The Child–Langmuir asymptotics for magnetized flows

Article type: Research Article

Authors: Ben Abdallah, Naoufel^; | Degond, Pierre | Méhats, Florian

Affiliations: MIP, Laboratoire CNRS (UMR 5640), Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France | Centre de Mathématiques Appliquées (URA CNRS 756), École Polytechnique, 91128 Palaiseau Cedex, France

Note: [] Corresponding author. E‐mail: naoufel@mip.ups‐else.fr.

Abstract: The Child–Langmuir asymptotics of the so‐called 1.5‐dimensional Vlasov–Maxwell, modelling cross field diodes, is investigated. A set of limit problems including magnetically insulated and noninsulated regimes are exhibited and analyzed. The solutions of the Vlasov–Maxwell system are shown to converge towards a solution of the limiting problem.

Journal: Asymptotic Analysis, vol. 20, no. 2, pp. 97-132, 1999