Transcript Beam energy through Spin depolarization at the ESRF

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
Spin polarsiation follows an exponential law:
P(t) = PST · (1-exp(-t/t0))
PST
P
P - vertical spin polarisation
PST - Sokolov-Ternov level
of polarsiation (92.38%)
tp - polarisation time
Build-up time of polarisation:
tP
time
tP = 8/5√3 (m2 c 2 r 2)/(e2 ħ g 5)
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/tT (t) = 1/tT (0) + < R(e) · 1/tT (0) > P(t)2 ,
Friederike Ewald
with e = dm /(g sx’)
DEELS workshop, ESRF, 12.– 13. May 2014
Polarisation time – measurement and fit
tT (t) = [ 1/tT (0) + const. · (1-exp(-t/t0)) ] -1
Theory:
tp = 15.75 min
Measurement:
tp = 15.9 ± 0.6 min
Vacuum lifetime:
tv ≈ 600 h
BL … bunch length
TLT … Touschek lifetime
Friederike Ewald
DEELS workshop, ESRF, 12.– 13. May 2014
Resonant depolarisation
Measure the spin tune by finding the resonant depolarisation frequency fdep
Electron energy :
E = m0 / ( ½ (ge- 2)) · (n0 + fdep / fref )
Spin tune: n = a · E/me = 13.707 @ E = 6.04 GeV
ns = 0.707
 fdep = 251 kHz
a … anomalous magnetic moment of the electron;
w0 … revolution frequency in the storage ring
Friederike Ewald
DEELS workshop, ESRF, 12.– 13. May 2014
Detecting the (de-)polarisation
Excitation with vertical shaker:
2 mT m < Bx · L < 10 mT m
↑
Depolarisation

Beam conditions:
16 bunch with 2 mA/bunch, ez = 5pm
tT = 12 h
tv = 600 h
 Lifetime is Touschek dominated
Touschek scattering cross section
Detectors for depolarisation :
 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)
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
vertical emittance
lifetime
time
Friederike Ewald
DEELS workshop, ESRF, 12.– 13. May 2014
excitation Bh L = 2 mT m
10 s sweeps of Df = 0.5 kHz
18
Center energy: 6.03 GeV
~ 0.15 % ∞ DE/E
Lifetime [hrs]
17.5
Lifetime change as function
of energy
Fit with error function
17
polarisation starting again ?
16.5
6.01
6.02
6.03
6.04
6.05
6.06
Electron energy [GeV]
• Why the depolarisation ''resonance'' is so wide ?
• Why the energy is lower than we expect ?
Friederike Ewald
DEELS workshop, ESRF, 12.– 13. May 2014
Spin tune sidebands responsible for wide “resonance” ??
fundamental spin tune resonance
18
17.8
side bands of the
spin tune
(schematic !)
Df ≈ 1.9 kHz
Lifetime [hrs]
17.6
17.4
17.2
17
16.8
16.6
16.4
225
230
235
240
245
250
255
260
265
Shaker frequency [kHz]
Friederike Ewald
DEELS workshop, ESRF, 12.– 13. May 2014
Up- and downward frequency scans
excitation Bh L = 2 mT m
10 s sweeps of Df = 0.5 kHz
Friederike Ewald
crossing of both scans not in the center
 beam already depolarised before reaching
the main resonance
 main resonance is at higher frequencies
DEELS workshop, ESRF, 12.– 13. May 2014
MDT 26. Nov. 2013
frequency
252 kHz
1) 2 kHz frequency sweep
(250 – 252 kHz),
80s ( = 25 Hz/s),
BxL = 2 mTm
250 kHz
0s
Friederike Ewald
80 s
DEELS workshop, ESRF, 12.– 13. May 2014
MDT 26. Nov. 2013
frequency
252 kHz
1) 2 kHz frequency sweep
(250 – 252 kHz),
80s ( = 25 Hz/s),
BxL = 2 mTm
D lifetime : ~ 4 %
time
250 kHz
0s
Friederike Ewald
80ss
80
DEELS workshop, ESRF, 12.– 13. May 2014
252 kHz
frequency
MDT 26. Nov. 2013
1) 2 kHz frequency sweep
(250 – 252 kHz),
80s ( = 25 Hz/s),
BxL = 2 mTm
0.1 kHz
2) single frequency excitation
over the same range,
0.1 kHz steps
4s excitation per step
same excitation strength
4s
250 kHz
0s
Friederike Ewald
80 s
DEELS workshop, ESRF, 12.– 13. May 2014
252 kHz
frequency
MDT 26. Nov. 2013
1) 2 kHz frequency sweep
(250 – 252 kHz),
80s ( = 25 Hz/s),
BxL = 2 mTm
0.1 kHz
4s
D lifetime : ~ 4 %
time
250 kHz
0s
2) single frequency excitation
over the same range,
0.1 kHz steps
4s excitation per step
same excitation strength
80 s
80 s
D lifetime : ~ 1.5 %
Friederike Ewald
DEELS workshop, ESRF, 12.– 13. May 2014
252 kHz
frequency
MDT 26. Nov. 2013
1) 2 kHz frequency sweep
(250 – 252 kHz),
80s ( = 25 Hz/s),
BxL = 2 mTm
0.1 kHz
4s
2) single frequency excitation
over the same range,
0.1 kHz steps
4s excitation per step
same excitation strength
250 kHz
0s
Friederike Ewald
3) single frequency excitation
at ~ 1KHz from the
presumed spin tune
frequency
DEELS workshop, ESRF, 12.– 13. May 2014
252 kHz
frequency
MDT 26. Nov. 2013
250 kHz
0s
1) 2 kHz frequency sweep
(250 – 252 kHz),
80s ( = 25 Hz/s),
BxL = 2 mTm
0.1 kHz
2) single frequency excitation
4s
over the same range,
0.1 kHz steps
4s excitation per step
 Depolarisation observable at about any
same excitation strength
single frequency excitation even if far from
the theoretical resonance (as far as ~ 5 kHz) !!
3) single frequency excitation
at ~ 1KHz from the
 Bandwidth of the shaker is very narrow
presumed spin tune
frequency
 Synchrotron resonance lines would have to
be very broad ?
 ?????
Friederike Ewald
DEELS workshop, ESRF, 12.– 13. May 2014
Simulated resonance width
Resonance width computed from our simple spin track code, with varying kicker strengths.
We observe clear
depolarisation at
BxL ≈ 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 !!
Dfres ≈ 15 Hz
Dfres ≈ 35 Hz
Dfres ≈ 280 Hz
kicker strength:
ncenter = 0.707 (251 kHz)
texitation = 2.8 s (10 6 turns)
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 ??
Friederike Ewald
DEELS workshop, ESRF, 12.– 13. May 2014