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.      E B 0 E Moment Electric Magnetic Monopole Yes No? Dipole Violates T and P Yes Quadrupole Yes Violates T and P 2

Dipole Moments: MDM and EDM • 1920s: Dirac equation: g e = 2, QED 2.00227…… • 1930s: Dirac finds that existence of a magnetic monopole gives electric charge quantization.  geS g 2    a 2 m 2 dS      * * B d E * dt 3

Spin Precession Due to MDM in SR 2   magic g G = a = ( g -2)/2 4

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.     dS dp        y z d E v B e E v B z x z y x z y dt dt 5

EDM Measurement Statistical Error • This talk covers the last factor. • Need polarimeter: A f   • Need lattice: E N T T av 0 fill fill sct  2 h 2 a   d  g P AE N f T T 0 av 0 TOT fill 6

Proton - Carbon Polarimeter FOM Fantastically Good at P magic 0.06 A f 0.05 0.04 sqrt(f) A “magic” 0.03 0.02 E. Stephenson 0.01 0.00 400 450 500 550 600 650 700 P (MeV/c) 7

Set MDM  a  0   dS g 1       d E v B d E a  2 dt 2 g 1  • At magic  : 1 a  2 2 8

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 .   dS g 1       d E v B d E a  2 dt 2 9

E 0 = 5MV/m (0.017T) 0.15 10 E 0 = 5MV/m 9 0.12 8 7 g/(a*gamma^2) 0.09 6 B (T) 5 B 0.06 4 (E+vxB)/E 3 0.03 2 1 0.00 0 5 6 7 8 9 10 11 12 13 14 15 P (MeV/c) 10

Bending Radius vs. Momentum 3 E 0 = 5MV/m 2.5 2 R (m) 1.5 1 0.5 0 5 6 7 8 9 10 11 12 13 14 15 P (MeV/c) 11

Ring Lattice Cartoon CW/CCW 12

Ring Lattice FOM • C  nL + 2  R • E av = 2  RE 0 / C • Ring Lattice FOM = E av (  SCT N 0 ) 1/2.  2 h 2 a     d g P AE N f T 0 av 0 TOT SCT 13

Want MDM  a  0 •  a t fill  1rad   dS g 1       d E v B d E a  2 dt 2    dS cos t d E d E g g   y a x z x   2 2 dt 2 a 2 a 14

Need Feed-back From Polarimeter! 0.4 Magic Momentum 0.3 w_a /E (rad-m/s-MV) 0.2 0.1 0 proton -0.1 electron -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 (p - p magic )/p magic 15

D. Eversmann et al., Phys. Rev. Lett. 115, 094801 (2015). D-C Polarimeter at COSY, Juelich 100s 16

Need NfA 2 P 2  10 2 Previous slide  10 6  a t fill 17

Systematic Error Due to Radial Magnetic Field   dS      y B v E x z y dt • Because of focusing, in the limit T   T   1        p e E v B dt 0 y y z x T 0        E v B y z x 18

pEDM-Type Experiment • Magic momentum.   ge    • All-electric lattice.  B  syst x 2   2 m • Shield magnetic fields. • Squid BPM with small vertical tune. 19

dEDM-Type Experiment • Not magic momentum.   • E and B fields. ge      E   syst y CW CCW , • Magnetic focusing. 2   2 m • Don’t know yet which is best: p or dEDM. 20

Atomic Electron Trapping in E  B • No trapping if | E | > | v  B | . • For E = 5MV/m, for example, • B < 0.02T. J.D. Jackson Classical Electrodynamics 21

BNL dEDM Proposal 2008 E = 12MV/m, B = 0.5T B = 0 22

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?  2 h 2 a   d  g P AE N f T T 0 av 0 TOT fill 24

Extras 25