Can Intrinsic Electron Spin Phase-Stabilize Coherent Synchrotron Radiation? A Quantitative No-Go Analysis for Magnetized Helical Channels

We examine whether the intrinsic magnetic moment of a relativistic electron can provide a Stern–Gerlach restoring torque strong enough to stabilize an orbital helical phase relevant to coherent synchrotron radiation (CSR). A scalar phase-oscillator reduction is mathematically consistent and yields an Ornstein–Uhlenbeck variance plateau, but its physical interpretation requires four simultaneous conditions: a Maxwell-compatible structured field, a spin phase that remains an independent reference, charge-coupled Lorentz dynamics that do not overwhelm the spin-gradient force, and a genuine slow phase coordinate. With θ = k z − ω t − ϕ , a fixed- z, t slice of the transverse ansatz is a rotated quadrupolar structure rather than a radial magnetic-charge field; the relevant magnetostatic obstruction is therefore counter-rotation and fast 2Ω c Stern–Gerlach torque averaging, together with strong suppression in co-moving helical realizations. Live T-BMT dynamics produces coherent precession and adiabatic averaging rather than dissipative spin relaxation, eliminating the fixed spin-phase reference assumed by the reduced model. A three-dimensional relativistic test-particle audit in prescribed electromagnetic fields, using a Boris pusher, a leading dipole-gradient Stern–Gerlach force, and T-BMT spin precession, does not recover the scalar rotor stiffness. At r h = 1 μ m , the decisive scale ratio is F S G / F L ≃ μ / ( e β c r h ) = 1.9 × 10 − 7 . We therefore obtain a quantitative no-go boundary for spin-gradient orbital phase stabilization in the magnetized helical channels studied here. The resulting criteria provide a pre-PIC screening framework for future spin-assisted coherence proposals and distinguish polarization control by relativistic spin dynamics from orbital CSR phase control.