Ecole Polytechnique Fédérale de Lausanne (EPFL) Laboratoire d’Electromagnétisme et...

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

http://lema.epfl.ch/

http://www.epfl.ch/


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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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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FRAMEWORK

LEMA has a solid expertise in numerical electromagnetics and

integral equation• Scattering parameters • High power phenomena




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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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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


(Propagation factor)

Dependency on (x,y)




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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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But we can use the trigonometric functions (modes of rectangular waveguide) as the basis set to develop the solutions for the beam pipe.


Beam pipe

BI-RME method(Boundary Integral-Resonant Mode

Expansion)

MODES ARE NON-ANALYTICAL!!!




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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




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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RESULTSRADIATED FIELD

200 MHz 5 ns




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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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