first spin simulations for a final edm storage...

Mem

bero

fthe

Hel

mho

ltz-A

ssoc

iatio

n

First Spin Simulations fora Final EDM Storage Ring

Darmstadt DPG-Fruhjahrstagung 2016 | March 15, 2016 Alexander Albert Skawran

For the JEDI Collaboration Institut fur Kernphysik, FZ-Julich — III. Physikalisches Institut

B, RWTH Aachen

Mem

bero

fthe

Hel

mho

ltz-A

ssoc

iatio

n

Contents

Electric Dipole Moment (EDM)

EDM Lattices

Spin Tracking - Quadrupole Misalignments

Effect of Gradient Fields

Darmstadt DPG-Fruhjahrstagung 2016 | March 15, 2016 First Spin Simulations for a Final EDM Storage Ring Slide 2

Mem

bero

fthe

Hel

mho

ltz-A

ssoc

iatio

n

Electric Dipole Moment

Classical

~d =∑

qi~ri

Subatomic particle

~d = d~s

T and P violation of EDM

H = −µ~s~B − d~s~ET :H = −µ~s~B + d~s~EP :H = −µ~s~B + d~s~E

Assuming CPT is conserved CPmust be violatedA permanent EDM could explainthe matter antimatter asymmetryand would be a sign for physicsbeyond the SM


Mem

bero

fthe

Hel

mho

ltz-A

ssoc

iatio

n

Measurement of EDM

T-BMT Equation

d~sdt

=~Ω×~s=− qm

G~B+

(1

γ2−1−G)~β×~E︸︷︷︸

MDM

+dmqs

(~E+~β×~B

)︸︷︷︸

EDM

×~s

(dx .doi .org/10.1103/PhysRevLett .2.435)(arXiv :1308.1580v3)


Mem

bero

fthe

Hel

mho

ltz-A

ssoc

iatio

n

Frozen Spin

d~sMDMdt =− q

m

G~B+

(1

γ2−1−G)~β×~E

×~s=0

0m 5m 10m 15m

QDA2

Cav

BPMQFA2QFA2 BPMQDA2QDA2 BPMQFA2QFA1SFP RBEBPMQDA1QDA1SDP

RBE

BPMQFA1QFA1

SFP

RBE

BPMQDA1QDA1

SDP

RBE

BPM

QFA1QFA1

SFP

RBE

BPM

QDA1QDA1

SDP

RBE

BPM

QFA1QFA1

SFP

RBE

BPM

QDA1QDA1

SDP

RBE

BPM

QFA1QFA1

SFP

RBE

BPM

QDA1QDA1

SDP

RBE

BPM

QFA1QFA1

SFP

RBE

BPM

QDA1QDA1

SDP

RBE

BPM

QFA1QFA1

SFP

RBE

BPMQDA1QDA1

SDP

RBE

BPMQFA1QFA1

SFP

RBE

BPMQDA1QDA1SDP

RBEBPMQFA1QFA2SFPBPMQDA2QDA2SDPBPMQFA2QFA2SFPBPMQDA2QDA2BPMQFA2QFA2BPMQDA2QDA2BPMQFA2QFA1SFPRBEBPMQDA1QDA1

SDP

RBE

BPMQFA1QFA1

SFP

RBE

BPMQDA1QDA1

SDP

RBE

BPM

QFA1

SFP

RBE

BPM

QDA1QDA1

SDP

RBE

BPM

QFA1QFA1

SFP

RBE

BPM

QDA1QDA1

SDP

RBE

BPM

QFA1QFA1

SFP

RBE

BPM

QDA1QDA1

SDP

RBE

BPM

QFA1QFA1

SFP

RBE

BPM

QDA1QDA1

SDP

RBE

BPM

QFA1QFA1

SFP

RBE

BPMQDA1QDA1

SDP

RBE

BPMQFA1QFA1QFA1

SFP

RBE

BPMQDA1QDA1SDPRBE BPMQFA1QFA2SFP BPMQDA2QDA2SDP BPMQFA2QFA2SFP BPMQDA2

Deuteronsp = 1024MeVBE×B = 0.46TEE×B = −12MV/m

OrientationPolarisation

OrientationMomentum

RBE

E ×B- Deflector

Senichev ,Y .,et al .(IPAC15)


Mem

bero

fthe

Hel

mho

ltz-A

ssoc

iatio

n

Quasi Frozen Spin⟨d~sMDM

dt

⟩=−⟨

qm

G~B+

(1

γ2−1−G)~β×~E

×~s⟩

=0

Main benefit is the simplification of bending elements

0m 5m 10m 15m

QDA2

Cav

BPM

QFA2QFA2

BPM

QDA2QDA2

BPM

QFA2QFA1

BDA

BPM

QDA1QDA1

SDP

BDA

BPMQFA1QFA2SFPR3BPMQDA2QDA2SDPR3BPMQFA2QFA2SFPR3BPMQDA2QDA2SDNR3BPMQFA2QFA2SFPR3BPMQDA2QDA2SDPR3BPMQFA2QFA2SFPR3BPMQDA2QDA2SDNR3BPMQFA2QFA1

BDA

BPM

QDA1QDA1

SDP

BDA

BPM

QFA1QFA2

SFP

BPM

QDA2QDA2

SDP

BPM

QFA2QFA2

SFP

BPM

QDA2QFA2

BPM

QFA2QFA2

BPM

QDA2QDA2

BPM

QFA2QFA1

BDA

BPM

QDA1QDA1

SDP

BDA

BPMQFA1QFA2SFP R3 BPMQDA2QDA2SDP R3 BPMQFA2QFA2SFP R3 BPMQDA2QDA2SDN R3 BPMQFA2QFA2SFN R3 BPMQDA2QDA2SDN R3 BPMQDA2QFA2SFP R3 BPMQDA2QDA2SDP R3 BPMQFA2QFA1SFP

BDA

BPM

QDA1QDA1

SDP

BDA

BPM

QFA1QFA2

SFP

BPM

QDA2QDA2

SDP

BPM

QFA2QFA2

SFP

BPM

QDA2

Deuteronsp = 1024MeVBE×B = 0.08TEE×B = −12MV/mBDeflector = 1.5T

OrientationPolarisation

OrientationMomentum

R3

E ×B- Deflector

BDA B- Deflector

Senichev ,Y .,et al .(IPAC15)


Mem

bero

fthe

Hel

mho

ltz-A

ssoc

iatio

n

Spin Tracking Software

COSY Infinity EDM LatticeCOSY Toolbox

ROOTAnalysis Spin tracking Plots

position (m)0 20 40 60 80 100 120 140 160

(m

)β

2

4

6

8

10

12

14

16

Dx

(m)

0

0.5

1

1.5

2

2.5

_x (m)β_y (m)β

Dx (m)

Turn0 2000 4000 6000 8000 10000

θ

0.014−

0.012−

0.01−

0.008−

0.006−

0.004−

0.002−

0

Preliminary

M.Rosenthal


Mem

bero

fthe

Hel

mho

ltz-A

ssoc

iatio

n

Quadrupole Misalignments Frozen Spin

position (m)0 20 40 60 80 100 120 140 160

(m

)β

2

4

6

8

10

12

14

16

Dx

(m)

0

0.5

1

1.5

2

2.5

_x (m)β_y (m)β

Dx (m)

Quadrupole strengths∂Bx∂y ≈ 10 T/m

Beam width 10−6 m∆pp = 10−6

η = 10−7 ∧≈d = 5 · 10−22 e cm

Quadrupole shift center YRMS (m)0 0.1 0.2 0.3 0.4 0.5

6−10×

Sy

per

turn

∆

1.5−

1−

0.5−

0

0.5

1

6−10× = 0η

-7 = 10η

PreliminaryPreliminary

First simulationsAt the moment only onerandom shift per quadrupole1,000 particles10,000 turns


Mem

bero

fthe

Hel

mho

ltz-A

ssoc

iatio

n

Gradient Fields

Beside the artificial vertical spin build up by spindecoherence other effects existDue to gradient fields additional spin rotations turn upHow large are these effects?

Spin motion due to gradient fields

(d~sdt

)∇

= 1γ+1

1m~s×(~β×∇

)µ~s· ~R1(~B,~E ,~v)+2dmes

~s· ~R2(~B,~E ,~v)︸︷︷︸≈0

Metodiev ,E .,et al .(arXiv : 1507.04440)


Mem

bero

fthe

Hel

mho

ltz-A

ssoc

iatio

n

Gradient Fields Frozen Spin

In a Frozen Spin ring is the spin parallel aligned along thedirection of momentum. Due to the Frozen Spin conditions~β⊥~s, ~β⊥~B, ~β⊥~E , ~B⊥~s,~E⊥~s

⇒(

d~sdt

)∇

=1

γ+11m~s×(~β×∇

)µ~s·~R(~B,~E ,~v)︸︷︷︸=0

=0

No effect on the spin motion for an ideal Frozen Spin ringfor the reference particle

Metodiev ,E .,et al .(arXiv : 1507.04440)


Mem

bero

fthe

Hel

mho

ltz-A

ssoc

iatio

n

Gradient Fields in Quasi Frozen Spin

z

y

x

In a Quasi Frozen Spin ring the spin is not always parallelaligned the momentumGradient fields appear in quadrupoles(

d~sdt

)∇

=∂Bx

∂y· µβγ+1

1m~s×(

sx0−sy

)A perfect Quasi Frozen ring evokes an artificial build up ofvertical polarisation by quadrupoles


Mem

bero

fthe

Hel

mho

ltz-A

ssoc

iatio

n

Effect of Gradient Fields in Quasi Frozen Spin

After a half turn the spin is rotated by an angle γGπ withrespect to the momentumCompare the vertical spin build up for a ring the referencebeam with and without gradient field effect. Particle motiondue to gradient fields is neglected

Preliminary


Mem

bero

fthe

Hel

mho

ltz-A

ssoc

iatio

n

Outlook

Examine further misalignments for Frozen SpinInclude misalignment simulations for Quasi Frozen SpinAnalyse of the effect of fringe fieldsExpand the analysis for gradient field effects, e.g. includethe motion relative to the beam


Mem

bero

fthe

Hel

mho

ltz-A

ssoc

iatio

n

Fukuyama, T., et al. ”Derivation of generalizedThomas-Bargmann-Michel-Telegdi equation for a particlewith electric dipole moment.” International Journal ofModern Physics A 28.29 (2013): 1350147.

Pretz, J., and JEDI collaboration. ”Measurement ofpermanent electric dipole moments of charged hadronsin storage rings.” Hyperfine Interactions 214.1-3 (2013):111-117.

Senichev, Yu, et al. QUASI-FROZEN SPIN METHODFOR EDM DEUTERON SEARCH. In: Proc. of the 6thInternational Particle Accelerator Conference (IPAC15),Richmond, Virginia, USA. 2015. S. 213.

Rosenthal, M. IKP Annual Report, (2014)


Mem

bero

fthe

Hel

mho

ltz-A

ssoc

iatio

n

Makino, K., et al. ”COSY INFINITY version 9.” NuclearInstruments and Methods in Physics Research Section A:Accelerators, Spectrometers, Detectors and AssociatedEquipment 558.1 (2006): 346-350.

Brun, R, and Rademakers, F.. ”ROOT - an object orienteddata analysis framework.” Nuclear Instruments andMethods in Physics Research Section A: Accelerators,Spectrometers, Detectors and Associated Equipment389.1 (1997): 81-86.

Anastassopoulos, V., et al. ”A storage ring experiment todetect a proton electric dipole moment.” arXiv preprintarXiv:1502.04317 (2015).


Mem

bero

fthe

Hel

mho

ltz-A

ssoc

iatio

n

Metodiev, Eric M, Thomas-BMT equation generalized toelectric dipole moments and field gradients,arXiv preprintarXiv:1507.04440,2015

Bargmann,et al., Precession of the polarization ofparticles moving in a homogeneous electromagneticfield, Physical Review Letters, (1959),APS


first spin simulations for a final edm storage...

Documents