The rapid development of laser technologies promises a significant growth of peak laser intensity from 1022 W/cm2 to >1023 W/cm2, allowing the experimental studies of strong field quantum-electrodynamics physics and laser nuclear physics. Here, we propose a method to realize the ultra-intense laser field amplification of petawatt-class laser pulse in moderate density plasma via relativistic self-focusing and tapered-channel focusing. Three-dimensional particle-in-cell simulations demonstrate that almost an order of magnitude enhancement of laser intensity is possible even though the γ-ray radiation results in massive laser energy loss. In particular, with a seed laser intensity of ∼1023 W/cm2, duration of 82.5 fs and power of 31 petawatt, one can obtain ∼1024 W/cm2 intensity and up to ∼60% energy conversion efficiency from the initial seed laser to the focused laser in plasma with density of 3.3 × 1022/cm3. This may pave the way to the new research field of ultra-intense laser plasma interaction in the upcoming laser facilities.
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