Skin depth criterion for foil thickness in laser pressure acceleration of monoenergetic ions

Abstract

An analytical formalism is developed to study the nonlinear laser penetration through radiation pressure accelerated thin foils, employed to produce high energy ions. We include the effects of relativistic mass increase and nonuniform electron density compression due to the ponderomotive force in plasma permittivity. For foils like diamond the usual optimum foil thickness lopt=λLncra0/πn0 (where λL and a0 are the wavelength and normalized amplitude of the laser), at which the ponderomotive force on electrons balances the space charge force due to the ions left behind, is significantly below the skin depth unless the laser intensity is excessively large and significant laser transmission through the foil reduces the radiation pressure on it. The reflection coefficient decreases with laser field strength, though the ponderomotive force led electron compression tends to raise it. The reflection coefficient also decreases significantly with foil velocity, which is a sensitive function of laser field strength and foil thickness.