Analysis of the anomalous Doppler effect from quantum theory to classical dynamics simulations

The fundamental physics of anomalous and normal Doppler resonances between electrons and electromagnetic (EM) waves is analyzed using a quantum model that incorporates angular-momentum conservation. This work extends prior theory by explicitly linking the resonant integer m to the EM wave’s angular-momentum quantum number. Numerical simulations based on the volume-preserving algorithm (VPA) further confirm this correspondence. Moreover, a direct comparison of the energy-transfer ratio from translational energy to gyrokinetic energy during resonance, between classical dynamics and quantum predictions, is presented and verified numerically.