8 research outputs found
Hamiltonian formulation for the classical EM radiation-reaction problem: application to the kinetic theory for relativistic collisionless plasmas
A notorious difficulty in the covariant dynamics of classical charged
particles subject to non-local electromagnetic (EM) interactions arising in the
EM radiation-reaction (RR) phenomena is due to the definition of the related
non-local Lagrangian and Hamiltonian systems. The lack of a standard
Lagrangian/Hamiltonian formulation in the customary asymptotic approximation
for the RR equation may inhibit the construction of consistent kinetic and
fluid theories. In this paper the issue is investigated in the framework of
Special Relativity. It is shown that, for finite-size spherically-symmetric
classical charged particles, non-perturbative Lagrangian and Hamiltonian
formulations in standard form can be obtained, which describe particle dynamics
in the presence of the exact EM RR self-force. As a remarkable consequence,
based on axiomatic formulation of classical statistical mechanics, the
covariant kinetic theory for systems of charged particles subject to the EM RR
self-force is formulated in Hamiltonian form. A fundamental feature is that the
non-local effects enter the kinetic equation only through the retarded particle
4-position, which permits the construction of the related non-local fluid
equations. In particular, the moment equations obtained in this way do not
contain higher-order moments, allowing as a consequence the adoption of
standard closure conditions. A remarkable aspect of the theory concerns the
short delay-time asymptotic expansions. Here it is shown that two possible
expansions are permitted. Both can be implemented for the single-particle
dynamics as well as for the corresponding kinetic and fluid treatments. In the
last case, they are performed a posteriori on the relevant moment equations
obtained after integration of the kinetic equation over the velocity space.
Comparisons with literature are pointed out
Exact solution of the EM radiation-reaction problem for classical finite-size and Lorentzian charged particles
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 self-field 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