Finemet Review September 14 th 15 th 2015 Acknowledgements S Gilardoni M Haase M Migliorati M Paoluzzi D Perrelet Simulation studies and measurements for the PS coupledbunch feedback ID: 797629
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Slide1
Slide22
L. Ventura, H. Damerau, G. Sterbini
Finemet Review
September 14
th
- 15
th 2015
Acknowledgements: S. Gilardoni, M. Haase, M. Migliorati, M. Paoluzzi, D. Perrelet.
Simulation studies and
measurements
for the
PS
coupled-bunch feedback
Slide3What can we expect with the new coupled-bunch feedback?
Simulation studies for coupled-bunch instabilities
Coupled-bunch instabilities
Mode analysis
technique
Excitation
mechanism
Measurements in 2015Frequency scan
Mode scan
Amplitude scanHigh Intensity free evolution
3
Slide4What can we expect with the new coupled-bunch feedback?
Simulation studies for coupled-bunch instabilities
Coupled-bunch instabilities
Mode analysis
technique
Excitation
mechanism
Measurements in
2015
Frequency scanMode scan
Amplitude scan
Beam naturally unstable
4
Slide55
h = 7
Eject 72 bunches
Inject 4+2 bunches
h = 21
Instability
h = 84
Triple splitting after 2nd injection
Split in four at flat top energy
LHC 25ns cycle in the PS
5
Slide66
How in the beam spectrum we can find coupled bunch mode?
The longitudinal spectrum in a cavity with a circulating beam contains the
RF frequencies and periodic
revolution frequencies harmonics f0
. In the case
of LHC beam in the PS with h=21, 21different modes of oscillations will show up as sidebands of revolution harmonic:
f
0
2f
0
5f
0
4f
0
3f
0
0
2f
0
+ω
s
2f
0
-ω
s
f
CB
=|pf
RF
+(qN
b
+μ)f
0
±mf
s
|
f
0
-ω
s
f
0
+
ω
s
RF line
μ= 1
q: integer -∞<q<+∞
N
b
: number of bunches
μ: mode number
m
=1 for dipolar
mode
μ=
2
μ=
19
μ=
20
6f
0
6
μ=
3
μ=
18
Slide77
Since the beam spectrum is symmetric the Finemet cavity is sufficient to cover all the oscillation modes in h=21 (@10 MHz)
.
f
RF
= 21frev
Finemet base-band
What can we expect with the new coupled-bunch feedback?
f
rev
10MHz cavity
Finemet
©
cavity
But even if the Finemet cavity covers all modes with its frequency range one cannot have large voltage at all the modes the same time. It is necessary to evaluate if the
V
RF
= 5
kV is enough.
Tunable 2.8-10.1 MHz;
V
RF
=20kV
0.4-5.5 MHz;
V
RF
=5kV
Slide8What can we expect with the new coupled-bunch feedback?
Simulation studies for coupled-bunch instabilities
Coupled-bunch instabilities
Mode analysis technique
Excitation mechanism
Measurements in
2015Frequency scan
Mode scan Amplitude scan
Beam naturally unstable
8
Finemet Review 2014
Slide9MuSiC
: a
Mu
lti-bunch/particle Si
mulation code
9
MuSiC is a new multibunch/multiparticle tracking code which simulates the longitudinal beam dynamics under the simultaneous effect of short range and long range wakefields.
• The impedance of resonant modes, responsible of coupled bunch instability, is used directly instead of the wakefield. The impedance is fitted with multiple resonators.
•
Only dipolar oscillation modes are simulated. • A frequency domain feedback system for controlling coupled bunch instabilities, similar to that used for the PS, is included.
Both the Finemet and 10 MHz system model have been fitted as a sum of resonant mode and implemented in the simulation code
.Impedance Model
MuSiC
Simulation Code
:
M.Migliorati
,
https://
espace.cern.ch
/be-
dep
/ABP/HSC/Meetings/ICE_201406_MuSiC.pdf
Slide1010
Measurements
Measurements
vs. simulations (1/3)
Measurements performed in 2013 with a full machine (21 bunches in h=21) evidence the mode pattern showed in figure where mode 2 is the stronger one.
Slide11Mode amplitude
11
Simulations with 10 MHz impedance model
Measurements
vs.
simulations (2/3)
Number
of turns
Mode number
Measurements
Simulations performed with Music code and using the impedance model of the 10 MHz system reproduce the same mode pattern as measurements.
Slide12Mode amplitude
12
Simulations with
10 MHz + Finemet impedance model
Measurements
vs.
simulations (3/3)
Number of turns
Mode number
From simulations the contribution of the Finemet cavity to the coupled bunch instability is negligible compared to the stronger effect of the 10 MHz cavities.
Measurements
10 MHz cavities impedance is supposed to be the main source of
coupled-bunch instability in the PS.
Slide13What can we expect with the new coupled-bunch feedback?
Simulation studies for coupled-bunch instabilities
Coupled-bunch instabilities
Mode analysis
technique
Excitation
mechanism
Measurements in 2015Frequency scan
Mode
scan Amplitude scanBeam naturally unstable
13
Slide14What can we expect with the new coupled-bunch feedback?
Simulation studies for coupled-bunch instabilities
Coupled-bunch instabilities
Mode analysis
technique
Excitation mechanism
Measurements in 2015
Frequency scanMode
scan
Amplitude scanBeam naturally unstable
14
Slide1515
Sampling frequency: 400 MHz (h
sampling≈841, 160 ms @ 2.5 ns sampling)
1) Bunch signal
Mode analysis
techniqueT
rev
IPAC2015
T
rev
changes during the acquisition since we are accelerating the beam:
the gating is complex
it is necessary the T
rev
signal to gate the beam signal
Slide1616
Longitudinal oscillation of the
centroid
~ 1ns
well
below the limit of 2.5 ns of the sampling.Centroid oscillations are small ≈ ns (even smaller then the Trev = 2.2μs) and their growth is in the range of ms small oscillations, fast growing.We find the center of mass using a fast algorithm which identifies the centroid of each bunch with a weighted average for each turn in
the measurements acquisition window.
2) Bunch centroid evolution
Slide17Fit on each centroid oscillation performed using a
moving window which covers about one synchrotron oscillation.
Centroid
evolution
IDFT(Xi) coupled-bunch mode evolution
3) Mode evolution
Using the formalism of circulant matrices, since in h=21 the system is circulant, starting from the information of the 21 centroid evolution along time it is possible to obtain the information about amplitude and phase of each oscillation mode.
X
i
=a.ejφ
w
here Xi is the phasor representing the complex amplitude of the bunch.
The IDFT allows
to compute
the amplitude A
i
and phase
Φ
i
for each oscillation mode from the
a
i
and
ϕ
i
of each bunch.
17
Slide18What can we expect with the new coupled-bunch feedback?
Simulation studies for coupled-bunch instabilities
Coupled-bunch instabilities
Mode analysis technique
Excitation mechanism
Measurements in
2015Frequency
scanMode scan
Amplitude scan
Beam naturally unstable18
Slide19Low-pass
Low-pass
ADC
DAC
Cavity return
Cavity drive
s
in(
h
FB
f
rev
t
+
f
)
sin(
h
FB
f
rev
t
)
cos(
h
FB
f
rev
t
+
f
)
cos(
h
FB
f
rev
t)
A
mplitude
Low freq.
DDS
A
mplitude
sin
cos
Side-band selection
Excitation frequency,
Δ
f
f
h
FB
f
rev
+Δ
f
Excitation frequency
f
exc
~
f
s
away from
hf
rev
Firmware
to excite coupled-bunch
oscillations
w
ith the Finemet cavity
19
-Δ
f
Slide2020
What can we expect with the new coupled-bunch feedback?
Simulation studies for coupled-bunch instabilities
Coupled-bunch instabilities
Mode analysis technique
Excitation mechanism
Measurements in
20151) Frequency scan
Δf2) Mode scan h
FB
3) Amplitude scan Amplitude
4) Beam naturally unstable
Slide2121
What can we expect with the new coupled-bunch feedback?
Simulation studies for coupled-bunch instabilities
Coupled-bunch instabilities
Mode analysis technique
Excitation mechanism
Measurements in
20151) Frequency scan
Δf2) Mode scan h
FB
3) Amplitude scan Amplitude4) Beam naturally unstable
Slide2222
f
1
f
rev
f
exc
1
f
rev
+
fexc
where
f
exc
~
f
s
Excite h=1
h
FB
= 1
V= 2 kV
pp
Settings
Frequency Scan (1/2)
?
The frequency scan is necessary to locate with accuracy the frequency where we are in resonance with the oscillation mode.
Slide2323
As
we approach the correct
excitation
frequency the beating becomes longer and as we move away the beating shortens.
Frequency Scan (2/2)
f
1
f
revfexc
h
FB= 1
V= 2 kV
pp
This is related with the fact that we excite at a fixed frequency
h
f
rev
+
f
exc
but the tune changes during the acquisition since we are accelerating.
M
oving
in frequency of a few
Hz, we observe no mode excited if we
works
at f
rev
and the mode growing when
we choose the correct excitation frequency fexc.
Slide2424
What can we expect with the new coupled-bunch feedback?
Simulation studies for coupled-bunch instabilities
Coupled-bunch instabilities
Mode analysis technique
Excitation mechanism
Measurements in
20151) Frequency scan
Δ
f2) Mode scan hFB
3) Amplitude scan
Amplitude4) Beam naturally unstable
Slide25Mode Scan (1/4)
LHC 25 ns beam with ≈
1.3
1011 ppb intensity, 4+2 and 4+3 bunches injected from PSB.Once selected the mode of interest with the Finemet we excited each mode with a fixed
voltage.
25
f
3
frev
Δ
f = +
385 Hz
h
f
rev
+
f
exc
=
3
f
rev
+385 Hz
where
f
exc
~
f
s
Excite h=3
h
FB
= 3
V
~
1.5
kV
pp
f
exc
= +385 Hz
Settings
Slide26Mode Scan (2/4)
26
Excitation of only mode 3!!!
Reproducible on different acquisitions
f
3
f
rev
Δ
f = +
385 Hz
h
f
rev
+
f
exc
=
3
f
rev
+385 Hz
where
f
exc
~
f
s
Excite h=3
h
FB
= 3
V ~
1.5 kV
pp
f
exc
= +385 Hz
Settings
Slide27Mode Scan (3/4)
27
f
18
f
rev
Δ
f =
-
385 Hz
h
frev+
f
exc
=
18
f
rev
-
385 Hz
where
f
exc
~
f
s
Excite h=18
Each mode appears in the spectrum as a lower and upper sideband.
f
3
f
rev
18
f
rev
m
ode 3
m
ode 3
Slide28Mode Scan (4/4)
28
Excitation of only mode 3!!!
Reproducible on different acquisitions
f
18
f
rev
Δ
f =
-
385 Hz
h
f
rev
+
f
exc
=
18
f
rev
-
385 Hz
where
f
exc
~
f
s
Excite h=18
h
FB
= 18
V ~
1.5 kV
pp
f
exc
= -385 Hz
Settings
Slide2929
Mode Scan:
Summary (1/2)
A linear fit is performed on the linear portion of the mode amplitude evolution to evaluate the slope and have an idea of how fast the mode get unstable.
Fit function
Ex: for mode 16
dW
i
/dt = 0.8 ns / 10 ms
h
FB
= 16
V ~
1.5 kV
pp
f
exc
= +385 Hz
Settings
Slide30Mode Scan:
Summary (2/2)
30
The slope resulting
from
the linear fit of each mode is roughly in the same range.
The Finemet cavity acts in the similar way over all the harmonics.
Fit function
h
FB
= 1-21
V ~
1.5 kV
pp
f
exc
= +385 Hz
Settings
Slide3131
What can we expect with the new coupled-bunch feedback?
Simulation studies for coupled-bunch instabilities
Coupled-bunch instabilities
Mode analysis technique
Excitation mechanism
Measurements in
20151) Frequency scan
Δ
f2) Mode scan hFB
3) Amplitude scan
Amplitude4) Beam naturally unstable
Slide3232
Amplitude excitation scan (1/3)
We selected one single harmonic, h=1, and excited the corresponding mode of oscillation with
different voltage from the Finemet cavity
.
f
1
f
rev
Δ
f = +
390 Hz
h
f
rev
+
f
exc
=
1
f
rev
+390 Hz
where
f
exc
~
f
s
Excite h=1
h
FB
= 1
V= 0-3.5 kV
pp
f
exc
= +390 Hz
Slide3333
Amplitude excitation:
Measurements are reproducible
Excitation of mode 1
@ 3 kV
Excitation of mode 1
@ 1 kVAmplitude excitation scan (2/3)
hFB
= 1
V= 0-3.5 kVppfexc= +390 Hz
Slide3434
I
ncreasing voltage by the Finemet
Amplitude excitation scan (3/3)
Observation of mode 1 excited with different voltage from the cavity.
Fit function
h
FB
= 1
V= 0-3.5 kV
pp
f
exc
= +390 Hz
Slide3535
Excitation Amplitude Scan:
Summary
Settings
h
FB
= 1
V= 0-3.5 kV
pp
fexc= +390 Hz
LINEAR
REGIME slope is proportional to the excitation voltage.
Slide3636
What can we expect with the new coupled-bunch feedback?
Simulation studies for coupled-bunch instabilities
Coupled-bunch instabilities
Mode analysis technique
Excitation mechanism
Measurements in
20151) Frequency scan
Δ
f2) Mode scan hFB
3) Amplitude scan
Amplitude4) Beam naturally unstable
Slide3737
Beam naturally Unstable
Observation of Mode 1 getting unstable
EXAMPLE of a particular
case
In
order to drive naturally the beam unstable during measurements the blow up of the 200 MHz cavities was disabled reduced longitudinal emittance, and the mode evolution was observed.
Fit function
Slide3838
I describe the system in the mode space as:
the
physics evolution of modes in the system
the correction applied by the feedback
The feedback has to compensate the mode rising!!
W
noise
AW
A=0.01 ms
-1
from measurements
W
noise
= 1 ns
Hypothesis
Is it possible to make
predictions
of the behavior of the beam with the new
coupled-bunch feedback system
with the information obtained from these data analysis?
Slide3939
Once obtained how the feedback should act
to
counteract the mode evolution, it is necessary to know if the voltage given by the cavity to damp such a rise time is in the range of the 5 kV available.
Excitation Amplitude Scan:
Summary
The voltage required to the cavity to compensate the mode 1 is V≈0.1
kV
pp
.
V≈0.1 kV
pp
Slide4040
Once obtained how the feedback should act
to
counteract the mode evolution, it is necessary to know if the voltage given by the cavity to damp such a rise time is in the range of the 5 kV available.
Excitation Amplitude Scan:
Summary
The voltage required to the cavity to compensate the mode 1 is V≈0.1
kV
pp
.
V≈0.1 kV
pp
This is not the work case
18 bunches in h=21 with LIU intensity.
The measurement presented are
only with
the full ring (21 bunches)
.
Slide4141
Feedback ON in
counter-phase
see Heiko presentation
20
ms/div
A=0.04 ms-1 from measurementsWnoise
= 1 ns Hypothesis
~ 4 times large damping rate than natural growing
rate
Excitation Measurements
f
s
sideband amplitude at 20
f
rev
Slide42Summary
Simulation code
MuSiC
Multibunch/multiparticle
Simulation Code has been used to
simulate CB instability.
Impedance model10 MHz cavities impedance implemented in the simulation code is supposed to be the main source of CB instability.
Finemet cavity impedance implemented in the simulation code and proved to have a negligible contribution to the coupled bunch instability compared to the stronger effect of the 10 MHz cavities.
Mode
analysis techniques The algorithm allows to analyze the longitudinal bunch oscillation with a ns precision and, through the formalism of circulant matrices, to obtain the coupled-bunch mode evolution.
Excitation
mechanisms
T
he beam has been excited using the Finemet cavity on a synchrotron frequency sideband.
42
Slide4343
From all the measurements it is possible to conclude that the Finemet not only excite the beam with precision (we are able to excite each sideband of the revolution frequency) but acts in the same way all over the harmonics.
Frequency scan:
as
we approach the correct excitation frequency the beating becomes longer and as we move away the beating shortens.
Mode scan: growing of each oscillation mode in similar range, the cavity acts in the same way over all the harmonics
Amplitude scan: linear behavior of the mode amplitude increasing the voltage from the cavity.In the particular case of natural instability with a full machine (21 bunches in h=21) the voltage required from the cavity to damp the unstable mode is low see Heiko presentation.
In excitation measurements with the Finemet cavity we observe ~ 4 times large damping rate than natural growing rate.
Measurements
With the available hardware of the coupled-bunch feedback it is possible to explore with new measurements the beam behavior
damping/growing rate and to study with simulations the instability conditions in the LIU space.
Slide4444
THANK YOU FOR YOUR ATTENTION!