Fully Electrostatic Machine for "Frozen Spin" Effect: Proton Electric Dipole Moment Detection

1. Introduction – Basic Idea Basic Equation to describe Spin Motion Fully Electrostatic Machine for “frozen Spin” Effect (build up of of vertical spin) with smallest EDM to be detected and Effect due to Gravity Residual Magnetic Fields and their Compensation Spin Rotations in an (imperfect) electrostatic Machine Conclusions, Summary and Outlook Electric Dipole MomentC. Carli PBC-WG Meeting, 13th June 2018

2. Introduction – Basic Idea Pushed by large Community with Proponents in several Institutes worldwide (e.g. BNL proposal) • Aim: • Investigate whether charged particles (proton, deuteron ..) have an Electric Dipole Moment (EDM) • Cannot be done by applying an electric field to particle at rest due to charge • Measurement in synchrotron (using magnetic and/or electric fields for bending and focusing) • Storage ring combining magnetic and electric field to bend the beam • Spin pointing in longitudinal direction (without electric dipole moment) “spin frozen lattice” • Beam energy fixes the ratio between magnetic and electric field to keep spin in longitudinal direction • An EDM generates a vertical spin • Fully electric ring with magnetic shielding to reducesystematic errors possible for “magic energy protons” • (Other option is a machine with non-frozen spin and an “RF Wien Filter” to generate a vertical spin component, experimental tests in view of this scheme at FZ Jülich) Electric Dipole Moment PBC WG Meeting, 13th June 2018

3. Basic Equation for Spin Motionand Proton magic Energy Next slides concentrate on this option considered the most promising one • Thomas-BMT-Equation to describe change of spin given by (with additional terms for EDM) • For most Investigations use the change of the spin direction w.r.t. to the direction of motion • With G = (g-2)/2 describing the magnetic moment (for Protons G = 1.728…) • h describes possible EDM (for the sensitivity ds = 10-29 e cm quoted in many publications hs = 1.9 10-15) • Relativistic factors b and g • Frozen spin condition for protons in fully electro-static machine • Magnetic field B vanishes and h set to zero • leads to condition • Magic momentum • Strictly fulfilled only for proton executing no betatron or synchrotron oscillations in perfect machine • (does not work for Deuterons having G < 0) Electric Dipole Moment PBC WG Meeting, 13th June 2018

4. Fully Electrostatic Machine for “frozen Spin” Protons Arrows indicating bunched with their polarization CW rotating beam in blue CCW rotating beam in red Bunches polarized opposite to beam direction Bunches polarized in beam direction • Circumference of about C=500 m • Average radial electric Field of E = 5.27 MV/m • Field in bends will be higher • Small vertical tunes around QV = 0.1 with large variations to estimate average residual horizontal magnetic field (see later) • Intra Beam Scattering a potential limitations for some proposals • Counter-rotating Beams and Polarization in Beam Direction or opposite to it • To mitigate systematic effects • Some proposals with simultaneously Bunches with polarization in and opposite to beam direction in both Rings (case sketched) • Proposals for weak focusing (no strong quadrupoles perturbing vertical orbit) and strong focusing (Higher horizontal tune, smaller dispersion, IBS more manageable) rings Electric Dipole Moment PBC WG Meeting, 13th June 2018

5. Effect (build up of of vertical spin) with smallest EDM to be detected and effect due to gravity • Spin precession angular frequency due to electric moment of ds = 10-29 e cm (sensitivity goal) • With average radial field and (corresponding to ds) inserted into equation for spin motion • Vertical spin component after 1000 s (about 360 million turns) of only 1.6 10-6(very small signal to be measured and a lot of statistics required!!) • Spin precession into vertical due to gravity • Vertical average electric field to compensate gravity with and the proton mass • Spin precession (into vertical plane) angular frequency generated by This is almost a factor 30 larger than the smallest spin precession to be identified! • Systematic measurement error compensated by using CW and CCW rotating beams (spin rotation into vertical plane due to EDM has opposite sign for the two beams) Electric Dipole Moment PBC WG Meeting, 13th June 2018

6. Residual Magnetic Fields and their Compensation Magnetic shielding test set-up at CAPP (Korea) • Total vertical deflection over one turn must vanish leading to with the average horizontal magnetic field (perturbation) and the average vertical electric field seen by beam • Gives • Inserting into equation for angular frequency of spin motion (with h = 0) gives • A radial field of 18 aT coupling to the magnetic moment gives the same effect than the EDM to be detected! • No cancellation with counter-rotating beams and, thus, a systematic effect • Static magnetic fields and low frequencies an issue • Around 1 nT residual field achievable with state-of the-art magnetic shielding • Average horizontal magnetic field lower dueto variations • Still many orders of magnitude further reduction of residual horizontal field to come close to sensitivity goal Electric Dipole Moment PBC WG Meeting, 13th June 2018

7. Residual Magnetic Fields and their Compensation CW beam Bx generated by beam(s) PU coil to measure Bx CCW beam Beam separation and Bx generated (note enhanced magnetic field due to separation) • Measure separation of vertical orbits due to horizontal magnetic field • Small vertical tune (say 0.1) to enhance effect • Gives a few pm separation with average fieldof 18 aT • SQUID-BPM to measure this orbit separation • A few aT field at the location of a pick-up coilconnected to a SQUID (averaging!!!) • No signal in perfect case with counter-rotating beam • Many SQUID-BPMs needed with very regular spacing • Tune modulation in some proposals to achieve requiredprecision (even more demanding for the orbit separation measurement and delicate for beam dynamics) • On-going discussions and questions • Imperfections of orbit separation measurements (e.g. unequal beam intensities and common offset) • Impact of variations (intentional and non-intentional) of betatron functions • Other imperfections as coupling • Tune modulations Electric Dipole Moment PBC WG Meeting, 13th June 2018

8. Spin rotations in an (imperfect) electrostatic machine • Spin rotations in horizontal plane and spin decoherence • With synchrotron oscillations particle energy oscillating around magic energy • Generates oscillations of spin in horizontal plane (head and tail of bunch have different horizontal spin) • Limitation of maximum bunch length and impact on number of bunches … ? • Spin coherence time: sources for spin decoherence? How to extrapolate from COSY (>1000 s spin coherence with “non frozen spin” deuterons in magnetic ring) results? • Vertical spin build-up in imperfect electro-static ring due to magnetic moment • Example • Energy fluctuations due to electric potentials and machine imperfections • Together with vertical electric field rotates longitudinal spin into vertical direction • Example • Vertical slope of closed orbit in bend rotates horizontal spin component (how well can this be controlled) into the vertical direction • Most studies done at several places so far with misaligned quads only • Effect of bend with horizontal offset (energy change) and tilt around longitudinal axis (introducing vertical electric field component) • Mitigations of systematic effects due to cancellations with two counter-rotating beams? Electric Dipole Moment PBC WG Meeting, 13th June 2018

9. Spin rotations in an (imperfect) electrostatic machine – very first simulation results at CERN Many simulations already done at other Institutes with misaligned quadrupoles…Preliminary results shown here by Malek Haj Tahar working since about two months on EDM Average slope inside bends yav’ = -.14 10-6 rad Vertical closed orbit with one quad misaligned by 100 mm • Case one: One quad misaligned vertically by 100 mm • Case two: • One quad misaligned vertically by 100 mm plus • One bend with two 0.17 mrad rotations aroundvertical and by horizontal axis • Approximately linear build up of horizontalpolarization with dsr/dt = 18 rad/s and dsr/dt = 108 rad/s for the two cases • Mechanism to be understood • Quadratic build up of vertical spin slopeproportional to horizontal component sr • Well explained by sr rotated into vertical with slopeof the vertical orbit inside bend (presentation by S. Haciomerogluin March in Jülich and in arXiv:1709.01.208 Electric Dipole Moment PBC WG Meeting, 13th June 2018

10. Conclusions, Summary and Outlook • Proposal to measure proton (or other charged particle) EDM • Proponents in several institutes worldwide • Concentrating here on “frozen spin” protons at “magic energy” in fully electro-static ring as most promising option • Limitations, discussions, open questions • Systematic effects due to residual magnetic fields and how to handle them • Systematic effects due to machine imperfections as misalignments • Polarimetry and statistics • Lattice type, beam preparation, number of bunches, • CERN activities • Still investigations on fundamental questions as systematic errors • Residual magnetic fields and how to handle them • Possible build up of vertical polarization due to imperfection of the machine as misalignements (simultaneous horizontal offset and tilt of bend? ..) • How many bunches per ring, bunch lengths • First investigations on design and construction of electric bends and quadrupole • Studies on integration of an EDM measurement in CERN complex on hold => Aim is to better understand fundamental limitations before going on with design Electric Dipole Moment PBC WG Meeting, 13th June 2018