“…Using the Green's function GðsÞ consisting only of a fundamental harmonic (a multimode case will be considered later) GðsÞ ¼ 2κ ∥ cos ðksÞθðsÞ, where κ ∥ is the loss factor of a point particle per unit length, k ¼ 2π=λ is the wave vector, λ is the wavelength, and θ is the Heaviside theta-function, we write for the longitudinal field inside of the electron bunch [14,15] …”