In the present work a closed system of kinetic equations is obtained from the truncation of the BBGKY hierarchy for the description of the vacuum creation of an electron - positron plasma and secondary photons due to a strong laser field. This trunca
tion is performed in the Markovian approximation for the one-photon annihilation channel which is accessible due to the presence of the strong external field. Estimates of the photon production rate are obtained for different domains of laser field parameters (frequency nu and field strength E). A huge quantity of optical photons of the quasiclassical laser field is necessary to satisfy the conservation laws of energy and momentum of the constituents (e-, e+, gamma) in this channel. Since the number of these optical photons corresponds to the order of perturbation theory, a vanishingly small photon production rate results for the optical region and strongly subcritical fields E << E_c. In the gamma-ray region nu <~ m the required number of laser photons is small and the production rate of photons from the one-photon annihilation process becomes accessible to observations for subcritical fields E <~ E_c. In the infrared region the photon distribution has a 1/k spectrum typical for flicker noise.
It is well known that in the presence of strong external electromagnetic fields many processes forbidden in standard QED become possible. One example is the one-photon annihilation process considered recently by the present authors in the framework o
f a kinetic approach to the quasiparticle e-e+ gamma plasma created from vacuum in the focal spot of two counter-propagating laser beams. In these works the domain of large values of the adiabaticity parameter gamma >> 1 (corresponding to multiphoton processes) was considered. In the present work we estimate the intensity of the radiation stemming from photon annihilation in the framework of the effective mass model where gamma < 1, corresponding to large electric fields E < E_c=m^2/e and high laser field frequencies (the domain characteristic for X-ray lasers of the next generation). Under such limiting conditions the resulting effect is sufficiently large to be accessible to experimental observation.
We consider the possibility of experimental verification of vacuum e^+e^- pair creation at the focus of two counter-propagating optical laser beams with intensities 10^{20}-10^{22} W/cm^2, achievable with present-day petawatt lasers, and approaching
the Schwinger limit: 10^{29} W/cm^2 to be reached at ELI. Our approach is based on the collisionless kinetic equation for the evolution of the e^+ and e^- distribution functions governed by a non-Markovian source term for pair production. As possible experimental signals of vacuum pair production we consider e^+e^- annihilation into gamma-pairs and the refraction of a high-frequency probe laser beam by the produced e^+e^- plasma. We discuss the dependence of the dynamical pair production process on laser wavelength, with special emphasis on applications in the X-ray domain (X-FEL), as well as the prospects for mu^+mu^- and pi^+pi^- pair creation at high-intensity lasers. We investigate perspectives for using high-intensity lasers as ``boosters of ion beams in the few-GeV per nucleon range, which is relevant, e.g., to the exploration of the QCD phase transition in laboratory experiments.
