Space-charge effect on residual energy under intense ultrashort pulse laser

Can the space-charge effect reduce the above-threshold-ionization (ATI) energy? This problem is analyzed by using the technique of multiple-time-scale perturbation. As the optical frequency is much larger than the plasma frequency, the space-charge effect is then reduced to the ponderomotive effect. It is found that the ponderomotive effect on residual energy is great as half plasma period is larger than pulse length, however, it cannot reduce the ATI energy over the whole density range. The relevant experiments are analyzed. Their results support our conclusions. Finally, it is pointed out that for a given pulse laser there may be a density range available for optical held ionization x-ray laser over which only the ATI heating plays role.