The reaction-free trajectories of a classical point charge

It is well-known that a classical point charge in 1+1 D hyperbolic motion in space and time is reaction-free. But this is a special case of a larger set of reaction-free trajectories that in general are curved paths through space, i.e. in 2+1 D. This note catalogs the full family of reaction-free trajectories, giving a geometrical interpretation by which means the curved path possibility is easily related to the better known case of hyperbolic motion in 1+1 D. Motivated by the geometry, it is shown how the catalog of motions can be naturally extended to include the possibility of lossless reaction-free closed spatial orbits that turn out to be classical pair creation and destruction events. The extended theory can accommodate a vacuum plenum of classical current that could be regarded as a classical version of the Fermionic ZPF of QFT, reminiscent of the relationship between the Electromagnetic ZPF and the classical imitation that characterizes `Stochastic Electrodynamics.