Cumulation and mixing of ions in a tubular focus of a high-power laser pulse

As applied to laser acceleration of ions, we have constructed an analytical solution to the Cauchy problem for the kinetic equation, which describes the radial motion of particles under the action of a ponderomotive force in a tubular focus of a high-power laser beam propagating in a transparent plasma. For axisymmetric geometry, we have obtained the time and spatial dependences of the ion distribution function and have found their integral characteristics, such as density, average velocity, and energy spectrum. The appearance of ion density peaks inside the laser caustics, the cumulation of ions on the axis, and the effect of the formation of a multi-flux regime of ion motion are described analytically. The efficiency of the generation of neutron bursts by a laser pulse in the focal region in the case of cylindrical cumulation of ions is estimated.