Multi-scale analysis of the electromagnetic self-force in a weak gravitational field

TL;DR

This paper analyzes the effects of electromagnetic self-force on a charged particle's orbit in a weak gravitational field, highlighting the importance of both conservative and radiation-reaction forces for accurate orbital evolution modeling.

Contribution

It provides a multi-scale analysis of electromagnetic self-force effects, distinguishing the roles of conservative and radiation-reaction components in orbital dynamics.

Findings

Radiation-reaction causes secular changes in orbit shape.

Conservative force affects periapsis regression and orbital timing.

Neglecting conservative force leads to significant phase errors.

Abstract

We examine the motion of a charged particle in a weak gravitational field. In addition to the Newtonian gravity exerted by a large central body, the particle is subjected to an electromagnetic self-force that contains both a conservative piece and a radiation-reaction piece. This toy problem shares many of the features of the strong-field gravitational self-force problem, and it is sufficiently simple that it can be solved exactly with numerical methods, and approximately with analytical methods. We submit the equations of motion to a multi-scale analysis, and we examine the roles of the conservative and radiation-reaction pieces of the self-force. We show that the radiation-reaction force drives secular changes in the orbit's semilatus rectum and eccentricity, while the conservative force drives a secular regression of the periapsis and affects the orbital time function; neglect of the conservative term can hence give rise to an important phasing error. We next examine what might be required in the formulation of a reliable adiabatic approximation for the orbital evolution; this would capture all secular changes in the orbit and discard all irrelevant oscillations. We conclude that such an approximation would be very difficult to formulate without prior knowledge of the exact solution.