Free-Electron Lasers from ACORN: Coherent Radiation as Synchronized Odd-Channel Curvature

Free-electron lasers (FELs) are traditionally explained through relativistic electron bunching and stimulated emission of synchrotron radiation. While accurate descriptively, this model does not explain the origin of coherence, why brightness scales quadratically with electron count, or why lasing requires relativistic energies. In this paper we show that FEL operation follows inevitably from the ACORN framework, in which every massive particle contains two orthogonal curvature channels: a neutral even component mNE and an electromagnetic odd component m_eq (m_eq = (4/(3.Pi)).m). The "channels" rotate as a hyperbolic phasor in the (x, cT) plane at a frequency closely related to the Compton frequency ωC = mc2/ℏ - which we term "the heartbeat frequency". An undulator does not merely accelerate electrons—it synchronizes their odd-channel curvature phases. Coherence of meq across a beamproduces constructive curvature interference, which projects into 4D as coherent electromagnetic radiation. The FEL gain condition is therefore not primarily spatial bunching, but phase alignment of Compton heartbeat curvature.This interpretation explains FEL coherence, tunability, saturation, brightness scaling, and the need for relativistic energies. It predicts new operational regimes, including heartbeat-limited linewidths and curvature-based gain control, and removes the conceptual dependence on photon exchange models. Electron lasers operate because ACORNs can be synchronized.