Abstract
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.