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A SIMPLE HAMILTONIAN MODEL OF RUNAWAY PARTICLE WITH SINGULAR INTERACTION
https://doi.org/10.1142/S0218202505000558Cited by:8 (Source: Crossref)
Abstract
We consider a Hamiltonian system given by a charged particle under the action of a constant electric field and interacting with a medium, which is described as a Vlasov fluid. We assume that the action of the charged particle on the fluid is negligible and that the latter has one-dimensional symmetry. We prove that if the singularity of the particle/medium interaction is integrable and the electric field intensity is large enough, then the particle escapes to infinity with a quasi-uniformly accelerated motion. A key tool in the proof is a new estimate on the growth in time of the fluid particle velocity for one-dimensional Vlasov fluids with bounded interactions.
AMSC: 82D10, 82C21, 76X05
