Hamiltonian formulation for the classical EM radiation-reaction problem: Application to the kinetic theory for relativistic collisionless plasmas (original) (raw)
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The European Physical Journal Plus, 2011
An exact solution is given to the classical electromagnetic (EM) radiation-reaction (RR) problem, originally posed by Lorentz. This refers to the dynamics of classical non-rotating and quasi-rigid finite size particles subject to an external prescribed EM field. A variational formulation of the problem is presented. It is shown that a covariant representation for the EM potential of the selffield generated by the extended charge can be uniquely determined, consistent with the principles of classical electrodynamics and relativity. By construction, the retarded self 4-potential does not possess any divergence, contrary to the case of point charges. As a fundamental consequence, based on Hamilton variational principle, an exact representation is obtained for the relativistic equation describing the dynamics of a finite-size charged particle (RR equation), which is shown to be realized by a second-order delay-type ODE. Such equation is proved to apply also to the treatment of Lorentzian particles, i.e., point-masses with finite-size charge distributions, and to recover the usual LAD equation in a suitable asymptotic approximation. Remarkably, the RR equation admits both standard Lagrangian and conservative forms, expressed respectively in terms of a non-local effective Lagrangian and a stress-energy tensor. Finally, consistent with the Newton principle of determinacy, it is proved that the corresponding initial-value problem admits a local existence and uniqueness theorem, namely it defines a classical dynamical system.
Charged relativistic fluids and non-linear electrodynamics
EPL (Europhysics Letters), 2010
The electromagnetic fields in Maxwell's theory satisfy linear equations in the classical vacuum. This is modified in classical non-linear electrodynamic theories. To date there has been little experimental evidence that any of these modified theories are tenable. However with the advent of high-intensity lasers and powerful laboratory magnetic fields this situation may be changing. We argue that an approach involving the self-consistent relativistic motion of a smooth fluid-like distribution of matter (composed of a large number of charged or neutral particles) in an electromagnetic field offers a viable theoretical framework in which to explore the experimental consequences of non-linear electrodynamics. We construct such a model based on the theory of Born and Infeld and suggest that a simple laboratory experiment involving the propagation of light in a static magnetic field could be used to place bounds on the fundamental coupling in that theory. Such a framework has many applications including a new description of the motion of particles in modern accelerators and plasmas as well * tdereli@ku.edu.tr † r.tucker@lancaster.ac.uk as phenomena in astrophysical contexts such as in the environment of magnetars, quasars and gamma-ray bursts.
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2010
The problem of radiation reaction and the self force is the oldest unsolved mystery in physics. At times it is considered a minor issue, a malefactor born of classical electrodynamics, while at other times it is public enemy number one, a major inconsistency and unsolved problem. This work derives some of the basic and most important results while reviewing some of the other known approaches to the problem. Some historical notes are given, and yet another approach is discussed that accounts for radiation reaction without the unphysical behavior that plagues so many theories. c
Il Nuovo Cimento B, 1988
divergence-free asymptotic approximation is developed for constructing an equation of motion for a radiating classical relativistic charged particle. The formulation employs the point particle limit in a sequence of solutions and the method developed by Dirac in his theory of classical charged particle. Since we use the initial-value approach proposed by Schutz, no runaway solutions exist and the irreversible nature of the particle motion is naturally derived. It is pointed out that the derived Lorentz-Dirac equation should not be regarded as an exact description of the motion of the charged particle holding at all times.
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The Exact Radiation-Reaction Equation for a Classical Charged Particle
AIP Conference Proceedings, 2008
An unsolved problem of classical mechanics and classical electrodynamics is the search of the exact relativistic equations of motion for a classical charged point-particle subject to the force produced by the action of its EM self-field. The problem is related to the conjecture that for a classical charged point-particle there should exist a relativistic equation of motion (RR equation) which results both non-perturbative, in the sense that it does not rely on a perturbative expansion on the electromagnetic field generated by the charged particle and non-asymptotic, i.e., it does not depend on any infinitesimal parameter. In this paper we intend to propose a novel solution to this well known problem, and in particular to point out that the RR equation is necessarily variational.
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Il Nuovo Cimento A, 1981
A model for ~V classical relativistic particles with actionat-a.distance interaction is proposed. It is the generalization of previous models for two particles. As in these models the interaction acts instantaneously among the particles in the centre-of-mass frame. There is a universal arbitrary potential, and therefore the system turns out to be only quasi-separable for long-range interactions. However, we find that there is separability for finite-range interactions. l. -Introduction.