Relativistic electron acceleration in focused laser fields after above-threshold ionization

Electrons produced as a result of above-threshold ionization of high-[Formula presented] atoms can be accelerated by currently producible laser pulses up to GeV energies, as shown recently by Hu and Starace [Phys. Rev. Lett. [Formula presented] 245003 (2002)]. To describe electron acceleration by general focused laser fields, we employ an analytical model based on a Hamiltonian, fully relativistic, ponderomotive approach. Though the above-threshold ionization represents an abrupt process compared to laser oscillations, the ponderomotive approach can still adequately predict the resulting energy gain if the proper initial conditions are introduced for the particle drift following the ionization event. Analytical expressions for electron energy gain are derived and the applicability conditions of the ponderomotive formulation are studied both analytically and numerically. The theoretical predictions are supported by numerical computations.