No Arabic abstract
A broad class of forces P is identified for which the Abraham-Lorentz-Dirac (ALD) equation has common solutions with a Newton type equation that do not present pre-acceleration or escape into infinity (runaway behavior). It is argued that the given class can approximate with arbitrary precision any continuous or piecewise continuous force. For the general case of such forces, the existence of common solutions to the ALD and the Newton type equations in terms of generalized functions defined on P is argued. The existence of such solutions is explicitly demonstrated here for the important example of the instantly connected constant force. Expressions for the position and velocity are defined by generalized functions with point support in the initial time in which force is applied. It follows that both, the velocity as the coordinates are discontinuous at the support point, at the instant where the force is applied. The unusual discontinuity in the position that appears is justified by the presence of impulsive forces that determine instantaneous jumps in the coordinates. This result is compatible with the non relativistic limit under consideration and is expected to be explained after a further relativistic generalization of the discussion here. The solution obtained for this class of forces reproduces the one obtained by A. Yaghjian, from his equations for the extended particle moving between the plates of a capacitor. This outcome suggests the possible link or equivalence between this two analysis. The common solution of the Newton like equations and the ALD ones for the case of a constant and homogeneous magnetic field is also presented. The extension the results to a relativistic limit will be investigated in future works.
From electromagnetic wave equations, it is first found that, mathematically, any current density that emits an electromagnetic wave into the far-field region has to be differentiable in time infinitely, and that while the odd-order time derivatives of the current density are built in the emitted electric field, the even-order derivatives are built in the emitted magnetic field. With the help of Faradays law and Amperes law, light propagation is then explained as a process involving alternate creation of electric and magnetic fields. From this explanation, the preceding mathematical result is demonstrated to be physically sound. It is also explained why the conventional retarded solutions to the wave equations fail to describe the emitted fields.
A stochastic model is proposed for the acceleration of non-relativistic particles yielding to energy spectra with a shape of a Weibulltextquoteright s function. Such particle distribution is found as the stationary solution of a diffusion-loss equation in the framework of a second order Fermitextquoteright s mechanism producing anomalous diffusion for particle velocity. The present model is supported by in situ observations of energetic particle enhancements at interplanetary shocks, as here illustrated by means of an event seen by STEREO B instruments in the heliosphere. Results indicate that the second order Fermitextquoteright s mechanism provides a viable explanation for the acceleration of energetic particles at collisioness shock waves.
In this paper we show that the Schrodinger-Newton equation for spherically symmetric gravitational fields can be derived in a WKB-like expansion in 1/c from the Einstein-Klein-Gordon and Einstein-Dirac system.
Accelerating electrons are known to radiate electromagnetic waves, a property that is central to the concept of many devices, from antennas to synchrotrons. While the electrodynamics of accelerating charged particles is well understood, the same is not true for charged matter waves: would a locally accelerating charged matter wave, like its particle counterpart, radiate? Here we construct a novel class of matter waves, angular accelerating electron waves, by superpositions of twisted electrons carrying orbital angular momentum. We study the electrodynamic behaviour of such accelerating matter waves and reveal the generation of a solenoidal magnetic field in each component, and an accelerating electron wave that does not radiate. These novel properties will have practical impact in spin flipping of qubits for quantum information processing, have been suggested for control of time dilation and length contraction, and raise fundamental questions as to the nature of wave-particle duality in the context of radiating charged matter.
We present an analysis of the general relativistic Boltzmann equation for radiation, appropriate to the case where particles and photons interact through Thomson scattering, and derive the radiation energy-momentum tensor in the diffusion limit, with viscous terms included. Contrary to relativistic generalizations of the viscous stress tensor that appear in the literature, we find that the stress tensor should contain a correction to the comoving energy density proportional to the divergence of the four-velocity, as well as a finite bulk viscosity. These modifications are consistent with the framework of radiation hydrodynamics in the limit of large optical depth, and do not depend on thermodynamic arguments such as the assignment of a temperature to the zeroth-order photon distribution. We perform a perturbation analysis on our equations and demonstrate that, as long as the wave numbers do not probe scales smaller than the mean free path of the radiation, the viscosity contributes only decaying, i.e., stable, corrections to the dispersion relations. The astrophysical applications of our equations, including jets launched from super-Eddington tidal disruption events and those from collapsars, are discussed and will be considered further in future papers.