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UID:4665@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20230306T110000
DTEND;TZID=Europe/Paris:20230306T120000
DTSTAMP:20230310T140008Z
URL:https://www.i2m.univ-amu.fr/evenements/a-bi-species-kinetic-model-for-
 cylindrical-langmuir-probe-existence-result-and-numerical-analysis/
SUMMARY:Ludovic Godard-Cadillac (Université de Nantes): A bi-species kinet
 ic model for cylindrical Langmuir probe : existence result and numerical a
 nalysis
DESCRIPTION:Ludovic Godard-Cadillac: We study a collisionless kinetic model
  for plasmas in the neighborhood of a cylindrical metallic Langmuir probe.
  This model consists in a bi-species Vlasov-Poisson equation in a domain c
 ontained between two cylinders with prescribed boundary conditions. The in
 terior cylinder models the probe while the exterior cylinder models the in
 teraction with the plasma core. We prove the existence of a weak-strong so
 lution for this model in the sense that we get a weak solution for the 2 V
 lasov equations and a strong solution for the Poisson equation. The first 
 parts of this work are devoted to explain the model and proceed to a detai
 led study of the Vlasov equations. This study then leads to a reformulatio
 n of the Poisson equation as a 1D non-linear and non-local equation and we
  prove it admits a strong solution using an iterative fixed-point procedur
 e. Eventually we proceed to a qualitative description of the solution unde
 r the so-called "generalized Bohm condition" on the incomming fluxes  and
  a numerical investigation of the obtained equation. Due to technical obst
 acles\, we mainly focussed on the "quasi-radial" fluxes for the numerical 
 analysis\, which turns out to be enough to validate the model. Curves of t
 he obtained trajectories of particles and curves of the collected current 
 versus the applied voltage are presented.
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 022/12/Ludovic_Godard-Cadillac.png
CATEGORIES:Séminaire,Analyse Appliquée
LOCATION:I2M Chateau-Gombert - CMI\, Salle de Séminaire R164 (1er étage)\
 , 39 Rue Joliot Curie\, 13013 Marseille\, France\, Campus Château-Gombert
 \, 
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=39 Rue Joliot Curie\, 13013
  Marseille\, France\, Campus Château-Gombert\, ;X-APPLE-RADIUS=100;X-TITL
 E=I2M Chateau-Gombert - CMI\, Salle de Séminaire R164 (1er étage):geo:0,
 0
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DTSTART:20221030T020000
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