The Vlasov-Poisson System with Radiation Damping

Abstract

We set up and analyze a model of radiation damping within the framework of continuum mechanics, inspired by a model of post-Newtonian hydrodynamics due to Blanchet, Damour and Schäfer. In order to simplify the problem as much as possible we replace the gravitational field by the electromagnetic field and the fluid by kinetic theory. We prove that the resulting system has a well-posed Cauchy problem globally in time for general initial data and that in all solutions the fields decay to zero at late times. In particular, this means that the model is free from the runaway solutions which frequently occur in descriptions of radiation reaction.

Post-Coulombian Dynamics at Order c-3

“…Moreover, assume that 10) with T > 0 from (3.9) (or any other T ). Then there exist constants C * , C v > 0 such that 11) and for α = 1, .…”

“…In the limit of small velocities (corresponding to c → ∞) this system is well approximated by the Vlasov-Poisson equations [5,17]. Corrections due to radiation damping are studied in [10].…”

Large-amplitude oscillations and chaos in a Hamiltonian plasma system with many degrees of freedom

“…It denotes the reaction force that is included in the motion equation of the particle to take into account the fact that energy is being carried out from the system by the waves. It has been shown to play an important role in different fields, such as, e.g., in accelerator physics, in gravitation physics, in the long time evolution of Vlasov-Poisson system [10], in the dynamics of earthquakes and brittle failures of materials where seismic waves or phonons are radiated [11], and in general in systems where Hamiltonians similar to this one can be used. Note that its presence does not necessarily require emission of electromagnetic waves from the system.…”

Simplified models of electromagnetic and gravitational radiation damping

“…The purpose of the present paper is to put this mathematical result into a wider context and to discuss its ramifications. For technical details of the proof the reader is referred to [15].…”

“…After reviewing the results of [15] on one model of this type for electromagnetic radiation we discuss various issues relating to the possibility of generalizing those results to related models for electromagnetism and gravitation. In the model of [15] the matter is described by kinetic theory.…”