  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 occur simultaneously when an intense laser pulse propagating
inside a 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) controlled plasma bubble undulation induced by the self steepening
laser pulse produces a unique electron injector: Expanding Phase controlled
Undulating Bubble (EPUB). The longitudinal structure of the electron bunch
injected 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 and
CEP controlled energy spectrum and angular distribution is analyzed as a
promising application of EPUB produced beams.
