Resonant Polarimetry for Frequency Domain EDM Measurements Richard - PowerPoint PPT Presentation

1 Resonant Polarimetry for Frequency Domain EDM Measurements Richard Talman Laboratory for Elementary-Particle Physics Cornell University Polarimetry Workshop Mainz, 10-11 September, 2015

2 Outline Why Measure EDM? Resonant Polarimeter Conceptual EDM Measurement Ring Why “Rolling Polarization”? and Why the EDM Signal Survives Achievable Precision BNL “AGS Analogue” Ring as EDM Prototype Resonant Polarimetry Tests Long Term EDM Program Survey of Practical Resonant Polarimeter Applications Extra Slides

3 Some of this presentation is extracted from the following papers: ◮ R. and J. Talman, Symplectic orbit and spin tracking code for all-electric storage rings, Phys. Rev. ST Accel Beams 18 , ZD10091, 2015 ◮ R. and J. Talman, Electric dipole moment planning with a resurrected BNL Alternating Gradient Synchrotron electron analog ring, Phys. Rev. ST Accel Beams 18 , ZD10092, 2015 ◮ R. Talman, Frequency domain storage ring method for Electric Dipole Moment measurement, arXiv:1508.04366 [physics.acc-ph], 18 Aug 2015

4 Why Measure EDM? ◮ Violations of parity (P) and time reversal (T) in the standard model are insufficient to account for excess of particles over anti-particles in the present day universe. ◮ Any non-zero EDM of electron or proton would represent a violation of both P and T, and therefore also CP. ◮ In all-electric rings “frozen spin” operation is only possible with electrons or protons.

5 Resonant (Longitudinal) Polarimeter l R b R r R c R t R s R Figure: Longitudinally polarized beam approaching a superconducting helical resonator. Beam polarization is due to the more or less parallel alignment of the individual particle spins, indicated here as tiny current loops. 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 ◮ The Faraday’s law E.M.F. induced in the resonator has one sign on input and the opposite sign on output. ◮ At high enough resonator frequency these inputs no longer cancel. ◮ The key parameters are particle speed v p and (transmission line) wave speed v r . ◮ The lowest frequency standing wave for a line of length l r , open at both ends, has λ r = 2 l r ; B z ( z , t ) ≈ B 0 sin π z sin π v r t , 0 < z < l r . (1) l r l r ◮ The (Stern-Gerlach) force on a dipole moment m is given by F = ∇ ( B · m ) . (2) ◮ The force on a magnetic dipole on the axis of the resonator is ∂ B z ∂ z = π m z B 0 cos π z sin π v r t F z ( z , t ) = m z . (3) l r l r l r

7 At position z = v p t a magnetic dipole traveling at velocity v p is subject to force F z ( z ) = π m z B 0 cos π z sin π ( v r / v p ) z . (4) l r l r l r Integrating over the resonator length, the work done on the particle, as it passes through the resonator, is � l r � π cos π z sin π ( v r / v p ) z � ∆ U ( v r / v p ) = m z B 0 . (5) dz l r l r l r z =0 ◮ See plot.

8 Energy lost in resonator Figure: Plot of energy lost in resonator ∆ U ( v r / v p ) as given by the bracketed expression in Eq. (5). ◮ For v r = 0 . 51 v p , the energy transfer from particle to resonator is maximized. ◮ With particle speed twice wave speed, during half cycle of resonator, B z reverses phase as particle proceeds from entry to exit.

9 EDM Measurement Ring (passive) resonant polarimeters wheel left−right wheel−upright ^ y stabilize sensor stabilize sensor bend electric θ R roll rate resonator field E rolling polarization ^ upper lower upper lower upper lower z + sideband sideband sideband sideband sideband sideband "Spin wheel" − M+ M+ M+ M z z M x M y x y f 0 + ∆ f f 0 − ∆ f h + f 0 + ∆ f f 0 − ∆ f f 0 + ∆ f f 0 − ∆ f ^ h h h h h x scaler scaler BPM system RF Moebius h f 0 0 cavity twist Wien filters (active) W S I I y z beam W B S B W B y z x polarity reversal solenoid (active) roll rate control I roll wheel−upright wheel roll rate wheel left−right torque torque torque Controlled temperature, vibration free, rigidly constructed, magnetic shielded Figure: Cartoon of the EDM ring and its spin control. The Koop polarization “wheel” in the upper left corner “rolls” along the ring, always upright, and aligned with the orbit. The boxes at the bottom apply torques to the magnetic moments without altering the design orbit.

10 ◮ Elements with superscript “W” are Wien filters; superscript “S” indicates solenoid. ◮ The frequency domain EDM signal is the frequency change of spin wheel rotation when the B W Wien filter polarity is x reversed. ◮ EDM measurement accuracy (as contrasted with precision) is limited by the reversal accuracy occurring in the shaded region. ◮ Precision is governed by scaler precision. This is a benefit obtained by moving the EDM sensitivity from polarimeter intensity to polarimeter frequency response.

11 Why “Rolling Polarization”? and Why the EDM Signal Survives ◮ Polarized “wheel” was proposed by Koop (for different reason). ◮ Here the primary purpose of the rolling polarization is to shift the resonator response frequency away from harmonic of revolution frequency. ◮ This is essential to protect the polarization response from being overwhelmed by direct response to beam charge or beam current. ◮ Since the EDM torque is always in the plane of the wheel its effect is to alter the roll rate. ◮ Reversing the roll direction (with beam direction fixed) does not change the EDM contribution to the roll. ◮ The difference between forward and backward roll-rates measures the EDM (as a frequency difference).

12 Rolling Magnetization Frequency Spectra RING a a a a a a 2/2 2/2 2/2 2/2 2/2 2/2 f/f 0 0 1 2 h 1−q 1+q 2−q 2+q h−q h+q LINAC a a a a a a 2/2 2/2 2/2 2/2 2/2 2/2 a a a a a a 4/2 4/2 4/2 4/2 a 4/2 a 4/2 a f/f 0 0 0 0 0 1−2q 1 1+2q 2−2q 2 2+2q h−2q h h+2q 1−q 1+q h−q h+q 2−q 2+q Figure: Frequency spectra of the beam polarization drive signal to the resonant polarimeter. In a storage ring (shown above) the drive is purely sinusoidal, producing sidebands of harmonics of the revolution frequency. For a resonant polarimeter test using a polarized linac beam (shown below) the drive is distorted, but can still be approximately sinusoidal, giving the same two dominant sideband signals. The operative polarimetry sideband lines are indicated by dark arrows.

13 Achievable Precision EDM in units of 10 − 29 e-cm = ˜ d 2 x EDM/MDM precession ratio = 2 η ( e ) = 0 . 92 × 10 − 15 ≈ 10 − 15 roll reversal error: ± η rev . e . g . = 10 − 10 duration of each one of a pair of runs = T run smallest detectable fraction of a cycle = η fringe = 0 . 001 e . g . = 10 − 10 fractional roll reversal error = ± σ roll FF N FF = number of fractional fringes per run ± σ rev . = roll reversal error measured in fractional fringes FF N FF =(2 η ( e ) ) ˜ � e . g . d 10 − 15 · 10 · 10 7 · 10 3 d � ≈ ˜ = 0 . 1 ˜ , h r f 0 T run d 10 − 3 η fringe ≈ ± 10 2 · 10 − 10 · 10 3 FF = ± f roll η rev . T run � e . g . = 10 − 2 � ± σ rev . . 10 − 3 η fringe error after 10 4 | d e | current particle excess fractional roll reversal upper limit cycles per pair pairs of runs error e-cm of 1000 s runs e-cm e-cm 3 × 10 − 26 neutron 8 × 10 − 25 ± 8 × 10 3 ± 10 − 30 ± 10 − 30 proton 10 − 28 ± 10 − 30 ± 10 − 30 electron ± 1

14 BNL “AGS Analogue” Ring as EDM Prototype Figure: The 1955 AGS-Analogue lattice as reverse engineered from available documentation—mainly the 1953 BNL-AEC proposal letter. Except for insufficient straight section length, and the 10 MeV rather than 14.5 Mev energy, this ring could be used to measure the electron EDM.

15 Polarimeter room temperature bench test I 0+ cycle 1/2− cycle 1/4 cycle I I V V z z 0 0 l r 0 l r B beam bunch standing wave z insulating tube (2inch OD) coupling loop coupling loop coax cable from spectrum analyser transmitter 44 turn copper coil to spectrum l r analyser receiver aluminum tube Figure: . Room temperaure bench test set-up of prototype resonant polarimeter, with results shown in next figure. The coil length is l r =11 inches. Beam magnetization is emulated by the spectrum analyser transmitter.

16 ◮ Resonator excitation is detected by a single turn loop connected to the spectrum analyser receiver. ◮ This would be an appropriate pick-up in the true polarimetry application though, like the resonator, the preamplifier would have to be at cryogenic temperature to maximize the signal to noise ratio. ◮ The figures above the apparatus are intended to complete the analogy to a situation in which the transmitter is replaced by the passage of a beam bunch. ◮ The particle and wave speeds are arranged to maximize the energy transfer from beam to resonator.

17 Figure: Frequency spectrum observed using the bench test shown in previous figure. Ten normal modes of the helical transmission line are visible.