A new method to determine the peak intensity of focused relativistic laser pulses is experimentally justified. It is based on the measurement of spectra of electrons, accelerated in the beam waist. The detected electrons were emitted from the plasma, generated by nonlinear ionization of low-density gases (helium, argon, and krypton) in the focal area of a laser beam with the peak intensity >10 20 W/cm 2 . The measurements revealed generation of particles with the maximum energy of a few MeV, observed at a small angle relative to the beam axis. The results are supported by numerical particle-in-cell simulations of a laser-low-density plasma interaction. The peak intensity in the focal region derived from experimental data reaches the value of 2.5 × 10 20 W/cm 2 .

The dynamics of an electron driven by a relativistically intense laser pulse is analyzed on the basis of the equation of motion with the Lorentz force in the cases of linear and circular polarizations. Laser fields with nonplane phase fronts accelerate electrons in the longitudinal direction. An electron initially at rest is found not to move along figure-eight trajectories for the linear polarization, and not to move along circular trajectories for the circular polarization.

The fusion of light nuclei is the main source of valuable energy. Recent experiments with intense, ultrafast laser pulses acting on deuterium clusters have shown that these clusters can explode with sufficient kinetic energy to produce DD nuclear fusion. In earlier work (2004) we discussed already the effect of microfields on fusion processes in ion clusters. In view of the relevance of the problem we take up the problem again and discuss enhancement effects due to nonequilibrium velocity distributions with long tails and their influence on the relative motions on the ions. In particlular we discuss fractional kinetic equations including the influence of plasma microfields and finite size effects. We study the influence of nonequilibrium effects in the velocity distribution due to the Coulomb explosion of the clusters. The role of Cauchy-Lorentz nonequilibrium distributions of the velocity including long tails is discussed and their influence on the fusion rates is estimated.

The dynamics and energy spectra of electrons driven by a relativistically intense laser pulse are analyzed. The description is based on the numerical solution of the relativistic Newton’s equation with the Lorentz force generated by a strong focused optical field. After the interaction with it, electrons retain a considerable fraction of the energy of their oscillations during the interaction. The electron postinteraction energy spectrum is calculated. The energies in the spectrum high-energy tail are determined by the laser pulse intensity at the focal spot. An approach to estimating absolute values of the laser pulse intensity based on the measurement of the energy spectra of the electrons is proposed.

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