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We demonstrate a sharp density transition for electron injection in laser wakefield acceleration through numerical study. This density transition is generated by a detached shock wave induced by a cylinder inserted into a supersonic helium gas flow. In a Mach 1.5 flow, the scale length of the density transition L_{grad} can approximately equal to plasma wavelength λ_{p} at the shock front, and can be further reduced with an increase of the flow Mach number. A density down ramp with L_{grad}≥λ_{p} can reduce the phase velocity of the wakefield and lower the energy threshold for the electrons to be trapped. Moreover, the quality of the accelerated beam may be greatly improved by precisely controlling of L_{grad} to be one λ_{p}. For an even sharper density down ramp with L_{grad}≪λ_{p}, the oscillating electrons in the plasma wave will up shift their phase when crossing the ramp, therefore a fraction of the electrons are injected into the accelerating field. For this injection mechanism, there is no threshold requirement for the pump laser intensity to reach wave breaking, which is a big advantage as compared with other injection mechanisms

Shock-wave-based density down ramp for electron injection