Post-Coulombian Dynamics at Order c-3

Abstract

We study the dynamics of N charges interacting with the Maxwell field. If their initial velocities are small compared to the velocity of light, c, then in lowest order their motion is governed by the static Coulomb Lagrangian. We investigate higher order corrections with an explicit control on the error terms. The Darwin correction, order |v/c| 2 , has been proved previously. In this contribution we obtain the dissipative corrections due to radiation damping, which are of order |v/c| 3 relative to the Coulomb dynamics. If all particles have the same charge-to-mass ratio, the dissipation would vanish at that order.

A non-relativistic model of plasma physics containing a radiation reaction term

“…[9, chapter 16]. In [13] it has been observed that in particle models this problem has the structure of a geometric singular perturbation problem, and the "physical" dynamics are obtained on a center-like manifold of the full dynamics. For sake of discussion let us assume for a moment that the first equation in (SGPP ε ) is an ODE instead of a PDE and to simplify notations in this subsection f denotes the couple (f + , f − ).…”

“…, which is just not sufficient for our purposes. We also can't make use of the smallness of ε; in order to swallow the |D [2] | 2 term we have to choose η = εM 2 and end with the factor 1 M in front of the |D [1] | 2 term which is just cancelled by the square of ||f ± || 1/2 1 in (13). It is because of this, that the existence of global classical solutions seems to be out of reach at the moment.…”

Quasi-static Limits in Nonrelativistic Quantum Electrodynamics

“…An additional aim is to point out similarities and differences between the two limits in the quantum context and to compare the results we get for the 2 In the classical case, a more refined and precise analysis is carried through in [15,16]. The authors consider, loosely speaking, initial conditions which represent free particles moving together with the field they generate ("dressed" particles or charge solitons), with a velocity of order O(ε 1/2 ) with respect to the speed of light.…”

Simplified models of electromagnetic and gravitational radiation damping

“…The purpose of this section is to see how this model relates to the effective equations for N -particle systems of Abraham-Lorentz type [16,17,22] in the limit N → ∞. As before we assume the fields E and B do satisfy the Maxwell equations (5), (6), and they are expanded as in (1), (2) in λ 1/2 = c −1 .…”

“…In [17] it was proved that to the order of radiation reaction the particle dynamics is governed over long times by…”