THE CHILD-LANGMUIR ASYMPTOTICS OF THE VLASOV-POISSON EQUATION FOR CYLINDRICALLY OR SPHERICALLY SYMMETRICAL DIODES .2. ANALYSIS OF THE REDUCED PROBLEM AND DETERMINATION OF THE CHILD-LANGMUIR CURRENT

This paper analyses the Child-Langmuir asymptotics of the Vlasov-Poiss on problem in cylindrical or spherical symmetry. The problem was state d in the first part of this paper [2]. We recall that the Child-Langmu ir asymptotics concerns the boundary value problem for the Vlasov-Pois son system in the situation where the thermal energy of the injected p articles at the boundary is small compared with the external applied b ias. In the first part, we derived the set of estimates which allow us to pass to the limit in the asymptotic problem. In the present part, we analyse the limit (or 'reduced') problem, which leads us to a chara cterization of the limit or 'Child-Langmuir' current which flows throu gh the system.