Frequency and time domain analysis of
trapped modes in the CERN
Proton Synchrotron
Serena Persichelli
CERN Impedance and collective effects
BE-ABP-ICE
Abstract
 The term “trapped mode” refers to a resonance that can be excited by the presence of
a discontinuity inside a cavity or a beam pipe. These modes cannot propagate into the
beam pipe but are localized near the discontinuity, producing narrow resonances in the
coupling impedance frequency spectrum. Resonances due to trapped modes can be
dangerous in accelerators like PSB, PS, SPS, LHC and CLIC project: for this reason,
each structure that is going to be installed in the CERN machines must be simulated in
order to identify trapped modes.
 We will show how CERN impedance team approaches this problem, using CST both
with time domain and frequency domain simulations. These results are needed to
understand performance limitations of the machines like instability thresholds and
beam induced heating.
 In particular, we will show a recent study of the impedance due to trapped modes in a
new septum that will be installed in the CERN Proton Synchrotron in 2013, where our
results show a good agreement between CST simulations in the two domains.
How a trapped mode looks like
Time domain: Wakefield solver
How a trapped mode looks like
Frequency domain: Eigenmode solver
Agenda
A general method for study the
impedance of an accelerator component
 Import and simplify the CATIA mechanical drawing
 Eigenmode simulation (frequency domain):
• Hexahedral mesh: extract parameters Rs, Q
• Tetrahedral mesh: extract parameters Rs, Q
 Wakefield simulation (time domain):
• Longitudinal and transvers impedance
• Extract parameters Rs, Q
 Evaluate effective imaginary impedance at low frequency (time domain)
 Compute longitudinal instabilities rise time
 Dump the modes with ferrite (time domain)
 Evaluate heating and power loss
Agenda
A general method for study the
impedance of an accelerator component
 Import and simplify the CATIA mechanical drawing
 Eigenmode simulation (frequency domain):
• Hexahedral mesh: extract parameters Rs, Q
• Tetrahedral mesh: extract parameters Rs, Q
 Wakefield simulation (time domain):
• Longitudinal and transvers impedance
• Extract parameters Rs, Q
 Evaluate effective imaginary impedance at low frequency (time domain)
 Compute longitudinal instabilities rise time
 Dump the modes with ferrite (time domain)
 Evaluate heating and power loss
Importing CATIA drawings in CST
From the mechanical drawing imported from
CATIA to the design used in CST for simulations
This “dummy” septum, located in
section 15 of the CERN PS, will absorb
particles during extraction, providing a
reduction in activation in the extraction
area.
PS SECTION 15
--Steel
--Copper
--AL2O3
During extraction the particles
will impact on a 40 cm long, 7
cm high and 4.2 mm thick
copper blade inside the “dummy”
septum, avoiding a strong
activation on the real extraction
septum, located in section 16.
Importing CATIA drawings in CST
Simplify the mechanical drawing imported
from CATIA
 The RF screen can not be processed correctly by
ACIS because of the holes: a screen without holes
has been considered for simulations.
 Elliptical beam pipes have to be extended to avoid
negative impedance effects
 RF fingers to allow continuity between the screen
and the tank has been considered in simulations
What should we expect from such geometry?
 Degeneration of the intrinsic modes of the
pillbox cavity brings trapped modes
Agenda
A general method for study the
impedance of an accelerator component
 Import and simplify the CATIA mechanical drawing
 Eigenmode simulation (frequency domain):
• Hexahedral mesh: extract parameters Rs, Q
• Tetrahedral mesh: extract parameters Rs, Q
 Wakefield simulation (time domain):
• Longitudinal and transvers impedance
• Extract parameters Rs, Q
 Evaluate effective imaginary impedance at low frequency (time domain)
 Compute longitudinal instabilities rise time
 Dump the modes with ferrite (time domain)
 Evaluate heating and power loss
Eigenmode simulation (CST Microwave Studio)
Evaluation of frequencies, Q, R/Q, shunt
impedances
NB. Modes with a frequency
lower than 150 MHz can be
source of coupled bunch
instability in the PS!
Freq
[MHz]
Q
R/Q
Rs [Ω]
1
119
2655
0.241
640
2
295
3975
0.199
794
3
331
3947
0.020
76
4
362
4727
0.006
25
5
420
4987
0.027
132
6
441
4885
0.046
226
7
495
5777
0.005
33
8
533
7597
0.012
94
9
616
3585
0.009
33
10
656
5805
0.031
184
Eigenmode simulation (CST Microwave Studio)
Trapped mode at 119 MHz
Agenda
A general method for study the
impedance of an accelerator component
 Import and simplify the CATIA mechanical drawing
 Eigenmode simulation (frequency domain):
• Hexahedral mesh: extract parameters Rs, Q
• Tetrahedral mesh: extract parameters Rs, Q
 Wakefield simulation (time domain):
• Longitudinal and transvers impedance
• Extract parameters Rs, Q
 Evaluate effective imaginary impedance at low frequency (time domain)
 Compute longitudinal instabilities rise time
 Dump the modes with ferrite (time domain)
 Evaluate heating and power loss
Wakefield simulation (CST Particle Studio)
Longitudinal impedance
Trapped modes excited on the real part of the longitudinal impedance by a bunch
of 26 cm length circulating at 5 mm from the blade
σ=26 cm
fMAX=0.7 GHz
Wakelength=100 m
Method: Direct
Wakefield simulation (CST Particle Studio)
Evaluation of frequencies, Q, R/Q, shunt
impedances
Considering only one trapped mode:
Lorentzian fit of the mode @118 MHz
 Q=2655 from CST MWS
 Q=f/Δf  WLmax=c/Δf≈ 6.7 km
 WLmax is the wake length to use to get
convergence the of peak’s amplitude
 The parameters of the resonances are
obtained with a Lorentzian fit of the
longitudinal impedance peak evaluated
for WLmax
R @-55
[Ω]
Q
R @27
[Ω]
R @0
[Ω]
118
2655
62
640
36176
119
2616
40
510
36386
Freq
[MHz]
CST MWS
CST PS
Agenda
A general method for study the
impedance of an accelerator component
 Import and simplify the CATIA mechanical drawing
 Eigenmode simulation (frequency domain):
• Hexahedral mesh: extract parameters Rs, Q
• Tetrahedral mesh: extract parameters Rs, Q
 Wakefield simulation (time domain):
• Longitudinal and transvers impedance
• Extract parameters Rs, Q
 Evaluate effective imaginary impedance at low frequency (time domain)
 Compute longitudinal instabilities rise time
 Dump the modes with ferrite (time domain)
 Evaluate heating and power loss
Effective imaginary impedance (time domain)
Contribution to the impedance budget
Longitudinal impedance before extraction
--Re
--Im
The contribution of the dummy septum
to the total imaginary part of longitudinal
impedance of the PS is predicted to be
less then 1%
M. Migliorati, S. Persichelli et al., Beam-wall interaction in the CERN Proton Synchrotron
for the LHC upgrade, Phys. Rev. ST Accel. 16, 031001 (2013)
Agenda
A general method for study the
impedance of an accelerator component
 Import and simplify the CATIA mechanical drawing
 Eigenmode simulation (frequency domain):
• Hexahedral mesh: extract parameters Rs, Q
• Tetrahedral mesh: extract parameters Rs, Q
 Wakefield simulation (time domain):
• Longitudinal and transvers impedance
• Extract parameters Rs, Q
 Evaluate effective imaginary impedance at low frequency (time domain)
 Compute longitudinal instabilities rise time
 Dump the modes with ferrite (time domain)
 Evaluate heating and power loss
Coupled bunch instability growth rate
Compute the instability growth rate for the
118 MHz mode
PS parameters (25 ns)
Displacement from
the centre [mm]
Rs [Ω]
R’s [Ω]
α [1/s]
@13 Gev
α [1/s]
@26 Gev
0
640
10
0.15
0.08
10
1484
23
0.35
0.18
20
3385
53
0.82
0.43
30
7301
114
1.77
0.95
40
14762
231
3.59
1.87
50
27397
428
6.65
3.47
60
49215
770
11.97
6.25
13 GeV
26 GeV
VRF [kV]
165
100
h
21
84
# of
bunches
18
72
charge
1.28 e-07
3.2 e-08
Slippage
factor
0.0163
0.0215
Gaussian shape of the beam
Agenda
A general method for study the
impedance of an accelerator component
 Import and simplify the CATIA mechanical drawing
 Eigenmode simulation (frequency domain):
• Hexahedral mesh: extract parameters Rs, Q
• Tetrahedral mesh: extract parameters Rs, Q
 Wakefield simulation (time domain):
• Longitudinal and transvers impedance
• Extract parameters Rs, Q
 Evaluate effective imaginary impedance at low frequency (time domain)
 Compute longitudinal instabilities rise time
 Dump the modes with ferrite (time domain)
 Evaluate heating and power loss
Ferrite proposal for trapped modes damping
119 MHz mode electric field (frequency domain)
Ferrite proposal for trapped modes damping
119 MHz mode magnetic field (time domain)
Ferrite proposal for trapped modes damping
Damping effect on longitudinal impedance
(time domain)
f=0.103 GHz
Q=11
K=2.6 e-12 V/pC
Rs=50 Ω
TT2-11R Ferrite
24x7x395 mm
Ferrite proposal for trapped modes damping
Ferrite effect on the growth rate
d[mm]
R’s [Ω]
α [1/s]
@13 Gev
α [1/s]
@26 Gev
-55
1.3
0.017
0.009
f=0.103 GHz
Q=11
K=2.6 e-12 V/pC
Rs=50 Ω
Procedure
A general method for study the
impedance of an accelerator component
 Import and simplify the CATIA mechanical drawing
 Eigenmode simulation (frequency domain):
• Hexahedral mesh: extract parameters Rs, Q
• Tetrahedral mesh: extract parameters Rs, Q
 Wakefield simulation (time domain):
• Longitudinal and transvers impedance
• Extract parameters Rs, Q
 Evaluate effective imaginary impedance at low frequency (time domain)
 Compute longitudinal instabilities rise time
 Dump the modes with ferrite (time domain)
 Evaluate heating and power loss
Heating and power loss
Estimation of the power loss considering the
heating from ferrite
At extraction energy the first mode is inside the beam
spectrum and the power at 118 MHz is about -20 dB
PdB(118 MHz)= -20 dB
Ploss=1.8 W
Ploss=0.71 W
Conclusions
 The proposed method uses CST not only for characterizing the impedance of
the device, but also to understand performance limitations of the machines
like instability thresholds and beam induced heating that can be dangerous in
accelerators like PSB, PS, SPS, LHC and CLIC project
 Each structure that is going to be installed in the CERN machines must be
simulated in order to identify trapped modes that are the main source of
instabilities.
 CST is used for impedance studies at CERN for many types of devices:






Kicker magnets
Experimental detectors
Instrumentation
Cavities
Septa
Collimators