Polarization control of electron injection and acceleration in the plasma by a self steepening laser pulse

We describe an interplay between two injection mechanism of background electrons into an evolving plasma bubble behind an intense laser pulse: one due to the overall bubble expansion, and another due to its periodic undulation. The two mechanisms are found to occur simultaneously when an intense laser pulse propagating inside plasma forms a shock like steepened front. Periodic undulations of the plasma bubble along the laser propagation path can either inhibit, or conspire with electron injection due to bubble expansion. We show that Carrier Envelope Phase (CEP) of the self steepening laser pulse produces a unique electron injector Expanding Phase controlled Undulating Bubble (EPUB). The longitudinal structure of the electron bunch trapped by the EPUB can be controlled by laser polarization and power, resulting in high charge (multiple nano Coulombs) high current (tens of kilo Amperes) electron beams with ultra short (femtosecond scale) temporal structure. Generation of high energy betatron radiation with polarization controlled spectrum is analyzed as a promising application of EPUB produced beams