Finite energy scattering for the Lorentz-Maxwell equation
نویسنده
چکیده
In the case where the charge of the particle is small compared to its mass, we describe the asymptotics of the Lorentz-Maxwell equation (Abraham model) for any finite-energy data. As time goes to infinity, we prove that the speed of the particle converges to a certain limit, whereas the electromagnetic field can be decomposed into a soliton plus a free solution of the Maxwell equation. It is the first instance of a scattering result for general finite energy data in a field-particle equation.
منابع مشابه
Physical wavelets : Lorentz covariant , singularity - free , finite energy , zero action , localized solutions to the wave equation
Abstract: Particle physics has for some time made extensive use of extended field configuations such as solitons, instantons, and sphalerons. However, no direct use has yet been made of the quite extensive literature on “localized wave” configurations developed by the engineering, optics, and mathematics communities. In this article I will exhibit a particularly simple “physical wavelet” — it i...
متن کاملNonlinear finite-difference time-domain modeling of linear and nonlinear corrugated waveguides
A multidimensional, nonlinear finite-difference time-domain (NL-FDTD) simulator, which is constructed from a self-consistent solution of the full-wave vector Maxwell equations and dispersive (Lorentz), nonlinear (finitetime-response Raman and instantaneous Kerr) materials models, is used to study finite-length, corrugated, optical waveguide output couplers and beam steerers. Multiple-cycle, ult...
متن کاملConvergence Analysis of Yee Schemes for Maxwell’s Equations in Debye and Lorentz Dispersive Media
We present discrete energy decay results for the Yee scheme applied to Maxwell’s equations in Debye and Lorentz dispersive media. These estimates provide stability conditions for the Yee scheme in the corresponding media. In particular, we show that the stability conditions are the same as those for the Yee scheme in a nondispersive dielectric. However, energy decay for the Maxwell-Debye and Ma...
متن کاملImplementation of the Fdtd Method Based on Lorentz-drude Dispersive Model on Gpu for Plasmonics Applications
We present a three-dimensional finite difference time domain (FDTD) method on graphics processing unit (GPU) for plasmonics applications. For the simulation of plasmonics devices, the Lorentz-Drude (LD) dispersive model is incorporated into Maxwell equations, while the auxiliary differential equation (ADE) technique is applied to the LD model. Our numerical experiments based on typical domain s...
متن کاملDerivation of the self-interaction force on an arbitrarily moving point-charge and of its related energy-momentum radiation rate: The Lorentz-Dirac equation of motion in a Colombeau algebra
The classical theory of radiating point-charges is revisited: the retarded potentials, fields, and currents are defined as nonlinear generalized functions. All calculations are made in a Colombeau algebra, and the spinor representations provided by the biquaternion formulation of classical electrodynamics are used to make all four-dimensional integrations exactly and in closed-form. The total r...
متن کامل