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Finite element modelling of ion convection by electrostatic forces

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  • Engineering
  • Computing & Technology :: Electrical & Electronics Engineering [C06]
  • Ingénierie
  • Informatique & Technologie :: Ingénierie électrique & électronique [C06]


1 Finite element modelling of ion convection by electrostatic forces Geoffrey Delie´ge � 1 � , Franc¸ois Henrotte � 2 � , Wim Deprez � 3 � and Kay Hameyer � 2 � (1) K.U. Leuven, Dept. Computer Science (TWR), Celestijnenlaan 200A, B-3001 Heverlee, Belgium (2) Institut fu¨r Elektrische Maschinen (RWTH), Schinkelstrasse 4, 52056 Aachen, Germany (3) K.U. Leuven, Dept. ESAT-ELECTA, Kasteelpark Arenberg 10, B-3001 Heverlee, Belgium Abstract— Different formulations of the problem of a cloud of ions convected by electrostatic forces are presented. Their influence on the ionic charge conservation is discussed. It is shown that a mixed electrostatic formulation is the most accurate for the studied example. Index Terms— Finite element, electrostatic, source field, mixed formulation. I. INTRODUCTION THE numerical analysis of an electrostatic paintingprocess [1] requires to solve the classical electrostatic equations coupled with a charge conservation equation, ∂t ρi � ∇ � j � 0 � (1) where ρi is the ion charge density. The purpose of this paper is to determine whether the current density is preferably expressed as j � µε d ρi or j � µeρi. At the discrete level, the first expression ensures continuity of the normal component of j, across material discontinuities and inter-element boundaries, which is the natural continuity for a flux density (here a flux of ionic charge, � j ��� �Cm 2 s 1 � ). On the other hand, the second This article is dedicated to Prof. G. Henneberger, who is released into his well deserved retirement with gratitude and appreciation for his meritorious scientific work. This text presents research results of the Belgian programme on Inter- university Poles of Attraction initiated by the Belgian State, Prime Minister’s Office, Science Policy Programming. expression, which is more customary, ensures the continuity of the tangential component of j. In particular, the influence on the conservation of the total charge in the system dur

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