1 Impedance and its link to vacuum chamber geometry T.F. Günzel Vacuum systems for synchrotron...
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Transcript of 1 Impedance and its link to vacuum chamber geometry T.F. Günzel Vacuum systems for synchrotron...
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Impedance and its link to vacuum chamber geometry
T.F. GünzelVacuum systems for synchrotron light sources
12th september 2005
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Outline– Motivation
– Basic properties of wakefields
– Resistive wall impedance
– Impedance budget
– Comparison to measured single bunch thresholds
– Incoherent tune shifts
– Effective impedance under different aspects
– Head-Tail instability
– Conclusion
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Motivation
• ESRF particularly concerned by impedance-related instabilities, the single bunch transverse thresholds are low <0.7mA vertically, <1.7mA horizontally
ESRF is an excellent case to study the link between vacuum chamber geometry and transverse impedance
• Verification of the impedance model by comparison of the calculated TMCI-thresholds to the measured ones
• Establishment of the impedance budget, identification of the elements with the largest detrimental effect
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Basic properties of wakefields
),,(),,( tsctzEdtq
csW zlong
rrr 0
long. wakefield excited by a particle at r0 and observed by a test (witness) particle at r
)),,(),,((),,( tsctzctsctzdt
q
cs z rBerErrW 0
r0
origin
test particle
r0
transverse wakefield (2-dimensional vector field) : ),( s0rr,W
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wakefield in a circular geometry with tapers
axial-symmetric taper geometry in the (z,r)-planesource particle at offset r0 to the origin
r0
origin
source particle
0rW )(),,( 0 sFsrr
all arrows point in the direction of the offset
no dependence of the test particle positionr0
if zero offset, the wake is also zero (everywhere!)
this dipolar field contributes to the impedance
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Without offset W only depends on the test particle position, it is locally quadrupolar
However, this field does not contribute to the impedance
wakefield in a rectangular chamber with vertical tapers and offset r0=0
magnification
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wakefield in a rectangular chamber with a vertical tapers and horizontal offset r0 0
the wakefield is a sum of a quadrupolar field (depending on the test particle position) and a dipole field (depending on the offset of the exciting particle)
source particle with a 1mm offset in x-direction
r0
a vertical taper produces horizontal impedance !
magnification
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The role of the vacuum chamber cross section
• 2D calculation possible• wakefield only depends on
source particle position• resistive wall impedance given
by
• 3D calculation necessary
• wakefield depends on source as well as on test particle position
• resistive wall impedance (chamber is approximated by 2 parallel plates)
a
3
1~
aZZ HV
3
1~2
aZZ HV
a
b
all quantities only depend on one geometric parameter: the vertical extension of the chamber a
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Resistive wall budget
form-factors as well -functions of vertical and horizontal plane taken into account
standard ESRF vacuum chamber (33mm x 79mm)makes up two third of the vertical budget
the horizontal RW-impedance budget even larger than the vertical one
chamber type V[m] H[m] ( ZVV)eff [MW] (ZHH)eff [MW]
all low-gap sections (invacuum open) 3.5 24 0.73 2.65ESRF standard beampipe + other elements 24.6 16.6 1.78 0.78
2.51 3.43
Vhorizontal values are high in the straight sections,vertical values are high in the dipoles.
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Geometrical Impedance budget
33 (39) different elements in the budget, 1775 elements in total (status of november 2004)
• 26 taper pairs (without in-vacuum)
• 8 invacuum undulators (all open)
• 293 RF-fingers
• 569 flanges
• 134 vertical pumps, 448 horizontal pumps
• 6 cavities and 3 cavity tapers
• 2 scrapers in operation position
• 277 BPM’s
• 7 kicker like chambers
• 1 septum
Calculation of impedance with GdfidL (W.Bruns)
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Effective dipolar impedance budget (geometric and resistive wall)
Vertical impedance distributed smoothly around the ring
Horizontal impedance concentrated in the low-gap sections
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• Coherent tune shift : dipolar impedance
Thresholds and tune shifts in single bunch
the thresholds only depend on the dipolar impedance• vertical measured 0.65mA calculated 1.05mA
• horizontal measured 1.7mA (nov. 2004) calculated 1.10mA
probably the horizontal (resistive wall) impedance is overestimated
for tune shift : dipolar impedance + quadrupolar wakefield
Incoherent tune shift deteriorates the operation in single bunch
• Incoherent tune shift : quadrupolar wakefield
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Coherent and incoherent tune shifts in single bunch
Synonym with calculation of kick factors (effective impedance)of dipolar and quadrupolar wakefields
This is what can be measured by the
bump method
• Vertical incoherent and coherent kick factors add up positively
• Horizontal incoherent and coherent kick factors cancel out each other
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Incoherent tune shift in multi-bunch
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
0.025
0.03
0 50 100 150 200
QH_close
QV_close
QH_open
QV_open
Explained by R. Nagoaka, PAC 2001 (Chigaco) 3531
horizontal
verticalMeasured in november 2004
160.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00
CV2000x19m mCV5000x20m mCV5000x19m m
APS-cham ber 12m m ins ideCV5000 SS 11m m gap
m inigap openm inigap closed 10m m
CV5000 Al 8m m gapWiggler cham berCV5000 SS 8m m
1.6m in-vacuum open1.6m in-vacuum closed 6m m2m in-vacuum s tandard open
2m in-vacuum s tandard closed 6m m
6 ESRF cavities3 cavity taper pairs
conical scrapertapered scraper
bellow-fingertaperfingerCV4-fingerCV7-fingerCV9-fingerCV2-finger
CV16-finger
long vertical pum pshort vertical pum p with absorber
short vertical pum p without absorberhorizontal pum p
kicker cham ber with absorbergeom etry around the septum
flange perim eter 150m m , s lit 0.15m mflange perim eter 150m m , s lit 0.1m m
BPM 33m m gapBPM 16m m gapBPM 8m m gap
piece in front of in-vacuum prototype
dipolar cham ber with absorber
Zeff(kOhm/m) dipolar+quad.
0.00 0.50 1.00 1.50 2.00 2.50 3.00
BPM 33mm gap
BPM 16mm gap
BPM 8mm gap
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Effective impedance map (dipolar + quadrupolar) (σ=40ps)
Calculated values about 2/3 of the measured values apart from invacuum undulators + 10mm SS-chambers (larger deviations)
effective Impedance (kOhm/m) dipolar+quad.
0
20
40
60
80
100
120
140
160
180Calculation
Measurement Measurements from Th. Perron
PhD thesis
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Head-Tail Instability (only general remarks)impedance not only has bad effects
• Head-Tail instability is driven by transverse impedance.
• P. Kernel (PhD thesis) showed that at the ESRF the vertical
head-tail instability is damped by the incoherent synchrotron
tune spread caused by longitudinal impedance.
• On the horizontal plane this finding has still to be checked
• The limit of stability is given by the Post-Head-Tail instability(P. Kernel, R. Nagaoka, JL Revol, EPAC 2000, Vienne)
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Conclusions
• The vertical impedance is determined by many different elements
• The horizontal impedance is mainly determined by the low gap chambers.
• The model explains 2/3 of the vertical mode detuning,• but in the horizontal plane it predicts a too small threshold compared
to the measured one
• Flat vacuum chambers give rise to an incoherent tune shift tune shift affects the beam in multibunch as well as in single bunch
• The Horizontal as well as vertical impedance are essentially created by the vertical walls : its geometrical variation and its
resistivity
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Conclusions
High impedance budget of the ESRF is mainly due to
• modularity of the vacuum system
• alternating vertical and horizontal β-function distribution
• stainless steel vacuum chambers (is evolving towards more aluminium chambers)
• flatness of the vacuum chambers