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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Workdevelopedunder the Swiss National Science Foundation (SNSF) project
SNF (contract no. 200021_129661)
(Laboratoire d’Electromagnétisme et d’Acoustique)
(Organisation européenne pour la Recherche Nucléaire)
Juan R. Mosig
LEMA has a solid expertise in numericalelectromagnetics and integralequation
I’m an ELECTRON and I’mgoing to annoyyou!
General expressions of em. fields over the waveguide cross-section
Dependency on (x,y)
Electric and magneticfields of the n-th mode
MODES ARE ANALYTICAL
MODES ARE NON-ANALYTICAL!!!
But wecan use the trigonometricfunctions (modes of rectangularwaveguide) as the basis set to develop the solutions for the beam pipe.
(BoundaryIntegral-Resonant Mode Expansion)
200 MHz 5 ns
* 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.