Time-dependent forces between a swift electron and a small nanoparticle within the dipole approximation

TL;DR

This study models the time-dependent electromagnetic forces between a fast-moving electron and a small metallic nanoparticle using classical dipole approximation, revealing attraction and repulsion effects due to delayed response.

Contribution

It introduces a classical electrodynamics approach to analyze dynamic forces on nanoparticles caused by swift electrons, considering the limits of the dipole approximation.

Findings

Forces alternate between attractive and repulsive over time.

The nanoparticle's electromagnetic response delay causes force sign changes.

The dipole approximation's validity is assessed against full multipole calculations.

Abstract

In this paper we calculate the time-dependent forces between a swift electron traveling at constant velocity and a metallic nanoparticle made of either aluminum or gold. We consider that the nanoparticle responds as an electric point dipole and we use classical electrodynamics to calculate the force on both the nanoparticle and the electron. The values for the velocity of the electron and the radius of the nanoparticle were chosen in accordance with electron microscopy observations, and the impact parameter was selected to fulfill the constraints imposed by the dipole approximation. We found that there are times when the force on the nanoparticle is attractive and others when it is repulsive, and show that this is due to the delayed electromagnetic response of the nanoparticle. To establish the limits of validity of our approach, we calculate the total linear momentum transfer to the nanoparticle, and compare it with results obtained, in frequency space, using the full multipole expansion of the fields induced on the nanoparticle, considering the effects of electromagnetic radiation.