VFEL operates as follows. An electron beam with electron velocity $u$ passes through a photonic crystal (resonator) of the length $L$. Under diffraction conditions two strong electromagnetic waves can be excited in the resonator. If simultaneously electrons are under synchronism condition, they emit electromagnetic radiation in directions depending on diffraction conditions. None of other electronic devices uses principles of dynamical diffraction of electromagnetic radiation in resonator.

In our previous investigations it is shown that VFEL is a dynamical system with multiple bifurcation points and chaotic dynamics. In this work a conservation law for integro-differential system presented here is obtained. VFEL efficiency analysis is proposed. Some steady-state regimes are investigated analytically and numerically.