Relativistic consideration of a cylindrical mirror field focusing for a distant charged particle source

The analytical study of the focusing properties of a cylindrical mirror field in the nonrelativistic and relativistic energy areas for a flow of charged particles from a distant source is presented. The first-order focusing over all energy area and the expressions for focusing length and dispersion were calculated. The relativistic features of the focusing properties, such as the decreasing of both focusing length and dispersion by energy increase into deep relativistic region were obtained. The properties found are highly suitable for nuclear measurements, space and plasma investigations.