2011/10/13 by Russel E. Caflisch, R. E. Caflisch, Mark Rosin +3
Engineering · Physics and Astronomy · #Classical Physics (physics.class-ph) #Electrohydrodynamics and Fluid Dynamics #Electrowetting and Microfluidic Technologies #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Plasma Diagnostics and Applications #Plasma Physics (physics.plasm-ph) #nlin.SI #physics.class-ph #physics.flu-dyn #physics.plasm-ph
paper · pdf · doi:10.48550/arxiv.1110.2840
4 pages, 4 figures, submitted for publication
arxiv created 2011/10/13 · openalex publication_date 2011/10/13 · arxiv updated 2011/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper describes a new solution formulation for fully nonlinear and unsteady planar flow of an electron beam in a diode. Using characteristic variables - i.e., variables that follow particle paths - the solution is expressed through an exact analytic, but implicit, formula for any choice of incoming velocity v0, electric field E0 and current J0. For steady solutions, this approach clarifies the origin of the maximal current Jmax, derived by Child and Langmuir for v0=0 and by Jaffe for v0>0. The implicit formulation is used to find (1) unsteady solutions having constant incoming flux J0>Jmax, which leads formation of a virtual cathode, and (2) time-periodic solutions whose average flux exceeds the adiabatic average of Jmax.