  We reveal the classical and quantum regimes of free electron interaction with
radiation, common to the general variety of radiation sources (e.g. FEL,
Smith-Purcell), Dielectric Laser Accelerator (DLA) and Photo-Induced Near-Field
Electron Microscopy (PINEM). Modelling the electron with initial conditions of
a coherent quantum electron wavepacket (QEW), its topology in phase-space
uniquely defines a universal distinction of three interaction regimes (and
their particle-wave duality transition): point-particle-like acceleration,
quantum wavefunction (PINEM), and a newly reported regime of anomalous PINEM
(APINEM). The quantum interference beat of APINEM is capable of improving the
spectral resolution of post-selective electron microscopy, and the
particle-wave duality transition reveals the history-dependent nature of
quantum electron interaction with light.
