We explore a regime of laser-driven plasma acceleration of electrons where the radial envelope of the laser-pulse incident at the plasma entrance is strongly mismatched to the nonlinear plasma electron response excited by it. This regime has been experimentally studied with the gemini laser using f/40 focusing optics in August 2015 and f/20 in 2008. The physical mechanisms and the scaling laws of electron acceleration achievable in a laser-plasma accelerator have been studied in the radially matched laser regime and thus are not accurate in the strongly mismatched regime explored here. In this work, we show that a novel adjusted-a0 model applicable over a specific range of densities where the laser enters the state of a strong optical shock, describes the mismatched regime. Beside several novel aspects of laser-plasma interaction dynamics relating to an elongating bubble shape and the corresponding self-injection mechanism, importantly we find that in this strongly mismatched regime when the laser pulse transforms into an optical shock it is possible to achieve beam-energies that significantly exceed the incident intensity matched regime scaling laws.
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