Fig. 1. Electron dynamics in an electric field with dimensionless amplitude eE/mcΩ = 2500 and a parallel magnetic field with dimensionless amplitude eB/mcΩ = 2000 rotating with angular frequency Ω, corresponding to the wavelength λ = 1 µm: (a) component of electron velocity transverse to the electric field; (b) component of electron velocity along the angular velocity vector Ω. Orange and cyan lines correspond to numerical solution of the nonreduced equations of motion (10) and (11) with radiation reaction taken into account via semiclassical and quantum approaches, respectively. Blue lines correspond to the average value of 100 “quantum” solutions. Black dashed lines correspond to the analytical solution (25) and (26).

Fig. 2. Dynamics of an electron with initial momentum p_x = −100 mc in a plane wave with amplitude a₀ = 500 and wavelength λ = 1 µm propagating along the x axis: (a) energy of electron normalized to its initial value; (b) maximum value of QED parameter χ: a₀(γ − p_x)/E_S. Red lines correspond to the classical solution without radiation reaction. Orange and blue lines correspond to numerical solution of the nonreduced equations of motion (10) and (11) with radiation reaction taken into account via semiclassical and quantum approaches, respectively. Black dashed lines correspond to the analytical solution (33) and (34). Note that for visual clarity, the black dashed line only depicts the amplitude of the oscillations of γ in (a).

Fig. 3. Electron dynamics in a model accelerator with E_acc = 30 TV/m and E_foc growing linearly from 0 to 30 TV/m at displacement 0.1 µm: (a) average rate of acceleration; (b) average value of QED parameter χ. Time is normalized to the initial value of the inverse betatron frequency ωb/γ0 of the electron. Blue lines correspond to the solution of the nonreduced equations of motion (10) and (11) without account of radiation reaction Orange lines correspond to the solution with radiation reaction taken into account via a semiclassical approach. The black dashed line corresponds to the analytical solution (46).