Averaging of the nonlinear Schrödinger equation with highly oscillatory magnetic potentials

We study a nonlinear Schrödinger equation with a time-dependent electromagnetic field potential which arises as an effective single particle model in X-ray Free Electron Lasers (XFEL). This equation is the fundamental model in XFEL. We prove the global well-posedness for this equation with an energy subcritical nonlinearity. We extend the study of Antonelli et al. (2014) to power nonlinearity with exponent 43≤σ<4, and our results confirm some numerical results of Huang et al. (2014).