1

Resonant Polarimetry for Frequency Domain EDMMeasurements

Richard Talman

Laboratory for Elementary-Particle PhysicsCornell University

Polarimetry Workshop Mainz, 10-11 September, 2015

2 Outline

Why Measure EDM?Resonant PolarimeterConceptual EDM Measurement RingWhy “Rolling Polarization”? and Why the EDM Signal SurvivesAchievable PrecisionBNL “AGS Analogue” Ring as EDM PrototypeResonant Polarimetry TestsLong Term EDM ProgramSurvey of Practical Resonant Polarimeter ApplicationsExtra Slides

3

Some of this presentation is extracted from the following papers:

I R. and J. Talman, Symplectic orbit and spin tracking code forall-electric storage rings, Phys. Rev. ST Accel Beams 18,ZD10091, 2015

I R. and J. Talman, Electric dipole moment planning with aresurrected BNL Alternating Gradient Synchrotron electronanalog ring, Phys. Rev. ST Accel Beams 18, ZD10092, 2015

I R. Talman, Frequency domain storage ring method forElectric Dipole Moment measurement, arXiv:1508.04366[physics.acc-ph], 18 Aug 2015

4 Why Measure EDM?

I Violations of parity (P) and time reversal (T) in the standardmodel are insufficient to account for excess of particles overanti-particles in the present day universe.

I Any non-zero EDM of electron or proton would represent aviolation of both P and T, and therefore also CP.

I In all-electric rings “frozen spin” operation is only possiblewith electrons or protons.

5 Resonant (Longitudinal) Polarimeter

rR

bR

sR

Rt

cR

lR

Figure: Longitudinally polarized beam approaching a superconductinghelical resonator. Beam polarization is due to the more or less parallelalignment of the individual particle spins, indicated here as tiny currentloops. The helix is the inner conductor of a helical transmission line,open at both ends. The cylindrical outer conductor is not shown.

6 Resonant (Longitudinal) Polarimeter Response

I The Faraday’s law E.M.F. induced in the resonator has one signon input and the opposite sign on output.

I At high enough resonator frequency these inputs no longer cancel.I The key parameters are particle speed vp and (transmission line)

wave speed vr .I The lowest frequency standing wave for a line of length lr , open

at both ends, has λr = 2lr ;

Bz(z , t) ≈ B0 sinπz

lrsin

πvr t

lr, 0 < z < lr . (1)

I The (Stern-Gerlach) force on a dipole moment m is given by

F = ∇(B ·m). (2)

I The force on a magnetic dipole on the axis of the resonator is

Fz(z , t) = mz∂Bz

∂z=πmzB0

lrcos

πz

lrsin

πvr t

lr. (3)

7 At position z = vpt a magnetic dipole traveling at velocity vp issubject to force

Fz(z) =πmzB0

lrcos

πz

lrsin

π(vr/vp)z

lr. (4)

Integrating over the resonator length, the work done on theparticle, as it passes through the resonator, is

∆U(vr/vp) = mzB0

[π

lr

∫ lr

z=0cos

πz

lrsin

π(vr/vp)z

lrdz

]. (5)

I See plot.

8 Energy lost in resonator

Figure: Plot of energy lost in resonator ∆U(vr/vp) as given by thebracketed expression in Eq. (5).

I For vr = 0.51 vp, the energy transfer from particle toresonator is maximized.

I With particle speed twice wave speed, during half cycleof resonator, Bz reverses phase as particle proceeds fromentry to exit.

9 EDM Measurement Ring

uppersideband sideband

lower

0 h f

0

uppersideband sideband

lower

f0 f∆+ f0 f∆−

BSz

Moebius twist

bend electricE field

f0 f∆ f0 f∆−h

M+x Mx M

+y My

roll ratecontrol

Iroll

θR

x

z

y^

uppersideband sideband

lower

M+z Mz

f∆ f0 f∆−f0

BWx yB

W

Wien filters(active)

torquewheel roll rate wheel−upright

torquewheel left−right

torque

scalerscaler

yWI z

SI

(passive) resonant polarimeters

cavityRF

h h

BPMsystem

h ++

polarity reversal

+h h

wheel left−right

roll rate resonatorstabilize sensor

wheel−upright

stabilize sensor

solenoid (active)

"Spin wheel"

rolling polarization

Controlled temperature, vibration free,rigidly constructed, magnetic shielded

beam

−

+

Figure: Cartoon of the EDM ring and its spin control. The Kooppolarization “wheel” in the upper left corner “rolls” along the ring,always upright, and aligned with the orbit. The boxes at the bottomapply torques to the magnetic moments without altering the design orbit.

10

I Elements with superscript “W” are Wien filters; superscript“S” indicates solenoid.

I The frequency domain EDM signal is the frequency change ofspin wheel rotation when the BW

x Wien filter polarity isreversed.

I EDM measurement accuracy (as contrasted with precision) islimited by the reversal accuracy occurring in the shadedregion.

I Precision is governed by scaler precision. This is a benefitobtained by moving the EDM sensitivity from polarimeterintensity to polarimeter frequency response.

11 Why “Rolling Polarization”? and Why the EDM Signal Survives

I Polarized “wheel” was proposed by Koop (for differentreason).

I Here the primary purpose of the rolling polarization is to shiftthe resonator response frequency away from harmonic ofrevolution frequency.

I This is essential to protect the polarization response frombeing overwhelmed by direct response to beam charge orbeam current.

I Since the EDM torque is always in the plane of the wheel itseffect is to alter the roll rate.

I Reversing the roll direction (with beam direction fixed) doesnot change the EDM contribution to the roll.

I The difference between forward and backward roll-ratesmeasures the EDM (as a frequency difference).

12 Rolling Magnetization Frequency Spectra

a2/2

a2/2

a2/2

a2/2

f/f0

a2/2

a2/2

a0

a4/2

a4/2

a2/2

a2/2

a0

a2/2

a2/2

a4/2

a4/2

f/f0

a0

a2/2

a2/2

a4/2

a4/2

RING

10 h

1+q

2

1−q 2−q 2+q h+qh−q

1

LINAC

0 h1+2q

1−q 1+q

2 2+2q

2−q 2+q

2−2q1−2q h+2q

h−q h+q

h−2q

Figure: Frequency spectra of the beam polarization drive signal to theresonant polarimeter. In a storage ring (shown above) the drive is purelysinusoidal, producing sidebands of harmonics of the revolution frequency.For a resonant polarimeter test using a polarized linac beam (shownbelow) the drive is distorted, but can still be approximately sinusoidal,giving the same two dominant sideband signals. The operativepolarimetry sideband lines are indicated by dark arrows.

13 Achievable Precision

EDM in units of 10−29 e-cm = d2 x EDM/MDM precession ratio = 2η(e) = 0.92× 10−15 ≈ 10−15

roll reversal error: ±ηrev. e.g.= 10−10

duration of each one of a pair of runs = Trun

smallest detectable fraction of a cycle = ηfringe = 0.001

fractional roll reversal error = ±σrollFF

e.g.= 10−10

NFF = number of fractional fringes per run±σrev.FF = roll reversal error measured in fractional fringes

NFF =(2η(e))d

ηfringehr f0Trun

(e.g.≈ d

10−15 · 10 · 107 · 103

10−3= 0.1d

),

±σrev.FF =± f rollηrev.Trun

ηfringe

(e.g.≈ ±102 · 10−10 · 103

10−3= 10−2

).

particle |de | current excess fractional error after 104 roll reversalupper limit cycles per pair pairs of runs error

e-cm of 1000 s runs e-cm e-cm

neutron 3× 10−26

proton 8× 10−25 ±8× 103 ±10−30 ±10−30

electron 10−28 ±1 ±10−30 ±10−30

14 BNL “AGS Analogue” Ring as EDM Prototype

Figure: The 1955 AGS-Analogue lattice as reverse engineered from availabledocumentation—mainly the 1953 BNL-AEC proposal letter. Except for insufficientstraight section length, and the 10 MeV rather than 14.5 Mev energy, this ring couldbe used to measure the electron EDM.

15 Polarimeter room temperature bench test

l r l r

l r

Bz

coax cable fromspectrum analyser

transmitter

analyser receiverto spectrum

0

VI

0

beam bunch

0+ cycle 1/4 cycle 1/2− cycle

VI

0

I

z z

standing wave

44 turn copper coil

aluminum tube

insulating tube (2inch OD)coupling loop coupling loop

Figure: . Room temperaure bench test set-up of prototype resonantpolarimeter, with results shown in next figure. The coil length is lr=11inches. Beam magnetization is emulated by the spectrum analysertransmitter.

16

I Resonator excitation is detected by a single turn loopconnected to the spectrum analyser receiver.

I This would be an appropriate pick-up in the true polarimetryapplication though, like the resonator, the preamplifier wouldhave to be at cryogenic temperature to maximize the signal tonoise ratio.

I The figures above the apparatus are intended to complete theanalogy to a situation in which the transmitter is replaced bythe passage of a beam bunch.

I The particle and wave speeds are arranged to maximize theenergy transfer from beam to resonator.

17

Figure: Frequency spectrum observed using the bench test shown inprevious figure. Ten normal modes of the helical transmission line arevisible.

18 Wien Filter

BW

x BW

y

y

z x

POSSIBLE AXIS of ROTATION

for ROLL REVERSAL or

INTERCHANGE of and

MAGNETIC FIELD PROBE

h

w

l

TERMINATION

RESISTANCE

V

BEAM DIRECTION

I

E

H

E x H

STRIP CONDUCTORS

−+

Figure: Stripline Wien filter dimensions. With electromagnetic power andbeam traveling in the same direction, the electric and magnetic forcestend to cancel. Termination resistance R is adjusted for exactcancelation.

19 Wien reversal current bridge monitor442 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 52, NO. 2, APRIL 2003

Fig. 3. Back-to-back comparison of PBCs.

easily observed across the 1-Mresistor (1 mV correspondsto one part in 10). Over the 0–10 V range the change wasless than one part in 10and saturation started at 10.2 V. Thismargin was felt too small and the design updated to improvethis to greater than 11 V. Second, the compliance dynamicperformance was tested, again using back-to-back, with theload on one of the PBCs being the CERN current calibrator.The winding resistance and inductance changes as windingsare switched in and out, but no instability or permanent changewas observed in the PBC output.

C. Isolation

Since calibration transfers between units are performed byreverse connecting them and sensing the current difference to0.1 nA, (1 nA corresponds to one part in 10) it is criticallyimportant that power supply current does not interfere. This re-quires very low leakage current back to ground via the externalsupply. Even the ac leakage current has to be kept very low toensure that it does not interfere with the current null measure-ment (see Fig. 3). The measured rms noise in this configurationwas 10 nA, mainly 8 kHz from the internal dc/dc converter.

D. Portability

The autonomy should permit travelling around the LHCduring a full working day without interruption i.e., 10 hincluding margin. The autonomy of the initial units decreasedwith time due to insufficient trickle charging and is now only6–9 h The charging circuit was redesigned and the autonomy isnow 16 h. Built-in monitoring provides warning if the batteryis low 1/2 h before the unit stops functioning. A warninglight indicates if the temperature control is lost, i.e., ambienttemperature is outside the specified range or a hardware failurehas occurred. Mains power was removed and returned severalhours later. The change was less than one part in 10. Thebatteries were allowed to discharge completely and the unitswere re-powered . An LED indicated that power had previouslyfailed, but after resetting with the front panel “calibrationreset,” the retrace was much better than five parts in 10.

IV. DESIGN DESCRIPTION

As shown in Fig. 4, the basic “Voltage” part of the designis similar to that of a commercial dc voltage source [2] witha number of modifications to generate the 10-mA referencecurrent and meet the above requirements. The gain step to10 V from the well-known and predictable zener reference

Fig. 4. Block diagram.

Fig. 5. Current path in voltage to current transfer.

LTZ1000A, at 7.2 V, is defined by “statistical” TaN film resistorarrays [2]. These have been shown to maintain stable ratios toless than one part in 10over time and temperature. The 10 V isthen converted to 1 mA in a transconductance stage, utilizing a10-k resistor constructed from four of Vishay’s new “Z-Foil”zero TC resistors. By converting to current at only 1 mA, it waspossible to use an optimum 10 kfor this critical part. The 1mA is amplified by a factor of 10, defined by further use ofTaN film arrays in a 10:1 current mirror referred up to 22 Vto achieve the compliance. This current is made adjustableover 5 parts in 10 via a front panel, 10 turn, indicatingpotentiometer in order to allow the transfer of current betweendevices to be an exact null, the potentiometer indication beingrecorded to track drift performance between calibrations.

V. DESIGN FORCOMPLIANCE

The current path for the most stringent dc compliance situa-tion, where reference units actively transfer voltage traceabilityconcurrently to current standards is shown in Fig. 5. In thismode, the reference 1-kresistor is in series, via PBC_1’s rearconnector, with the front panel output, which in turn is used in“back-to-back” configuration to calibrate PBC_2.

A. Current Mirror

In an opamp assisted current mirror, in its simplest form, theoutput compliance is a function of the loop gain of the control-ling opamp. This means that reactive loads can interfere withthe performance to the point of becoming unstable. This cir-cuit adds a cascode stage, making it very “stiff” with the opampbeing buffered from the output voltage. Furthermore, by using

Figure: Current bridge used for high precision current monitoring. Copiedfrom CERN, PBC reference. One current is the active current, the othera highly stable reference current. Even hand-held, 1 part in 108 precisionis obtained. Wien current reversal precision will be monitored every runby recording the potentiometer voltage with Wien current in one arm andstandard current in the other.

20 Long Term EDM Program

I Design and build resonant polarimeter and circuitry

I Develop rolling-polarization 15 MeV electron beam (e.g atWilson Lab or Jefferson Lab or Mainz)

I Confirm (longitudinal, helical) resonant polarimetry usingpolarized electron or proton beam

I Confirm (transverse, TE101) resonant polarimetry usingpolarized electron or proton beam

I Build 5 m diameter, 14.5 MeV electron ring (e.g. at WilsonLab, J-Lab, Mainz, etc.)

I Measure electron EDM

I Attack electron EDM systematic errors

I Same program as above for 235 MeV protons in 50 mdiameter, all electric ring (e.g. at BNL, FNAL, or COSY)

21 Possible polarimeter tests and applicationsTable: Signal level and signal to noise ratio for various applications. In all cases thepolarization is taken to be 1. In spite of the quite high Qc values achievable with HTS, theeconomy this promises is overwhelmed by the signal to noise benefit in running at far lowerliquid helium temperature. The bottom row is the most important.

experiment TEST TEST e-EDM e-EDM p-EDM TEST

parameter symbol unit electron electron electron electron proton protonbeam J-LAB linac J-LAB linac ring ring ring COSY

conductor HTS SC HTS SC SC SC

ring frequency f0 MHz 10 10 1 9.804magnetic moment µp eV/T 0.58e-4 0.58e-4 0.58e-4 0.58e-4 0.88e-7 0.88e-7

magic β βp 1.0 1.0 1.0 1.0 0.60 0.6

resonator frequency fr MHz 190 190 190 190 114 114resonator radius rr cm 0.5 0.5 2 2 2 2resonator length lr m 1.07 1.07 1.07 1.07 1.80 1.80

temperature T ◦K 77 1 77 1 1 4phase velocity/c βr 0.68 0.68 0.68 0.68 0.408 0.408

quality factor Qres. 1e6 1e8 1e6 1e8 1e8 1e6response time Qres./fr s 0.53 0.0052 0.52 0.88 0.0088

beam current I A 0.001 0.001 0.02 0.02 0.002 0.001bunches/ring Nb 19 19 114 116

particles Ne 1.2e10 1.2e10 1.2e10 6.4e9particles/bunch Ne/Nb 3.3e7 3.3e7 0.63e9 0.63e9 1.1e8 5.5e7

magnetic field Hr Henry 2.6e-7 2.6e-6 1.3e-6 1.3e-4 2.3e-6 1.15e-8resonator current Ir A 2.2e-8 2.2e-6 2.2e-7 2.2e-5 0.50e-6 2.6e-9

magnetic induction Br T 3.3e-13 3.3e-11 1.6e-12 1.6e-10 2.8e-12 1.4e-19max. resonator energy Ur J 2.9e-23 2.9e-19 2.9e-21 2.9e-17 1.5e-20 3.8e-25

noise energy Um J 0.53e-21 0.69e-23 0.53e-21 0.69e-23 0.69e-23 2.8e-23

S/N(ampl.)√

Ur/Um 0.23 205 2.3 2055 45.8 0.117

S/N(ph-lock) (S/N)√f0 s−1/2 3.2e3 2.8e6 3.2e4 2.8e7 4.9e5 1248

22 Extra Slides

23 JLAB Polarized Electron Beamline

WienFilter

IncomingPolarization

OutgoingPolarization

z

x

Figure 3.19: The Wien filter is calibrated by rotating the incoming polarization (par-allel to the beam momentum) to 12 orientations within ≈ ±110◦. The outgoingpolarization was then measured at the Mott polarimeter.

tion Px is the measured experimental asymmetry divided by the effective Sherman

function. The value of the Sherman function used is Seff = −0.391 as measured for

the 1µm gold target foil (Section 3.3.6). The error bars are statistical only. The

absolute uncertainty in the amplitude of the polarization is about 5%. The best–fit

parameters are P0 = (−69.9±0.1)%, k = (12.09± 0.08)deg

A, and φ0 = (0.98± 0.22) ◦.

The χ2 of the fit is 1.09 per degree of freedom. A correction to the phase, φ0, must

be made to account for the polarization rotation incurred when the beam is steered

by (−12.5± 0.4) ◦ from the injector beamline to the polarimeter beamline. The total

beam energy at this location is 5.52± 0.10MeV (KE = 5.01MeV) and the correction

to the measured precession is (−0.156± 0.005) ◦. Consequently φ0 = (1.14± 0.21) ◦.

3.3.8 Solenoid Spin Rotator Calibration

A calibration of the two solenoid spin rotators was performed using the Mott po-

larimeter. Using the calibration data for the Wien filter the beam polarization was

oriented transversely prior to the solenoid magnets. For each solenoid the coil cur-

rents were set to produce 7 different precession angles. Each set of coil currents must

74

Figure: Figure (copied from Grames’s thesis), showing the front end ofthe CEBAF injector. The 100 KeV electron beam entering the DC Wienfilter is longitudinally polarized. The superimposed transverse electric andmagnetic forces exactly cancel, therefore causing no beam deflection. Butthe net torque acting on the electron MDM rotate the polarization vectorangle to the positions depending on their strength.

24 Replace J-Lab Polarized Source DC Wien Filter with 1.5 KHz Wien Filter

Figure: Time dependences of the Wien filter drive voltage and theresulting longitudinal polarization component for linac beam following theWien filter polarization rotater. The range of the output is less than ±1because Θmax = 0.8π is less than π. Note the frequency doubling of theoutput signal relative to the drive signal and the not-quite-sinusoidal timedependence of the output.

25

to reliably make photocathodes with no quantum efficiencyat large radius. These changes are described below.

The Pierce electrode angle was changed from 39� to25�, greatly reducing the focusing at the cathode. Thereplacement of the Z spin manipulator with a combinationof a Wien filter and a solenoid eliminated both electrostaticbends and many solenoids. A Wien filter is a device withstatic electric and magnetic fields perpendicular to eachother and to the velocity of charged particles passingthrough it, as shown in Fig. 4. Unit charged particles with

a velocity of �c � E=B are undeflected in passing throughthe Wien filter, while the spin is rotated in the plane of theelectric field.

Our Wien filter design was scaled from the SLAC designused on their original 66 keV GaAs polarized source to our100 keV energy. A window-frame dipole magnet providedthe magnetic field. The magnet was terminated at each endwith a nickel plate having a 20 mm diameter beam aper-ture. The full magnet, assembled on the Wien filter vacuumchamber, was carefully mapped with a precision Hallprobe. The profile of the electric field plates was calcu-lated, using the code POISSON [23], to produce an electricfield profile closely matching the magnetic field profile.Since the beam lines through the injector and in each ex-perimental hall are purely horizontal, the Wien filter had ahorizontal electric field. The Wien filter was capable of�110� spin rotation at 100 keV. The calibration andperformance of this Wien filter is described in Grameset al. [24].

All solenoids following the Wien filter were ‘‘counter-wound’’—i.e., they had two identical coils separated by asoft steel yoke, wired to produce equal and opposite lon-gitudinal fields. These solenoids thus focused the beamwithout rotating any transverse polarization component.Two of these lenses had separate power supplies for eachcoil, allowing any small net spin rotation out of the hori-zontal plane to be compensated while maintaining thecorrect focusing.

The elimination of the Z spin manipulator substantiallyreduced the distance between the photocathode and thechopping apertures, reducing the bunch lengthening due tospace charge [compare Figs. 5(a) and 5(b)]. The pre-

FIG. 4. The Wien filter spin manipulator used with CEBAF’ssecond and third polarized electron sources. The magnet is notshown in the cutaway view.

FIG. 3. The second polarized electron source, originally oriented in the vertical plane and later in the horizontal plane.Nonevaporable getter modules surround the cathode/anode gap. Other improvements are described in the text.

DEVELOPMENT OF A HIGH AVERAGE CURRENT . . . Phys. Rev. ST Accel. Beams 10, 023501 (2007)

023501-5

Figure: The Wien filter spin manipulator used with CEBAF’s second andthird polarized electron sources. (Figure copied from Sinclair et al.paper.) The maximum field integrals are approximately

∫Bxds ≈0.003 T

m and∫Eyds ≈500 KV

.

26

Mem

bero

fthe

Hel

mho

ltz-A

ssoc

iatio

n

The RF-ExB Dipole

RF-B Dipole RF-E Dipoleshielding Box

ferrite blocks

coil: 8 windings, length 560 mm

two electrodes in vacuum camber

distance 54 mm, length 580 mm

ceramic beam chambertwo separate resonance circuits

August 27, 2014 s.mey@fz-juelich.de The RF-ExB Dipole 8

Figure: RF Wien filter currently in use at the COSY ring in JuelichGermany. (Copied and cropped from a poster presentation by SebastianMey.) For RF frequencies near 1 MHz the maximum field integrals are∫Bxds=0.000175 T m and

∫Eyds=24 KV. These limits are about 20

times weaker than the CEBAF Wien filter. But the COSY frequency isunnecessarily high by a factor of 106/3× 103 ≈ 300. This suggests thatthe required Wien filter, oscillating for example at 3 KHz, should befeasible.

27 Spin wheel stabilizing torques

θR

x

z

y^

x

z

y^

θR

x

z

y^

L∆

L∆

WBx

^zB

Sz

y^By

W

BW^x x

ByW

L∆

L∆

SBz upright stabilityroll−rate steer stability

Figure: Roll-plane stabilizers: Wien filter BWx x adjusts the “wheel” roll

rate, Wien filter BWy y steers the wheel left-right, Solenoid BS

z z keeps thewheel upright.

28 I A Wien filter does not affect the particle orbit (because thecrossed electric and magnetic forces cancel) but it acts on theparticle magnetic moment (because there is a non-zero magneticfield in the particle’s rest frame).

I A Wien torquex× (y, z)S = (z,−y)S

changes the roll-rate.I A Wien torque

y × (z, x) S = (x,−z) S

steers the wheel left-right.I (Without affecting the orbit) a solenoid torque

z× (x, y) S = (y,−x) S

can keep the wheel upright.

29 Dr. T.H. Johnson Page 3,

Fi eld str ength (magn etic typ e)

at injection 10.5 gauss

' at i0 MeV 74 gauss

Field strength ( electrostatic type)

at injection 3 kV/cm

at I0 MeV 22 kV/em

Rise time .01 see!

! Phase transition energy 2.8 MeV

Frequ ency (final) 7 mc

. Frequency change 5_ %

Volts /turn 150 Va

RF power about I kw

_ No. of betatron wavelengths about 6.2

I ' aperture 1 X 1 in.

Betatron amplitude for 10 - 3 rad. error 0.07 in.

Maxim um stable amplitude, synchrotron osc.-0.16 in.

Radial spacing of betatron resonances about 0.4 in.

Vacl Lum requirement about 10 -6 mm Hg

Total pow _.rrequirements will be small and available with existing

installations. The test shack seems to be a sui table location since the ring

will be erected inside a thin magne tic shield which can be thermally insulated

and heated economically.

We estimate the cost to be approximately $600,000, distributed as shown

in the following table:

Model .Dire ct Overhead Total

Staff S. & W. $135,000 $ 65,000 $200,000

Van de Graaff 70,000 - 70,000

. Other E. & S. 130,000 - 130,000

Shops 135,000 65___000 20_$470,000 $130,000 $600,000

Inflate to 2015

$M 1.76

1.76_______$M 5.27

0.621.14

30 Proton EDM Ring

~

B

B

B

B

A

C

A

4

6

7

8

9

10

1411

5

magnetometers

solenoid

electric sector bend

tune−modulating quadrupole

polarimeters

injectionetc.

rollable Mobius insert

B

B

B

B

A

A

C

or cyclotron RF

Wideroe linac

40 m

3 cm

10 m

Figure: Proton EDM lattice. With the Mobius insert rolled by 45 degrees,horizontal and vertical betatron oscillations interchange every turn. Thisprovides long spin coherence time (SCT).