Nonlinear quantum effects in electromagnetic radiation of a vortex electron

There is a controversy of how to interpret interactions electrons with large spatial coherence light and matter. When such an electron emits photon, it can do so either as if its charge were confined point within length, the region where square modulus wave function $|\psi|^2$ localized, or continuous cloud space spread over it. This problem was addressed in recent study R.~Remez, et al., Phys. Rev. Lett. {\bf 123}, 060401 (2019) conclusion drawn favor first (point) interpretation. Here we argue that there alternative explanation for measurements reported paper, which relies on purely classical arguments does not allow one refute second We propose experiment Smith-Purcell radiation from non-relativistic vortex carrying orbital angular momentum, unambiguously lead opposite conclusion. Beyond paraxial approximation, packet has non-point electric quadrupole moment, grows spreads results non-linear $L^3$-growth intensity length $L$ grating when much larger than packet's Rayleigh length. Such effect never been observed single and, detected, would be hallmark nature packet. Thus, two views are complementary each other radiates flow depending experimental conditions quantum state. Our conclusions hold class non-Gaussian packets emission processes formation exceed Cherenkov radiation, transition diffraction forth.