Estimates for the efficient production of antihydrogen by lasers of very high intensities

Abstract

Starting from the non-linear relativistic equations of motion for charged particles in the very high intensity fields of laser radiation, the maximum kinetic energy ɛkin of the resulting oscillation is derived exactly. In non-relativistic conditions ɛkin agrees with the well-known valuee2Ev2/(2m0ω2|n|), showing a dependence on the rest massm0 of the particle. In the relativistic case, the mass dependence vanishes. The multipole radiation is calculated on the basis of Sommerfeld's formula for relativistic conditions. It is shown that this radiation is not important for oscillation energies up to\( \in _{kin^{mr} } \)=70m0c2 for electrons in neodymium glass laser radiation and up to higher values for CO2 lasers and for protons. With the limitationm0c2 < ekin <\( \in _{kin^{mr} } \), the formula for ɛkin is used to calculate the pair production (a) for singly oscillating particles in vacuum without collisions and (b) for plasmas with collisions. Taking into account the local increase of the effective electric laser field near the cut-off density due to the decrease of ¦n¦ (n is the complex refractive index), there is the possibility of efficient proton pair production at intensities of 1019 W cm−2 for neodymium glass lasers and of 1017 W cm−2 for CO2 lasers, besides electron pair production.