Study by Spin Tracking of A Storage Ring for Deuteron Electric Dipole Moment (dEDM)

Study by Spin Tracking of A Storage Ring for Deuteron Electric Dipole Moment (dEDM)

Fanglei Lin

The 18th International Symposium on Spin Physics

U. of Virginia, Oct. 6-11 2008

The 18th International Symposium on Spin Physics F.Lin

Acknowledgements

dEDM experiment particle tracking group:

BNL Physics Dept. : Yannis K. Semerzidis (Leader) Bill Morse, Vasily Dzhordzhadze BNL CAD : Alfredo U. Luccio BNL NSLS II : Nikolay Malitsky Cornell University : Yuri F.Orlov Indiana University : Edward J. Stephenson KVI : Gerco Onderwater


Motivation of Deuteron EDM

High sensitivity to CP-violation, complementary and better than nEDM

Physics beyond the SM (esp. SUSY) expect CP-violation within reach

Great sensitivity to T-odd Nuclear Forces If observed it will provide a new, large source of

CP-violation that could explain the Baryon Asymmetry of our Universe (BAU)

Marciano 9/2006


Concept of dEDM Experiment

Method: Searching for the EDM in a storage ring using the longitudinally polarized deuteron beam.

ESdBSdt

dS

Spin precession due to electric dipole momentSpin precession due to magnetic moment

])1

1([

2 c

EaBa

m

ea

][ B

c

Ecdedm

0 EB

B

E

(vertical) (radial)

Rotating spin about the vertical direction Increasing vertical component of spin

)sin()( 0

tPtP edm

V22aedm The change in the vertical polarization

due to EDM signal :

VPP Prolong polarization life time

a edm Choose proper radial and vertical B

E


Deuteron Storage Ring

can be controlled by tuning

and

BE section :

• is vertical magnetic field

• is radial electric field

VB

RE

]))(([ 2RVa E

p

mcaaB

m

e

Spin precess frequency :

VB RE

a

Frozen Spin


Deuteron Storage Ring

Deuteron Momentum (Gev/c)

1.0

Rigidity (Tm) 3.336

Length of orbit (m)

85.4

Magnetic field (T)

0.482

Electric field (MV/m)

12.0

BE section length (m)

3.3

BE section radius (m)

8.406

Maximum of beta function (x;y) (m)

12 ; 15

Length of straight section (m)

9.44


Correction of Spin Frequency Perturbation

222)( yaxap

pa yxp

a

a

Spin frequency perturbation comes from the second order effects of betatron and synchrotron violation:

)( 22'' yxBB sexty Sextupole produces a quadratic field as

)cos(0

sstp

p

p

p

p

p

p

psDtsx xyxx

)()cos()(

)cos()( yyyy tsy

Conclusion:

The proposed of is possible in principle with the help of sextupoles

s

xD Three sets of sextupoles, locating at large dispersion , large horizontal beta function and large vertical beta function , and are needed for the correction of spin frequency perturbation respectively

x

y


Simulation tools : UAL (courtesy of N. Malitsky ) + SPINK (courtesy of A.U. Luccio ) Multiparticles with Gaussian distribution All Initial spin vectors points to the longitudinal direction Distribution categories:

Horizontal distribution with Vertical distribution with Momentum spread

Definition of Sx, Sy, Sz, S <Sx> : radial component of polarization <Sy> : vertical component of polarization <Sz> : longitudinal component of polarization S :

1 million turns ~ 1.5 second

Simulation Conditions

222 zyx SSSS

mradmmx 0.3

mradmmy 0.5

310p

p


The horizontal beta function is maximum at focusing quads. Those sextupoles next to focusing quads. are mainly used to correct the spin frequency perturbation due to the horizontal betatron motion.

Searching for optimum sextupoles (I)


The vertical beta function is maximum at defocusing quads. Those sextupoles next to defocusing quads. are mainly used to correct the spin frequency perturbation due to the vertical betatron motion.

Searching for optimum sextupoles (II)


Searching for optimum sextupoles (III)

Two sets of sextupoles are next to focusing and defocusing quads. Both horizontal and vertical motion are included.


Searching for optimum sextupoles (IV)

Besides two sets of sextupoles next to focusing and defocusing quads, a third set of sectuopole component is introduced in the BE section . Both horizontal and vertical motion are included.


Searching for optimum sextupoles (V)

Three sets of sextupoles are located next to focusing, defocusing quads and in the BE section . Particles with horizontal, vertical motion and momentum spread are included.


Summary

Deuteron EDM experiment has the potential to increase the sensitivity to CP violation by several orders of magnitude larger than nEDM

Storage ring provides a clear environment to maintain an intense polarized deuteron beam

Frozen spin method can be implemented by dipoles combining vertical magnetic and radial electric field

Quadratic perturbation in the spin precession frequency can be cancelled with a proper arrangement of sextupoles

Preliminary particle trackings in simulation have already shown a prolonged polarization lifetime with the help of sextupoles.


Thank You !

Documents

Study by Spin Tracking of A Storage Ring for Deuteron Electric Dipole Moment (dEDM)