Maxwell-Lorentz without self-interactions: Conservation of energy and momentum

Since a classical charged point particle radiates energy and momentum it is argued that there must be a radiation reaction force. Here we present an action for the Maxwell-Lorentz without self interactions model, where each particle only responds to the fields of the other charged particles. The corresponding stress-energy tensor automatically conserves energy and momentum in Minkowski and other appropriate spacetimes. Hence there is no need for any radiation reaction.

Reaction force of gravitational radiation in an effective-one-body theory based on the post-Minkowskian approximation

Effective-one-body (EOB) theory based on the post-Newtonian (PN) approximation presented by Buonanno and Damour plays an important role in the analysis of gravitational wave signals. Based on the post-Minkowskian (PM) approximation, Damour introduced another novel EOB theory which will lead to theoretically improved versions of the EOB conservative dynamics and might be useful in the upcoming era of high signal-to-noise-ratio gravitational-wave observations. Using the 2PM effective metric obtained by us recently, in this paper we study the radiation reaction force experienced by the particle with the help of the energy-loss-rate, which is an important step to construct the EOB theory based on the PM approximation.

A Poynting theorem formulation for the gravitational wave stress pseudo tensor

A very simple and physical derivation of the conservation equation for the propagation of gravitational radiation is presented. The formulation is exact. The result takes the readily recognisable and intuitive form of a Poynting-style equation, in which the outward propagation of stress energy is directly related to the volumetric equivalent of a radiation reaction force acting back upon the sources, including the purely gravitational contribution to the sources. Upon averaging, the emergent pseudo tensor for the gravitational radiation is in exact agreement with that found by much more labour-intensive methods.

On the Schott Term in the Lorentz-Abraham-Dirac Equation

The equation of motion for a radiating charged particle is known as the Lorentz–Abraham–Dirac (LAD) equation. The radiation reaction force in the LAD equation contains a third time-derivative term, called the Schott term, which leads to a runaway solution and a pre-acceleration solution. Since the Schott energy is the field energy confined to an area close to the particle and reversibly exchanged between particle and fields, the question of how it affects particle motion is of interest. In here we have obtained solutions for the LAD equation with and without the Schott term, and have compared them quantitatively. We have shown that the relative difference between the two solutions is quite small in the classical radiation reaction dominated regime.

Velocity of Transmission of Electrical Force and Aberration of Electric Field

An electron of rest mass mo and charge –e moving with velocity v at angle θ to an electric field of intensity E and magnitude E, is subject to aberration of electrid field, as a result of relativity (c – v) of velocity between the electric force, transmitted with velodity of light c of magnitude c and the electron moving with velocity v. The accelerating force, at time t, in accordance with Newton’s second law of motion, put as F = - (eE/c) (c – v) = m (dv/dt), is less than the electrostatic force–eE, the difference being the radiation reaction force. At the velocity of light F become zero and the electron continues to move with speed c as a limit. Motion of the electron with constant mass m and its radiation power are treated under acceleration with θ=0 or deceleration with θ=π radians or at constant speed v, in a circle of radiua r, with θ=π/2 radians. It is shown that circular motion of an electron round a central force of attraction, as in the Rutherford’s nuclear model of the hydrogen atom, is without radiation.

Modified Vlasov equation and dispersion relations for a relativistic radiating electron plasma

A modified Vlasov equation is obtained by developing a covariant statistical mechanics for a system of electrons without considering the effects of the ions and including the Landau–Lifshitz equation of motion. General dispersion relations for the transverse and longitudinal modes for any temperature are expressed. The results are similar to those found by Hakim & Mangeney (Phys. Fluids, vol. 14, 1971, pp. 2751–2781) for both the modified Vlasov equation and the dispersion relations. However, for the longitudinal mode, unlike the development of Hakim and Mangeney, correct expansions are done in order to give a numerical approach to obtain the longitudinal relativistic dispersion relations for any value of the wavenumber. Accordingly, new loop solutions, with turning points, crossing the super-luminous region and the super-thermal region are found. Although the expressions for the Landau damping and the damping due to the radiation reaction force coincide with the Hakim and Mangeney results for some particular cases, in general they are different. A Landau anti-damping appears in the second branch of the loop in a small region between the cutoff point and the intersection with the super-thermal line. The analysis of this effect leads us to a kind of wave pulse. We will call them bipolar waves. The treatment contains the relativistic interactions between all the electrons in the system with retarded effects. This explain the differences with Zhang’s recent work (Phys. Plasmas, vol. 20, 2013, 092112–092132). It is shown that for low densities, the cutoff of the wave is due to the dispersion relations and not due to the radiation reaction force damping. While for both high densities and temperatures, the damping due to the radiation reaction force is important.