DEELS workshop, ESRF, 12.– 13. May 2014 Friederike Ewald Difficulties to measure the absolute electron beam energy using spin depolarisation at the ESRF

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?

Friederike Ewald DEELS workshop, ESRF, 12.– 13. May 2014

Polarisation time – measurement and fit

P - vertical spin polarisationPST - Sokolov-Ternov level of polarsiation (92.38%)tp - polarisation time

Touschek lifetime changes during current decay due to:

1. decrease of total current2. bunch length shortening

3. increase with the square of the polarisation:

1/tT (t) = 1/tT (0) + < R(e) · 1/tT (0) > P(t)2 , with e = dm /(g sx’)

Spin polarsiation follows an exponential law:

P(t) = PST · (1-exp(-t/t0))

Build-up time of polarisation: tP = 8/5√3 (m2 c 2 r 2)/(e2 ħ g 5)

time

P PST

tP


Polarisation time – measurement and fit

Theory: tp = 15.75 min

Measurement: tp = 15.9 ± 0.6 min

BL … bunch lengthTLT … Touschek lifetime

Vacuum lifetime:tv ≈ 600 h

tT (t) = [ 1/tT (0) + const. · (1-exp(-t/t0)) ] -1


Resonant depolarisation

Measure the spin tune by finding the resonant depolarisation frequency fdep

Electron energy : E = m0 / ( ½ (ge- 2)) · (n0 + fdep / fref )

a … anomalous magnetic moment of the electron; w0 … revolution frequency in the storage ring

Spin tune: n = a · E/me = 13.707 @ E = 6.04 GeV

ns = 0.707 fdep = 251 kHz


Detecting the (de-)polarisation

Excitation with vertical shaker: 2 mT m < Bx · L < 10 mT m

Depolarisation Touschek scattering cross section ↑

Beam conditions: 16 bunch with 2 mA/bunch, ez = 5pmtT = 12 htv = 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 :


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 emittancelifetime


• Why the depolarisation ''resonance'' is so wide ? • Why the energy is lower than we expect ?

6.01 6.02 6.03 6.04 6.05 6.06

16.5

17

17.5

18

Electron energy [GeV]

Lifeti

me

[hrs

]

Center energy: 6.03 GeV

Lifetime change as function of energy

Fit with error function~ 0.15 % ∞ DE/E

polarisation starting again ?

excitation Bh L = 2 mT m 10 s sweeps of Df = 0.5 kHz


Spin tune sidebands responsible for wide “resonance” ??

fundamental spin tune resonance

225 230 235 240 245 250 255 260 265

16.4

16.6

16.8

17

17.2

17.4

17.6

17.8

18

Lifeti

me

[hrs

]

Shaker frequency [kHz]

side bands of the spin tune (schematic !)Df ≈ 1.9 kHz


Up- and downward frequency scans

excitation Bh L = 2 mT m 10 s sweeps of Df = 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


MDT 26. Nov. 2013

1) 2 kHz frequency sweep (250 – 252 kHz), 80s ( = 25 Hz/s),

BxL = 2 mTmfreq

uenc

y

250 kHz

252 kHz

0 s 80 s


freq

uenc

y

250 kHz

252 kHz

0 s 80 s

MDT 26. Nov. 2013


BxL = 2 mTm

time

80 s

D lifetime : ~ 4 %


MDT 26. Nov. 2013


BxL = 2 mTm

2) single frequency excitation over the same range, 0.1 kHz steps4s excitation per step

same excitation strength

freq

uenc

y

250 kHz

252 kHz

0 s

0.1 kHz

4 s

80 s


freq

uenc

y

250 kHz

252 kHz

0 s

0.1 kHz

4 s

80 s

MDT 26. Nov. 2013


BxL = 2 mTm


same excitation strengthtime

80 s

D lifetime : ~ 4 %

D lifetime : ~ 1.5 %


MDT 26. Nov. 2013


BxL = 2 mTm



3) single frequency excitation at ~ 1KHz from the presumed spin tune frequency

freq

uenc

y

250 kHz

252 kHz

0 s

0.1 kHz

4 s


MDT 26. Nov. 2013


BxL = 2 mTm



3) single frequency excitation at ~ 1KHz from the presumed spin tune frequency

freq

uenc

y

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 ?

?????


Simulated resonance width

We observe clear depolarisation atBxL ≈ 2 mTm

An integrated field of 2 mTm corresponds to an angular kick strength of ~ 0.1 mrad.

simulated resonance width only a fraction of Hz !!

Resonance width computed from our simple spin track code, with varying kicker strengths.

ncenter = 0.707 (251 kHz)texitation = 2.8 s (10 6 turns)

kicker strength:

Dfres ≈ 15 HzDfres ≈ 35 HzDfres ≈ 280 Hz


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 ??

Documents

DEELS workshop, ESRF, 12.– 13. May 2014 Friederike Ewald Difficulties to measure the absolute electron beam energy using spin depolarisation at the ESRF