The dynamics of an electron bunch irradiated by two focused colliding super-intense laser pulses and the resulting γ and e − e + production are studied. Due to attractors of electron dynamics in a standing wave created by colliding pulses the photon emission and pair production, in general, are more efficient with linearly polarized pulses than with circularly polarized ones. The dependence of the key parameters on the laser intensity and wavelength allows to identify the conditions for the cascade development and γe − e + plasma creation. With the advent of 10 PW laser facilities, the new and so far unexplored field of ultra-intense laser matter interaction will become accessible experimentally [1]. The intensities of the order of 10 23−24 W/cm 2 will be achieved in these interactions, therefore the possibility of efficient generation of gamma-ray photons or even electronpositron pairs has attracted much attention in the last decade (see review article [2] and references therein). In a strong electromagnetic field, electrons can be accelerated to such high energy that the radiation reaction starts to play an important role [3]. Moreover, a new regime of the interaction can be entered, dominated by quantum electrodynamics (QED) effects such as pair production and cascade development [2,4]. If a photon with sufficient energy is emitted due to multiphoton Compton scattering and then interacts with n laser photons, new electron-positron pair can be created via the multiphoton Breit-Wheeler process [5]. Since the probabilities of the photon emission and pair creation depend on the particle momentum, on the electromagnetic field strength, and on their mutual orientation, it is necessary to elucidate the motion of electrons (positrons) in the electromagnetic field in the strong radiation reaction regime.In this Letter we present the analysis of the electron motion and photon emission modeled as a discreet process in the electromagnetic (EM) standing wave (SW) generated by two colliding focused short super-intense laser pulses interacting with an electron bunch. The interaction of charged particles with an intense EM fields is characterized by two dimensionless relativistically invariant parameters [6]. First parameter is a 0 = eE 0 /m e ω 0 c, the dimensionless EM field amplitude, which measures the energy gain of an electron over the field wavelength in units of 2πm e c 2 . It is often referred to as the classical nonlinearity parameter. Here e and m e are the electron charge and mass, E and ω 0 are EM field strength and frequency, c is the speed of light, respectively.
The second parameter is, where E S = m 2 e c 3 /e ≃ 1.3 × 10 18 V/m [7], is the Planck constant, and F µν is the EM field tensor. The parameter χ e,γ characterizes the interaction of electrons (positrons) and photons with the EM field. Depending on the energy of charged particles and field strength the interaction happens in one of the following regimes parametrized by a 0 and χ e,γ : (i) a 0 > 1, the electron dynamics is relativistic; (ii) a 0 > ǫ −1...