1. DEELS workshop, ESRF, 12.– 13. May 2014 Friederike Ewald Difficulties to measure the absolute electron beam energy using spin depolarisation at the ESRF Friederike Ewald, Boaz Nash, Nicola Carmignani, Laurent Farvacque Several attempts have been made to measure the absolute electron beam energy at the ESRF using the depolarisation method. Depolarisation and repolarisation can be well observed and correlated with theoretical predictions (such as polarisation time). However, the precise determination of the spin tune frequency (and therefore energy) still fails. Depolarisation occurs in a very large region (several kHz) around the presumed resonance frequency despite the application of very weak excitation fields (in line with field strengths reported by Diamond and Soleil). What is going wrong?

2. Friederike Ewald DEELS workshop, ESRF, 12.– 13. May 2014 Polarisation time – measurement and fit P - vertical spin polarisation P ST - Sokolov-Ternov level of polarsiation (92.38%)  p - polarisation time Touschek lifetime changes during current decay due to: 1.decrease of total current 2.bunch length shortening 3.increase with the square of the polarisation: 1/  T (t) = 1/  T (0) + P(t) 2, with  =  m /(   x’ ) Spin polarsiation follows an exponential law: P(t) = P ST · (1-exp(-t/  0 )) Build-up time of polarisation:  P = 8/5√3 (m 2 c 2 r 2 )/(e 2 ħ  5 ) time P P ST PP

3. Friederike Ewald DEELS workshop, ESRF, 12.– 13. May 2014 Polarisation time – measurement and fit Theory:  p = 15.75 min Measurement:  p = 15.9 ± 0.6 min BL … bunch length TLT … Touschek lifetime Vacuum lifetime:  v ≈ 600 h  T (t) = [ 1/  T (0) + const. · (1-exp(-t/  0 )) ] -1

4. Friederike Ewald DEELS workshop, ESRF, 12.– 13. May 2014 Resonant depolarisation Measure the spin tune by finding the resonant depolarisation frequency f dep Electron energy : E = m 0 / ( ½ (g e - 2)) · ( 0 + f dep / f ref ) a … anomalous magnetic moment of the electron;  0 … revolution frequency in the storage ring  Spin tune: = a · E/m e = 13.707 @ E = 6.04 GeV s = 0.707  f dep = 251 kHz

5. Friederike Ewald DEELS workshop, ESRF, 12.– 13. May 2014 Detecting the (de-)polarisation Excitation with vertical shaker: 2  T m < B x · L < 10  T m Depolarisation  Touschek scattering cross section ↑ Beam conditions: 16 bunch with 2 mA/bunch,  z = 5pm  T = 12 h  v = 600 h  Lifetime is Touschek dominated  Lifetime ↓ : Lifetime calculated from sum signal of all 224 Libera-BPMs with an average over ~ 20 s. That is a compromise between fast reaction and enough averaging time to reduce noise.  Beamloss ↑ : Average of all BLDs (and averaged over 20 s) Detectors for depolarisation :

6. Friederike Ewald DEELS workshop, ESRF, 12.– 13. May 2014 MDT 17. July 2012 Measurement conditions: Lattice: 7/8 bunch number: 16 SR current: 32 mA All gaps open no feedback SRCO ON after injection we leave the beam polarise for 60 min frequency scans time vertical emittance lifetime

7. Friederike Ewald DEELS workshop, ESRF, 12.– 13. May 2014 Why the depolarisation ''resonance'' is so wide ? Why the energy is lower than we expect ? Center energy: 6.03 GeV Lifetime change as function of energy Fit with error function ~ 0.15 % ∞  E/E polarisation starting again ? excitation B h L = 2  T m 10 s sweeps of  f = 0.5 kHz

8. Friederike Ewald DEELS workshop, ESRF, 12.– 13. May 2014 Spin tune sidebands responsible for wide “resonance” ?? fundamental spin tune resonance side bands of the spin tune (schematic !)  f ≈ 1.9 kHz

9. Friederike Ewald DEELS workshop, ESRF, 12.– 13. May 2014 Up- and downward frequency scans excitation B h L = 2  T m 10 s sweeps of  f = 0.5 kHz crossing of both scans not in the center  beam already depolarised before reaching the main resonance  main resonance is at higher frequencies

10. Friederike Ewald DEELS workshop, ESRF, 12.– 13. May 2014 MDT 26. Nov. 2013 1)2 kHz frequency sweep (250 – 252 kHz), 80s ( = 25 Hz/s), B x L = 2  Tm frequency 250 kHz 252 kHz 0 s 80 s

11. Friederike Ewald DEELS workshop, ESRF, 12.– 13. May 2014 frequency 250 kHz 252 kHz 0 s 80 s MDT 26. Nov. 2013 1)2 kHz frequency sweep (250 – 252 kHz), 80s ( = 25 Hz/s), B x L = 2  Tm time 80 s  lifetime : ~ 4 %

12. Friederike Ewald DEELS workshop, ESRF, 12.– 13. May 2014 MDT 26. Nov. 2013 1)2 kHz frequency sweep (250 – 252 kHz), 80s ( = 25 Hz/s), B x L = 2  Tm 2)single frequency excitation over the same range, 0.1 kHz steps 4s excitation per step same excitation strength frequency 250 kHz 252 kHz 0 s 0.1 kHz 4 s 80 s

13. Friederike Ewald DEELS workshop, ESRF, 12.– 13. May 2014 frequency 250 kHz 252 kHz 0 s 0.1 kHz 4 s 80 s MDT 26. Nov. 2013 1)2 kHz frequency sweep (250 – 252 kHz), 80s ( = 25 Hz/s), B x L = 2  Tm 2)single frequency excitation over the same range, 0.1 kHz steps 4s excitation per step same excitation strength time 80 s  lifetime : ~ 4 %  lifetime : ~ 1.5 %

14. Friederike Ewald DEELS workshop, ESRF, 12.– 13. May 2014 MDT 26. Nov. 2013 1)2 kHz frequency sweep (250 – 252 kHz), 80s ( = 25 Hz/s), B x L = 2  Tm 2)single frequency excitation over the same range, 0.1 kHz steps 4s excitation per step same excitation strength 3) single frequency excitation at ~ 1KHz from the presumed spin tune frequency frequency 250 kHz 252 kHz 0 s 0.1 kHz 4 s

15. Friederike Ewald DEELS workshop, ESRF, 12.– 13. May 2014 MDT 26. Nov. 2013 1)2 kHz frequency sweep (250 – 252 kHz), 80s ( = 25 Hz/s), B x L = 2  Tm 2)single frequency excitation over the same range, 0.1 kHz steps 4s excitation per step same excitation strength 3) single frequency excitation at ~ 1KHz from the presumed spin tune frequency frequency 250 kHz 252 kHz 0 s 0.1 kHz 4 s  Depolarisation observable at about any single frequency excitation even if far from the theoretical resonance (as far as ~ 5 kHz) !!  Bandwidth of the shaker is very narrow  Synchrotron resonance lines would have to be very broad ?  ?????

16. Friederike Ewald DEELS workshop, ESRF, 12.– 13. May 2014 Simulated resonance width We observe clear depolarisation at B x L ≈ 2  Tm An integrated field of 2  Tm corresponds to an angular kick strength of ~ 0.1  rad.  simulated resonance width only a fraction of Hz !! Resonance width computed from our simple spin track code, with varying kicker strengths. center = 0.707 (251 kHz) t exitation = 2.8 s (10 6 turns) kicker strength:  f res ≈ 15 Hz  fres ≈ 35 Hz  fres ≈ 280 Hz

17. Friederike Ewald DEELS workshop, ESRF, 12.– 13. May 2014 Questions The beam may be depolarized within a broad range of ~ 5kHz, whatever we do. Why don’t we see narrow resonances at the synchrotron tune and its side bands ? However, our calculated resonance widths are extremely narrow for the applied shaker strengths. This is in opposition to our experimental findings. What may be wrong about our understanding / simulation of the resonance width ? Simulation shows that, when “ switching off " the synchrotron frequency, the resonance width approaches the energy spread. What could lead in real conditions to a reduction of the synchrotron frequency ??