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Ecole Polytechnique Fédérale de Lausanne (EPFL)
Laboratoire d’Electromagnétisme et d’Acoustique (LEMA)
P. O. Box ELB-Station 11
1015 Lausanne, Switzerland
Edén Sorolla & Michael Mattes
e-Cloud workshop, CERN (Genève), 16th june 2011
Modelling microwave-electron interaction in
the LHC
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e-Cloud workshop, CERN (Genève), 16th june 2011
SNF (contract no. 200021_129661) – Modelling microwave-electron interaction in the LHC
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Outline
1.Framework (motivation)
2.Electromagnetic model (Radiated fields)
3.Results in the LHC beampipe
4.Next steps
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e-Cloud workshop, CERN (Genève), 16th june 2011
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Work developed under the Swiss National Science Foundation (SNSF)
project
FRAMEWORK
CERN:(Organisation européenne
pour la Recherche Nucléaire)
LEMA:(Laboratoire
d’Electromagnétisme et d’Acoustique)
Juan R. MosigMichael Mattes
Edén Sorolla
Frank Zimmermann
SNF (contract no. 200021_129661)
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e-Cloud workshop, CERN (Genève), 16th june 2011
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FRAMEWORK
LEMA has a solid expertise in numerical electromagnetics and
integral equation• Scattering parameters • High power phenomena
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e-Cloud workshop, CERN (Genève), 16th june 2011
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FRAMEWORK (motivation)
MAIN IDEA
ELECTRON RADIATION
(POWER SPECTRUM)DIAGNOSE
Hi there!I’m an
ELECTRON and I’m going to annoy you!
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ELECTROMAGNETIC MODEL
EJ
S'
E x, y,z G x, y;x ', y '; z z ' J x ', y ',z ' dx 'dy 'dz '
EJG x, y;x ', y '; z z '
J x ', y ',z '
2 2EJ EJG k G r r '
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e-Cloud workshop, CERN (Genève), 16th june 2011
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nj t zn n
n 1
x, y,z; t A E x, y e
nj t zn n
n 1
x, y,z; t B H x, y e
General expressions of em. fields over the waveguide cross-section
nE
nH Electric and magnetic fields of the n-th
mode
n n nj
ELECTROMAGNETIC MODEL
(Propagation factor)
Dependency on (x,y)
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e-Cloud workshop, CERN (Genève), 16th june 2011
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ELECTROMAGNETIC MODEL
Rectangular cavity
2 22
n
p q
a b
MODES ARE ANALYTICAL
n n
qcos
bpcos
a qsin
bE , H
qcos
bpsin
a qsin
b
n p,q
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e-Cloud workshop, CERN (Genève), 16th june 2011
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But we can use the trigonometric functions (modes of rectangular waveguide) as the basis set to develop the solutions for the beam pipe.
ELECTROMAGNETIC MODEL
Beam pipe
BI-RME method(Boundary Integral-Resonant Mode
Expansion)
MODES ARE NON-ANALYTICAL!!!
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e-Cloud workshop, CERN (Genève), 16th june 2011
SNF (contract no. 200021_129661) – Modelling microwave-electron interaction in the LHC
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z nnt
n
nz n
u E TM modes
H x, y
u E TE modes
POWER SPECTRUM
*n n n
1N E H
2
Lossless waveguides total *
n nn 1
1N E H
2
Time-average(harmonic signals)
z zH 0; E 0
z zE 0; H 0
Transversal
component
totaln
n 1
P N dS
Radiated power
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RESULTS
Beam pipe
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RESULTS
TE 1TE1E TE
1H
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RESULTS TM 1TM1E TM
1H
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RESULTS
“Eight” pipe
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RESULTSTE 1
TE1E TE
1H
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RESULTS
TE 2TE2E TE
2H
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RESULTS TM 1TM1E TM
1H
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RESULTS TM 2TM2E TM
2H
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RESULTS
Bone pipe
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RESULTS TE 1
TE1E TE
1H
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RESULTS TE 2
TE2E TE
2H
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RESULTS
TM1E
TM1H
TM 1
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RESULTS
TM2E TM
2H
TM 2
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e-Cloud workshop, CERN (Genève), 16th june 2011
SNF (contract no. 200021_129661) – Modelling microwave-electron interaction in the LHC
RESULTSRECTANGULAR CAVITY
24TE10
TE10E
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RESULTS
POSITION
SPEED
J x '; t ' e v t ' x x ' t '
nj t zn n
n 1
x, y,z; t A E x, y e
T.D.
5 ns
5 ns
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e-Cloud workshop, CERN (Genève), 16th june 2011
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RESULTSRADIATED FIELD
200 MHz 5 ns
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e-Cloud workshop, CERN (Genève), 16th june 2011
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NEXT STEPS
* Combine BI-RME method to calculate the modes of the waveguides in LHC with e-Cloud.
In the worst case BI-RME calculates in a second the fields for the LHC beam pipe in 10000 positions per electron; further improvements can still be done.
* Implement the calculation of the radiated power spectrum of the electrons accelerated by the proton beam (alternatively an external RF field) using the ‘history’ of the electrons’ motion provided by e-Cloud.
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