AE N f T T    

A f

av fill fill sct

E N T T  

6

Proton - Carbon Polarimeter FOM Fantastically Good at Pmagic

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0.00 0.01 0.02 0.03 0.04 0.05 0.06 400 450 500 550 600 650 700

sqrt(f) A P (MeV/c)

A f

“magic”

• E. Stephenson

Set MDM a  0

• At magic  :

8

2

1 1 2 g a 

 

2

1 2 dS g d E v B d E dt a      

Spin Precession due to EDM

• Below magic momentum, the two terms add.
• Above magic momentum, the two terms

subtract.

• At magic momentum, spin precession due to

edm: dE.

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 

2

1 2 dS g d E v B d E dt a      

E0 = 5MV/m (0.017T)

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1 2 3 4 5 6 7 8 9 10 0.00 0.03 0.06 0.09 0.12 0.15 5 6 7 8 9 10 11 12 13 14 15

g/(a*gamma^2) B (T) P (MeV/c)

E0 = 5MV/m

B (E+vxB)/E

Bending Radius vs. Momentum

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0.5 1 1.5 2 2.5 3

5 6 7 8 9 10 11 12 13 14 15

R (m) P (MeV/c)

E0 = 5MV/m

Ring Lattice Cartoon

12

CW/CCW

Ring Lattice FOM

• C  nL + 2 R
• Eav = 2 RE0/C
• Ring Lattice FOM = Eav (SCT N0)1/2.

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2

2

d av TOT SCT

h a g P AE N f T     

Want MDM a  0

• a tfill  1rad

14

 

2

1 2 dS g d E v B d E dt a      

 

2 2

cos 2 2

y a x z x

dS t d E d E g g dt a a     

Need Feed-back From Polarimeter!

15

• 0.4
• 0.3
• 0.2
• 0.1

0.1 0.2 0.3 0.4

• 3.E-07
• 2.E-07
• 1.E-07

0.E+00 1.E-07 2.E-07 3.E-07

w_a /E (rad-m/s-MV)

(p - pmagic)/pmagic

proton electron

Magic Momentum

16

• D. Eversmann et al.,
• Phys. Rev. Lett. 115,

094801 (2015). D-C Polarimeter at COSY, Juelich

100s

Need NfA2P 2  102

17

a tfill

Previous slide 106

Systematic Error Due to Radial Magnetic Field

• Because of focusing, in the limit T  

18

 

1

T y y z x

p e E v B dt T      



 

y x z y

dS B v E dt     

y z x

E v B       

pEDM-Type Experiment

• Magic momentum.
• All-electric lattice.
• Shield magnetic fields.
• Squid BPM with small vertical tune.

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2

2

syst x

ge B m         

dEDM-Type Experiment

• Not magic momentum.
• E and B fields.
• Magnetic focusing.
• Don’t know yet which is best: p or dEDM.

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, 2

2

syst y CW CCW

ge E m  



       

Atomic Electron Trapping in EB

• No trapping if |E| > |vB|.
• For E = 5MV/m, for example,
• B < 0.02T.

21

J.D. Jackson Classical Electrodynamics

BNL dEDM Proposal 2008 E = 12MV/m, B = 0.5T

22

B = 0

BNL dEDM Proposal 2008

• E = 12MV/m, B = 0.5T.
• Did not get funding to pursue R&D.
• Common electric field plates for CW/CCW

channels.

• Theory was since magnetic field passed

through zero in the center, this would take care of trapped atomic electrons.

23

Questions

• Need Polarimeter FOM, feed-back from

polarimeter.

• Need Lattice FOM.
• Is it a dEDM-type experiment, or a pEDM-type

experiment? Both?

24

2

2

d av TOT fill

h a g P AE N f T T    

Extras

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