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. The approach is based on two key elements: 1) the adoption of the relativistic hybrid synchronous Hamilton variational principle recently pointed out (Tessarotto et al, 2006). Its basic feature is that it can be expressed in principle in terms of arbitrary "hybrid" variables (i.e., generally non-Lagrangian and non-Hamiltonian variables); 2) the variational treatment of the EM self-field, taking into account the exact particle dynamics.
We study radiation reaction in a Lorentz violating electrodynamics [1]. We explore the possible modification whatsoever present in the radiation reaction force experienced by an accelerating charge in the modified Maxwell theory. However it turns out that radiation reaction receives no change due to Lorentz violation whereas electromagnetic mass manifests anisotropy.
As it is known a model of a charged particle with finite size is a good tool to consider the effects of self- action and backreaction, caused by electromagnetic radiation. In this work the "size" of a charged particle is induced by its stochastic Brownian vibration. Appropriate equation of particle's motion with radiation force is derived. It is shown that the solutions of this equation correctly describe the effects of radiation reaction.
A generalization of the force approach to radiation reaction is given, taken into consideration an arbitrary motion of the charged particle . The expression obtained brings about the expression already given for the linear an the circular acceleration cases.
Abraham Lorentz (AL) formula of Radiation Reaction and its relativistic generalization, Abraham Lorentz Dirac (ALD) formula, are valid only for periodic (accelerated) motion of a charged particle, where the particle returns back to its original state. Thus, they both represent time averaged solutions for radiation reaction force. In this paper, another expression has been derived for radiation reaction following a new approach, starting from Larmor formula, considering instantaneous change (rather than periodic change) in velocity, which is a more realistic situation. Further, it has been also…
The difficulty of usual approach to radiation reaction is pointed out , and a possible approach based on the force acting to the charged particle which produces the acceleration itself, is presented. This approach brings about an expression such that acceleration is zero whenever the external force is zero.
A detailed analysis is given of the angular distribution of an charged particle moving along the arc of a circle. The areas of different angular distribution behavior are highlighted and studied.
The radiation reaction fields are calculated for an accelerated changing dipole in scalar and electromagnetic radiation fields. The acceleration reaction is shown to alter the damping of a time varying dipole in the EM case, but not the scalar case. In the EM case, the dipole radiation reaction field can exert a force on an accelerated monopole charge associated with the accelerated dipole. The radiation reaction of an accelerated charge does not exert a torque on an accelerated magnetic dipole, but an accelerated dipole does exert a force on the charge. The technique used is that originally d…
We study a system of a finite size charged particle interacting with radiation field by exploiting the Hamilton's principle for non-conservative system introduced recently by Galley[1]. The said formulation leads to the equation of motion of the charged particle that turns out to be the same as obtained by Jackson[3]. We show that radiation reaction stems from the non-conservative piece of the effective Lagrangian. We notice that a charge interacting with radiation field modeled as heat bath affords a way to justify that radiation reaction is a non-conservative force. The topic is suitable for…
The Abrahamn Lorentz radiation reaction force term, with da/dt, derived in text books is shown to be incomplete. We show that, with the addition of a term, the classical radiation reaction force can be generalized to the relativistic force expression. This addition is the Poynting Robertson term, seen mostly in astrophysics and usually missing from texts in electromagnetism. With this term added, it takes into account the rate of change of mass dm/dt of the particle and makes the generalization to the relativisitic formula for force very straight forward.
We consider the 1-D motion of an electron under a periodic force and taking into account the effect of radiation reaction dissipation force on its motion, using the formulation of the radiation reaction force as a function of the external force. Two cases are considered: a simple sinusoidal time depending force, and sinusoidal electromagnetic force with position and time dependence. We found that the difference of the normalized (with respect the speed of light) velocities, with and without radiation reaction, are quite small between $10^{-31}$ to $10^{-14}$ for intensities on the electric fie…
We study the radiation reaction acting on an accelerating charge moving in noncommutative spacetime and obtain an expression for it. Radiation reaction, due to a nonrelativistic point charge, is found to receive a small noncommutative correction term. The Abraham-Lorentz equation for a point charge in noncommutative spacetime suffers from the pre-acceleration and the runaway problems. We explore as an application the radiation reaction experienced by a charge which undergoes harmonic oscillations in a noncommutative plane.
We study the electromagnetic fields of an arbitrarily moving charged particle and the radiation reaction on the charged particle using a novel approach. We first show that the fields of an arbitrarily moving charged particle in an inertial frame can be related in a simple manner to the fields of a uniformly accelerated charged particle in its rest frame. Since the latter field is static and easily obtainable, it is possible to derive the fields of an arbitrarily moving charged particle by a coordinate transformation. More importantly, this formalism allows us to calculate the self-force on a c…
The usual radiation self-force of a point charge is obtained in a mathematically exact way and it is pointed out to that this does not call forth that the spacetime motion of a point charge obeys the Lorentz--Abraham--Dirac equation.
The emission of radiation from an accelerated charge is analyzed. It is found that at zero velocity, the radiation emitted from the charge imparts no counter momentum to the emitting charge, and no radiation reaction force is created by the radiation. A reaction force is created by the stress force that exists in the curved electric field of the charge, and the work done in overcoming this force is the source of the energy carried by the radiation.
On the model of moving rigid charged body is shown that the Lorentz-Dirac approach to radiation reaction in classical electrodynamics does not work for trajectories of body close to the light cone.
In classical electrodynamics for rotating with variable angular velocity charged rigid sphere are found: the exact values of electromagnetic fields, the flux of radiating energy and the exact integral equation of rotation including the terms of self-rotation. The analysis of this eq. shows that on one hand, there is no "runaway" solutions, peculiar to the Lorentz-Dirac eq. of radiating point particle, on the other hand, there appear new problems, among them is the nonexistence of solution for some external moments of force.
The self force of electrodynamics is derived from a scalar field. The resulting equation of motion is free of all of the problems that plague the Lorentz Abraham Dirac equation. The age-old problem of a particle in a constant field is solved and the solution has intuitive appeal.
The problem of self forces and radiation reaction is solved by conservation of energy methods. The longstanding problem of constant acceleration is solved, and it is shown that the self force does indeed affect the particle's motion, as expected on physical grounds. The relativistic generalization is also presented.
We address some questions related to radiation and energy conservation in classical electromagnetism. We first treat the well-known problem of energy accounting during radiation from a uniformly accelerating particle. We present the problem in the form of a paradox, and then answer it using a modern treatment of radiation reaction and self-force, as it appears in the expression due to Eliezer and Ford and O'Connell. We clarify the influence of the Schott force and the total radiated power, which differs from Larmor's formula. Finally, we present a simple and highly visual argument which enable…
Photon emission from a uniformly accelerated charge is among the most mysterious physical phenomena. Theories based on the Lorentz-Abraham-Dirac equation mostly conclude that a uniformly accelerated point charge cannot feel radiation reaction. Such a conclusion suggests that the origin of the photon energy is unclear. In this paper, we determine the self-force of a uniformly accelerated charged sphere using the Lorentz force equation, with an assumption that the sphere is Lorentz-contracted during the acceleration. For large acceleration, the calculated self-force converges to the radiation re…
The radiation from a relativistic charged particle uniformly moving through the centre of a dielectric ball is investigated. Analytical expressions for spectral and spectral-angular distributions of the radiated energy are derived and numerical results for the spectrum of radiation are given. It is shown, that the spectral distribution of Cherenkov radiation generated by the relativistic particle inside a dielectric ball at specified frequencies is strongly influenced by the ballvacuum boundary.
Radiation of relativistic charged particles in a system of randomly spaced plates is considered in the paper. It is shown that for large number of plates ($N \gg 1$), in the wavelength range $λ\ll l\ll L$ (where $l$ is the photon mean free path and $L$ is the system characteristic size) and for angles $|\cos θ|\gg (λ/2πl)^{1/3}$, pseudophoton diffusion represents the major mechanism of radiation. Total intensity of radiation is investigated and its strong dependence on the particle energy and plate number is obtained.
We discuss radiation reaction effects on charges propagating in ultra-intense laser fields. Our analysis is based on an analytic solution of the Landau-Lifshitz equation. We suggest to measure radiation reaction in terms of a symmetry breaking parameter associated with the violation of null translation invariance in the direction opposite to the laser beam. As the Landau-Lifshitz equation is nonlinear the energy transfer within the pulse is rather sensitive to initial conditions. This is elucidated by comparing colliding and fixed target modes in electron laser collisions.
The influence of radiation reaction (RR) on multiphoton Thomson scattering by an electron colliding head-on with a strong laser beam is investigated in a new regime, in which the momentum transferred on average to the electron by the laser pulse approximately compensates the one initially prepared. This equilibrium is shown to be far more sensitive to the influence of RR than previously studied scenarios. As a consequence RR can be experimentally investigated with currently available laser systems and the underlying widely discussed theoretical equations become testable for the first time.
We propose a new method of detecting radiation reaction effects in the motion of particles subjected to laser pulses of moderate intensity and long duration. The effect becomes sizeable for particles that gain almost no energy through the interaction with the laser pulse.
We derive effective equations of motion for a massless charged particle coupled to the dynamical electromagnetic field having regard to the radiation back reaction. It is shown that unlike the massive case not all the divergences resulting from the self-action of the particle are Lagrangian, i.e. can be canceled out by adding appropriate counterterms to the original action. Besides, the order of renormalized differential equations governing the effective dynamics turns out to be greater than the order of the corresponding Lorentz-Dirac equation for a massive particle. For the case of homogeneo…
I show that the main statement of [Phys. Rev. Lett. 105, 094802 (2010), arXiv:1005.2617] is wrong. Other inconsistences of this Letter are also discussed.
The subject of radiation reaction in classical electromagnetism remains controversial over 120 years after the pioneering work of Lorentz. We give a simple but rigorous treatment of the subject at the textbook level that explains the apparent paradoxes that are much discussed in the literature on the subject. We first derive the equation of motion of a charged particle from conservation of energy and momentum, which includes the self-force term. We then show that this theory is unstable if charged particles are pointlike: the energy is unbounded from below, and charged particles self-accelerat…
Starting from the Dirac equation coupled to a classical radiation field a set of equations of motion for charged quasi-particles in the classical limit for slowly varying radiation and matter fields is derived. The radiation reaction term derived in the paper is the Abraham-Lorentz-Dirac term.
The effects of coherently enhanced radiation reaction on the motion of subwavelength electron bunches in interaction with intense laser pulses are analyzed. The radiation reaction force behaves as a radiation pressure in the laser beam direction, combined with a viscous force in the perpendicular direction. Due to Coulomb expansion of the electron bunch, coherent radiation reaction effects only occur in the initial stage of the laser-bunch interaction while the bunch is still smaller than the wavelength. It is shown that this initial stage can have observable effects on the trajectory of the b…
A self-action problem for a pointlike charged particle arbitrarily moving in flat spacetime of three dimensions is considered. Outgoing waves carry energy-momentum and angular momentum; the radiation removes energy and angular momentum from the source which then undergoes a radiation reaction. We decompose Noether quantities carried by electromagnetic field into bound and radiative components. The bound terms are absorbed by individual particle's characteristics within the renormalization procedure. Radiative terms together with already renormalized 3-momentum and angular momentum of pointlike…
