Scaling high-order harmonic generation from laser-solid interactions to ultrahigh intensity

Coherent x-ray beams with a subfemtosecond (<10(-15)  s) pulse duration will enable measurements of fundamental atomic processes in a completely new regime. High-order harmonic generation (HOHG) using short pulse (<100  fs) infrared lasers focused to intensities surpassing 10(18)  W cm(-2) onto a solid density plasma is a promising means of generating such short pulses. Critical to the relativistic oscillating mirror mechanism is the steepness of the plasma density gradient at the reflection point, characterized by a scale length, which can strongly influence the harmonic generation mechanism. It is shown that for intensities in excess of 10(21)  W cm(-2) an optimum density ramp scale length exists that balances an increase in efficiency with a growth of parametric plasma wave instabilities. We show that for these higher intensities the optimal scale length is c/ω0, for which a variety of HOHG properties are optimized, including total conversion efficiency, HOHG divergence, and their power law scaling. Particle-in-cell simulations show striking evidence of the HOHG loss mechanism through parametric instabilities and relativistic self-phase modulation, which affect the produced spectra and conversion efficiency.