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Outline. Framework (motivation) Electromagnetic model ( Radiated fields ) Results in the LHC beampipe Next steps. FRAMEWORK. Work developed under the Swiss National Science Foundation (SNSF) project. SNF (contract no. 200021_129661). LEMA:

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Outline

  • Framework (motivation)

  • Electromagneticmodel (Radiatedfields)

  • Results in the LHC beampipe

  • Nextsteps


FRAMEWORK

Workdevelopedunder the Swiss National Science Foundation (SNSF) project

SNF (contract no. 200021_129661)

LEMA:

(Laboratoire d’Electromagnétisme et d’Acoustique)

CERN:

(Organisation européenne pour la Recherche Nucléaire)

Juan R. Mosig

Michael Mattes

Edén Sorolla

Frank Zimmermann


FRAMEWORK

LEMA has a solid expertise in numericalelectromagnetics and integralequation

  • High power phenomena

  • Scattering parameters


FRAMEWORK (motivation)

MAIN IDEA

ELECTRON RADIATION

(POWER SPECTRUM)

DIAGNOSE

Hi there!

I’m an ELECTRON and I’mgoing to annoyyou!


ELECTROMAGNETIC MODEL


ELECTROMAGNETIC MODEL

General expressions of em. fields over the waveguide cross-section

(Propagation factor)

Dependency on (x,y)

Electric and magneticfields of the n-th mode


ELECTROMAGNETIC MODEL

Rectangular cavity

MODES ARE ANALYTICAL


ELECTROMAGNETIC MODEL

Beam pipe

MODES ARE NON-ANALYTICAL!!!

But wecan use the trigonometricfunctions (modes of rectangularwaveguide) as the basis set to develop the solutions for the beam pipe.

BI-RME method

(BoundaryIntegral-Resonant Mode Expansion)


POWER SPECTRUM

Transversal

component

Time-average

(harmonicsignals)

Losslesswaveguides

Radiated power


RESULTS

Beam pipe


RESULTS

TE 1


RESULTS

TM 1


RESULTS

“Eight” pipe


RESULTS

TE 1


RESULTS

TE 2


RESULTS

TM 1


RESULTS

TM 2


RESULTS

Bone pipe


RESULTS

TE 1


RESULTS

TE 2


RESULTS

TM 1


RESULTS

TM 2


RESULTS

RECTANGULAR CAVITY

TE10


RESULTS

POSITION

5 ns

SPEED

5 ns

T.D.


RESULTS

RADIATED FIELD

200 MHz  5 ns


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; furtherimprovementscanstillbedone.

* Implement the calculation of the radiated power spectrum of the electronsaccelerated by the proton beam (alternatively an external RF field) using the ‘history’ of the electrons’ motion provided by e-Cloud.


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