Attosecond and femtosecond forces exerted on gold nanoparticles induced by swift electrons

We report time-dependent calculations of attosecond and femtosecond forces imposed by a kilovolt swift electron during passage near a nanometer-sized metal particle. Contrary to expectations based on dielectric theory, which suggest that the forces should always be attractive, we find that for very close approaches, attosecond forces are repulsive, and are caused by interaction of the magnetic field of the relativistic electron with currents within even nominally nonmagnetic nanoparticles. These results suggest an explanation for the observation of both attractive and repulsive nanoparticle movement during the first use of \AA{}ngstrom-sized electron beams in electron microscopy.