Updated status of the PSB impedance model
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![Page 1: Updated status of the PSB impedance model](https://reader036.fdocuments.net/reader036/viewer/2022070417/56815397550346895dc19d96/html5/thumbnails/1.jpg)
Updated status of the PSB impedance model
C. Zannini and G. Rumolo
Thanks to: E. Benedetto, N. Biancacci, E. Métral, B. Mikulec, N. Mounet, T. Rijoff, B. Salvant, W. Weterings
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Overview• Introduction• Present PSB impedance model
– Indirect space charge• Numerical form factor for ISC computation
– Resistive wall– Extraction kicker– Broadband impedance of step transitions– KSW
• Global PSB impedance model– Comparison with tune shift measurements– Summary and future plans
• Other devices studied– Shielding of pumping ports– Insulated flanges
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Impedance calculations for b < 1
In the LHC, SPS, PS CST EM simulation are performed in the ultra-relativistic approximation ( b = 1)
Analytical calculation (applies only to simple structures)
3D EM simulation (CST Particle Studio)
The use of 3D EM simulations for b < 1 is not straightforward at all
9.03.0 PSBext
PSBinj
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3D CST EM simulation for b < 1
SCdirect
total ZZZ )(
To single out the impedance contribution the direct space charge must be removed
Depend only on the source
contribution due to the interaction of beam and external surroundings
Z
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Overview• Introduction• Present PSB impedance model
– Indirect space charge• Numerical form factor for ISC computation
– Resistive wall– Extraction kicker– Broadband impedance of step transitions– KSW
• Global PSB impedance model– Comparison with tune shift measurements– Summary and future plans
• Other devices studied– Shielding of pumping ports– Insulated flanges
![Page 6: Updated status of the PSB impedance model](https://reader036.fdocuments.net/reader036/viewer/2022070417/56815397550346895dc19d96/html5/thumbnails/6.jpg)
Present PSB transverse impedance model• Elements included in the database:
– Analytical calculation of the resistive wall impedance that takes into account the different PSB vacuum chambers weighted by the respective length and beta function. Also the iron in the magnet is taken into account
Beam pipe
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Present PSB transverse impedance model• Elements included in the database:
– Analytical calculation of the resistive wall impedance that takes into account the different PSB vacuum chambers weighted by the respective length and beta function. Also the iron in the magnet is taken into account
– Extraction kicker• impedance due to the ferrite loaded structure• impedance due to the coupling to the external circuits (analytical calculation)
KickersBeam pipe
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Present PSB transverse impedance model• Elements included in the database:
– Analytical calculation of the resistive wall impedance that takes into account the different PSB vacuum chambers weighted by the respective length and beta function. Also the iron in the magnet is taken into account
– Extraction kicker• impedance due to the ferrite loaded structure• impedance due to the coupling to the external circuits (analytical calculation)
– Indirect space charge impedance
KickersBeam pipe
Indirect space charge impedance
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Present PSB transverse impedance model• Elements included in the database:
– Analytical calculation of the resistive wall impedance that takes into account the different PSB vacuum chambers weighted by the respective length and beta function. Also the iron in the magnet is taken into account
– Extraction kicker• impedance due to the ferrite loaded structure• impedance due to the coupling to the external circuits (analytical calculation)
– Indirect space charge impedance
KickersBeam pipe
Indirect space charge impedance
![Page 10: Updated status of the PSB impedance model](https://reader036.fdocuments.net/reader036/viewer/2022070417/56815397550346895dc19d96/html5/thumbnails/10.jpg)
Present PSB transverse impedance model• Elements included in the database:
– Analytical calculation of the resistive wall impedance that takes into account the different PSB vacuum chambers weighted by the respective length and beta function. Also the iron in the magnet is taken into account
– Extraction kicker• impedance due to the ferrite loaded structure• impedance due to the coupling to the external circuits (analytical calculation)
– Indirect space charge impedance
KickersBeam pipe
Indirect space charge impedance
![Page 11: Updated status of the PSB impedance model](https://reader036.fdocuments.net/reader036/viewer/2022070417/56815397550346895dc19d96/html5/thumbnails/11.jpg)
Present PSB transverse impedance model• Elements included in the database:
– Analytical calculation of the resistive wall impedance that takes into account the different PSB vacuum chambers weighted by the respective length and beta function. Also the iron in the magnet is taken into account
– Extraction kicker• impedance due to the ferrite loaded structure• impedance due to the coupling to the external circuits (analytical calculation)
– Indirect space charge impedance
KickersBeam pipe
Indirect space charge impedance
![Page 12: Updated status of the PSB impedance model](https://reader036.fdocuments.net/reader036/viewer/2022070417/56815397550346895dc19d96/html5/thumbnails/12.jpg)
Present PSB transverse impedance model• Elements included in the database:
– Analytical calculation of the resistive wall impedance that takes into account the different PSB vacuum chambers weighted by the respective length and beta function. Also the iron in the magnet is taken into account
– Extraction kicker• impedance due to the ferrite loaded structure• impedance due to the coupling to the external circuits (analytical calculation)
– Indirect space charge impedance– Broadband impedance of step transitions
KickersBeam pipe
Indirect space charge impedance Step transitions
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Present PSB transverse impedance model• Elements included in the database:
– Analytical calculation of the resistive wall impedance that takes into account the different PSB vacuum chambers weighted by the respective length and beta function. Also the iron in the magnet is taken into account
– Extraction kicker• impedance due to the ferrite loaded structure• impedance due to the coupling to the external circuits (analytical calculation)
– Indirect space charge impedance– Broadband impedance of step transitions– KSW magnets
Extraction KickerBeam pipe
Indirect space charge impedance Step transitions KSW
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Overview• Introduction• Present PSB impedance model
– Indirect space charge• Numerical form factor for ISC computation
– Resistive wall– Extraction kicker– Broadband impedance of step transitions– KSW
• Global PSB impedance model– Comparison with tune shift measurements– Summary and future plans
• Other devices studied– Shielding of pumping ports– Insulated flanges
![Page 15: Updated status of the PSB impedance model](https://reader036.fdocuments.net/reader036/viewer/2022070417/56815397550346895dc19d96/html5/thumbnails/15.jpg)
Indirect space chargeAnalytical calculation based on the PSB aperture model (provided by O. Berrig)
22
20
01
01
20
22
k
bkI
bkK
LjZZ
K. Y. Ng, Space charge impedances of beams with non-uniform transverse distributions
iyx
N
i
ISCi
yx
ISCyx i
ZZ ,1,
,
1
Circular pipeRectangular pipe
Elliptic pipe
[a, b, L, βx , βy , Apertype]i
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PSB: indirect space charge impedance
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Overview• Introduction• Present PSB impedance model
– Indirect space charge• Numerical form factor for ISC computation
– Resistive wall– Extraction kicker– Broadband impedance of step transitions– KSW
• Global PSB impedance model– Comparison with tune shift measurements– Summary and future plans
• Other devices studied– Shielding of pumping ports– Insulated flanges
![Page 18: Updated status of the PSB impedance model](https://reader036.fdocuments.net/reader036/viewer/2022070417/56815397550346895dc19d96/html5/thumbnails/18.jpg)
Indirect space charge: refinement of the calculation
Using numerical form factors
round
GyxG
yx Z
ZF ,
,
46.1diamondyF
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Indirect space charge: refinement of the calculation
Using numerical form factors
24.1dipolesyF
round
GG
Z
ZF
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PSB: indirect space charge impedance
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Overview• Introduction• Present PSB impedance model
– Indirect space charge• Numerical form factor for ISC computation
– Resistive wall– Extraction kicker– Broadband impedance of step transitions– KSW
• Global PSB impedance model– Comparison with tune shift measurements– Summary and future plans
• Other devices studied– Shielding of pumping ports– Insulated flanges
![Page 22: Updated status of the PSB impedance model](https://reader036.fdocuments.net/reader036/viewer/2022070417/56815397550346895dc19d96/html5/thumbnails/22.jpg)
Resistive wall impedance Wall thickness Wall (σel) Background
materialDipoles 0.4 mm 7.7 105 S/m Iron (silicon steel)Quadrupoles 1.5 mm 1.3 106 S/m Iron (silicon steel)Straight sections 1 mm 1.3 106 S/m Vacuum
Analytical calculation based on the PSB aperture model (provided by O. Berrig)
Calculation performed with the TLwall code
[a, b, L, βx , βy , Apertype]i
iyx
N
i
RWi
yx
RWyx i
ZZ ,1,
,
1
MeVEkin 160
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Resistive wall impedance Wall thickness Wall (σel) Background
materialDipoles 0.4 mm 7.7 105 S/m Iron (silicon steel)Quadrupoles 1.5 mm 1.3 106 S/m Iron (silicon steel)Straight sections 1 mm 1.3 106 S/m Vacuum
Analytical calculation based on the PSB aperture model (provided by O. Berrig)
Calculation performed with the TLwall code
[a, b, L, βx , βy , Apertype]i
iyx
N
i
RWi
yx
RWyx i
ZZ ,1,
,
1
Vertical
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Overview• Introduction• Present PSB impedance model
– Indirect space charge• Numerical form factor for ISC computation
– Resistive wall– Extraction kicker– Broadband impedance of step transitions– KSW
• Global PSB impedance model– Comparison with tune shift measurements– Summary and future plans
• Other devices studied– Shielding of pumping ports– Insulated flanges
![Page 25: Updated status of the PSB impedance model](https://reader036.fdocuments.net/reader036/viewer/2022070417/56815397550346895dc19d96/html5/thumbnails/25.jpg)
is the impedance calculated using the Tsutsui formalismMZ
A theoretical calculation for the C-Magnet model
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PSB extraction kicker: impedance due to the ferrite loaded structure ZM
Vertical
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PSB extraction kicker: impedance due to the coupling to the external circuits ZTEM
MeVEkin 160
Cables in the open-short configuration
Horizontal
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Overview• Introduction• Present PSB impedance model
– Indirect space charge• Numerical form factor for ISC computation
– Resistive wall– Extraction kicker– Broadband impedance of step transitions– KSW
• Global PSB impedance model– Comparison with tune shift measurements– Summary and future plans
• Other devices studied– Shielding of pumping ports– Insulated flanges
![Page 29: Updated status of the PSB impedance model](https://reader036.fdocuments.net/reader036/viewer/2022070417/56815397550346895dc19d96/html5/thumbnails/29.jpg)
Broadband impedance of a step transition
• Based on the results of 3D EM simulations, the broadband impedance contribution due to an abrupt transition is independent of the relativistic beta. Therefore, based on the aperture model, the generalized broadband impedance of the PSB transitions has been calculated as:
C. Zannini, Electromagnetic simulations of CERN accelerator components and experimental applications. PhD thesis, Lausanne, EPFL, 2013. CERN-THESIS-2013-076.
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Broadband impedance of step transitions
Weak dependence on the relativistic beta and L
L
i
N
i
bbbb nZZistransition
1
1Z
1Z
12ZZ
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Overview• Introduction• Present PSB impedance model
– Indirect space charge• Numerical form factor for ISC computation
– Resistive wall– Extraction kicker– Broadband impedance of step transitions– KSW
• Global PSB impedance model– Comparison with tune shift measurements– Summary and future plans
• Other devices studied– Shielding of pumping ports– Insulated flanges
![Page 32: Updated status of the PSB impedance model](https://reader036.fdocuments.net/reader036/viewer/2022070417/56815397550346895dc19d96/html5/thumbnails/32.jpg)
3D model of the KSW kicker
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Coating of the ceramic chamber
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Coating of the ceramic chamber
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Analytical model: axially symmetric multilayer structure
coating
coating
tr
LR
2
Assuming uniformity of the coating thickness
Resistance of the coating
The beam coupling impedance strongly depends on the resistance of the coating
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Effect of the ceramic chamber on the KSW longitudinal impedance
mtcoating 12.0Titanium coating
The shielding (coated ceramic chamber) strongly reduces the longitudinal impedance
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Effect of the ceramic chamber on the KSW longitudinal impedance
Real part of the longitudinal impedance
kHzf 500
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Real part of the longitudinal impedance
Effect of the ceramic chamber on the KSW longitudinal impedance
kHzf 110
mtcoating 2Titanium coating
Minimum R defined by the required kicker
rise time
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Real part of the longitudinal impedance
Effect of the ceramic chamber on the KSW longitudinal impedance
Increasing the coating resistance the impedance should converge to the case without coating
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Effect of the ceramic chamber on the KSW transverse impedance
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Effect of the ceramic chamber on the KSW transverse impedance
Increase of the impedance due to the smaller aperture
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Effect of the ceramic chamber on the KSW transverse impedance
The coating shifts the impedance spectrum to lower frequencies
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Effect of the ceramic chamber on the KSW transverse impedance
The frequency shift is proportional to the coating resistance
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The frequency shift is proportional to the coating resistance
Effect of the ceramic chamber on the KSW transverse impedance
Real part of the transverse impedance
fr
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Effect of the ceramic chamber on the KSW transverse impedance
Rfr
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KSW: transverse impedance optimization
beamI fff First possible unstable betatron line Maximum frequency excited by the beam
Frequency range of interest
Shift the KSW impedance spectrum out of the PSB frequency range of interest
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KSW: transverse impedance optimization
beamI fff First possible unstable betatron line Maximum frequency excited by the beam
Frequency range of interest
Shift the KSW impedance spectrum out of the PSB frequency range of interest
KHzf I 3403.0 Worst case at extraction (smallest bunch length)
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Determination of fbeam for a generic element of impedance Z
Zfbeam
elembudgetbeam ZZ
Nbeam PZZ
Z
ZP
elembudget
N
Normalized beam power spectrum
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Determination of fbeam: example for the KSW transverse impedance
mZ KSWbudget /100
MHzfbeam 40
mZ KSWbudget /1
MHzfbeam 400
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beamI fff
MHzfMHz 4034.0
242.0 R
24
2.0
R
R
KSW: transverse impedance optimizationFrequency range of interest
Shift of the KSW impedance spectrum significantly out of the PSB frequency range of interest
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Overview• Introduction• Present PSB impedance model
– Indirect space charge• Numerical form factor for ISC computation
– Resistive wall– Extraction kicker– Broadband impedance of step transitions– KSW
• Global PSB impedance model– Comparison with tune shift measurements– Summary and future plans
• Other devices studied– Shielding of pumping ports– Insulated flanges
![Page 52: Updated status of the PSB impedance model](https://reader036.fdocuments.net/reader036/viewer/2022070417/56815397550346895dc19d96/html5/thumbnails/52.jpg)
Present PSB transverse impedance model• Elements included in the database:
– Analytical calculation of the resistive wall impedance that takes into account the different PSB vacuum chambers weighted by the respective length and beta function. Also the iron in the magnet is taken into account
– Extraction kicker• impedance due to the ferrite loaded structure• impedance due to the coupling to the external circuits (analytical calculation)
– Indirect space charge impedance (analytical calculation)– Broadband impedance of step transitions– KSW magnets
Extraction KickerBeam pipe
Indirect space charge impedance Step transitions KSW fZfZ
N
i
ii
PSB
1
)(
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Total horizontal driving impedance of the PSB
E
E
Contributions of the extraction kicker due to the coupling with external circuits
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Total vertical driving impedance of the PSB
E
E
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Overview• Introduction• Present PSB impedance model
– Indirect space charge• Numerical form factor for ISC computation
– Resistive wall– Extraction kicker– Broadband impedance of step transitions– KSW
• Global PSB impedance model– Comparison with tune shift measurements– Summary and future plans
• Other devices studied– Shielding of pumping ports– Insulated flanges
![Page 56: Updated status of the PSB impedance model](https://reader036.fdocuments.net/reader036/viewer/2022070417/56815397550346895dc19d96/html5/thumbnails/56.jpg)
D. Quatraro, Collective effects for the LHC injectors: non-ultrarelativistic approaches. PhD thesis, Bologna, University of Bologna, 2011. CERN-THESIS-2011-103.
Measurement data
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Effective impedance of the PSB
Measurements at different energies are consistent with a missing ~2 MΩ/m
Zeffx,y[MΩ/m] Ekin=160 MeV Ekin=1.0 GeV Ekin=1.4 GeV
Indirect space charge 1.50/10.00 0.29/1.91 0.19/1.25
Kicker cables 0.0084/0 0.012/0 0.0105/0
Kicker ferrite -0.044/0.13 -0.04/0.11 -0.04/0.11
Steps 0.53/0.63 0.53/0.63 0.53/0.63
Resistive wall 0.03/0.05 0.04/0.07 0.04/0.07
KSW 0/0.013 0/0.0013 0/0.0004
Total (expected) 2.03/10.9 0.83/2.7 0.73/2.0
Total (measured ) ?/13.0 ?/4.6 ?/3.8
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Comparison between measurements and model of the vertical coherent tune shifts at different energies
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Comparison between measurements and model of the vertical coherent tune shift at Ekin=160 MeV
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Comparison between measurements and model of the vertical coherent tune shift at Ekin=160 MeV
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Comparison between measurements and model of the vertical coherent tune shift at Ekin=1.0 GeV
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Comparison between measurements and model of the vertical coherent tune shift at Ekin=1.0 GeV
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Comparison between measurements and model of the vertical coherent tune shift at Ekin=1.4 GeV
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Comparison between measurements and model of the vertical coherent tune shift at Ekin=1.4 GeV
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90 %
100 %
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Overview• Introduction• Present PSB impedance model
– Indirect space charge• Numerical form factor for ISC computation
– Resistive wall– Extraction kicker– Broadband impedance of step transitions– KSW
• Global PSB impedance model– Comparison with tune shift measurements– Summary and future plans
• Other devices studied– Shielding of pumping ports– Insulated flanges
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Summary and future plans
• Measurements at different energies are consistent with a missing ~2 MΩ/m of the PSB impedance model
• Measurements of the coherent horizontal and vertical tune shift
• Update of the model according to new understandings and identification of significant impedance sources
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Overview• Introduction• Present PSB impedance model
– Indirect space charge• Numerical form factor for ISC computation
– Resistive wall– Extraction kicker– Broadband impedance of step transitions– KSW
• Global PSB impedance model– Comparison with tune shift measurements– Summary and future plans
• Other devices studied– Shielding of pumping ports– Insulated flanges
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Impedance of pumping ports
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Impedance of pumping ports
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Impedance of pumping ports
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Longitudinal impedance
well above the PSB beam spectrum
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Longitudinal impedance
mn
Z5Im
well above the PSB beam spectrum
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Transverse impedance
well above the PSB beam spectrum
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Transverse impedance
mZ eff
y/100
The effective vertical impedance for 1 pumping port is expected to be well below 0.01% of the total PSB broadband impedance
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Summary: impedance considerations on the pumping ports of the new PSB H- injection region
Obviously, a proper shielding can only be beneficial in terms of impedance, although no special issues from the beam coupling impedance point of view are expected even without shielding.
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Overview• Introduction• Present PSB impedance model
– Indirect space charge• Numerical form factor for ISC computation
– Resistive wall– Extraction kicker– Broadband impedance of step transitions– KSW
• Global PSB impedance model– Comparison with tune shift measurements– Summary and future plans
• Other devices studied– Shielding of pumping ports– Insulated flanges
![Page 77: Updated status of the PSB impedance model](https://reader036.fdocuments.net/reader036/viewer/2022070417/56815397550346895dc19d96/html5/thumbnails/77.jpg)
Insulated flanges• In circular accelerators with high acceleration rate the fast variation of the main
magnetic field induce currents in the ground loop.
• To overcome the problem one has to cut the vacuum chamber in several sectors and reconnect them with isolated flanges.
• The isolated flange forms a capacitor which inserted in series with the ground loop constitutes a parallel RLC equivalent circuit.
• To shift the resonant frequency to a much lower value and to reduce the longitudinal impedance, the so called RF-bypass are connected in parallel to the flange.
Without RF-bypass With RF-bypass
R. Cappi, RF bypass on the proton synchrotron vacuum chamber flanges
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C=1 nF L=10 µH R=100 ΩCbypass=0.4 μF Rbypass=1 Ω
Beam coupling impedance of insulated flanges: example
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Insulated flanges
C=0.01-100 nF L=0.5-15 µH R=1-100 ΩCbypass=0.4 μF Rbypass=1 Ω
Parameter sweep analysis
Case of study two bypasses in parallel
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Conclusion on the beam coupling impedance of insulated flanges
The RF bypass is expected to shift the impedance spectrum to low frequency (well below the first possible unstable betatron line of the PSB) avoiding possible detrimental effect which could not be excluded in the case without RF bypass.
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Additional impedance sources not discussed here
• Vacuum chamber of the new H- injection region– Comparison between Inconel undulated chamber and
titanium coated ceramic chamber• Finemet cavities– The longitudinal impedance does not depend on the
relativistic beta• Foil section of the new H- injection region– Preliminary simulations do not show narrow
impedances below 100 MHz
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Thank you for your attention
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Resistive wall impedance: impact of the iron
Resistive wall vertical generalized impedance of the PSB
MeVEkin 160
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Resistive wall impedance
rel
ir ffj
BB
/1100
frel = 10 kHz
K. G. Nilanga et al., Determination of complex permeability of silicon-steel for use in high frequency modelling of power transformers, IEEE TRANS. ON MAGNETICS, VOL. 44, NO. 4, APRIL 2008.
A. Asner et al., The PSB main bending magnets and quadrupole lenses, Geneva, April 1970.
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PSB extraction kicker: impedance due to the coupling to the external circuits ZTEM
Cables in the open-short configuration
Horizontal
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Indirect space chargeAnalytical calculation based on the PSB aperture model (provided by O. Berrig)
22
20
01
01
20
22
k
bkI
bkK
LjZZ
K. Y. Ng, Space charge impedances of beams with non-uniform transverse distributions
brEE SCs
vs 0
bk
I
bkK
A
m
m
m
0
0
330
20
2 LZjpk
Qp
iyx
N
i
ISCi
yx
ISCyx i
ZZ ,1,
,
1
Circular pipeRectangular pipe
Elliptic pipe
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Definition of impedance
Longitudinal component of the electric field in (x, y) induced by a source charge placed in (x0, y0)
SCss
tots EEE
Depend only on the source
SCdirectZ
Z
contribution due to the interaction of beam and accelerator components
EM simulator uses the total fields
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Finemet cavities
The impedance does not depend on the relativistic beta
S. Persichelli et al., Finemet cavities impedance studies, CERN-ACC-NOTE-2013-0033, 2013.
Ps and PSB cell cavity