Differential geometric analysis of radiation-particle interaction

TL;DR

This paper uses differential geometry to analyze how charged particles move under electromagnetic fields, revealing conditions for integrability, stability, and resonance, and clarifying the limits of the ponderomotive approximation.

Contribution

It introduces a geometric framework to study particle dynamics in electromagnetic fields, linking curvature to motion properties and resonance phenomena.

Findings

Particle motion in plane-wave fields is integrable when curvature vanishes.

The dynamical response depends on the impulse factor, affecting stability and resonance.

A precise mathematical definition of the ponderomotive oscillation center is provided.

Abstract

On the basis of the Lorentz equations of motion, the orbit of a charge driven by a generic E.M. field with planar symmetry is formulated and analyzed within the framework of a Lorentzian geometry with a curvature whose order of magnitude is parametrized by the radiation intensity and frequency. This reformulation leads to (i) a demonstration of the integrability of the particle motion in a plane-wave field as a result of the vanishing of the curvature, (ii) a manifestation of the parametric dependence of the dynamical response of the particle orbit to the E.M. field on the impulse factor in terms of local stability and the occurrence of parametric resonance and (iii) a mathematically precise meaning to the ponderomotive oscillation center of the charge executing oscillatory motion in a sufficiently low impulsive E.M. field, which is subsequently used to raise (iv) a discussion of the domain of applicability of the ponderomotive approximation.