an:00447123
Zbl 0787.35110
Degond, P.; Raviart, P. A.
On the paraxial approximation of the stationary Vlasov-Maxwell system
EN
Math. Models Methods Appl. Sci. 3, No. 4, 513-562 (1993).
00014881
1993
j
35Q60 35B20 35C10 78A25
small parameter; perturbation; Vlasov-Maxwell equations; beams; nonrelativistic stationary dimensionless Vlasov equation; asymptotic expansion
The paper deals with the study of the paraxial model of approximation of the Vlasov-Maxwell equations which is widely used to analyze the confinement of beams. One first introduces scaling for the nonrelativistic stationary dimensionless Vlasov equation, and then an asymptotic expansion of its solution is derived. The paraxial model is obtained by retaining only those equations which provide the determination of transverse components from longitudinal components (loosely speaking). The axisymmetric case is considered with pure external fields on the one hand, and self-consistent fields on the other hand. Finally one deals with the three-dimensional case, an application to beam emittance is considered.
G.Jumarie (Montreal)