Particle beams guided by electromagnetic vortices: New solutions of the Lorentz, Schr\"odinger, Klein-Gordon, and Dirac equations

It is shown that electromagnetic vortices can act as beam guides for charged particles. The confinement in the transverse directions is due to the rotation of the electric and magnetic fields around the vortex line. Large class of exact solutions describing various types of relativistic beams formed by an electromagnetic wave with a simple vortex line is found both in the classical and in the quantum case. In the second case, the motion in the transverse direction is fully quantized. Particle trajectories trapped by a vortex are very similar to those in a helical undulator.