Resonantly Interacting Quantum Plus Classical Waves

Abstract: Dynamics of electrons subjected to a constant amplitude classical elec-

tromagnetic (EM) wave is investigated as a fundamental, representative

problem in the physics of interacting quantum and classical waves. In

the nonrelativistic regime (electrons as Schr¨odinger waves), the elec-

tron energy acquires a constant and a time dependent part. Driven by

EM waves, both parts scale strongly with the amplitude, but we expect

no resonant enhancement since the parallel electron “speed” of nonrel-

ativistic electrons could never match the wave phase velocity. In the

relativistic regime (electron as a Klein–Gordon wave), however, a class

of electron waves (with parallel speed matching the EM phase speed)

are resonantly excited to extremely high energies. Such a direct reso-

nant energy transfer from intense electromagnetic waves constitutes a

mechanism that could, in principle, power the most energetic of cos-

mic rays (this mechanism will work on protons just as well). Some

predictions of the theory will, hopefully, be tested in laboratory laser

experiments. The nonrelativistic calculations will also be examined

in the context of recent experiments using photon-induced near-field

electron microscopy in detail.