Carrier-envelope phase effects in plasma-based electron acceleration with few-cycle laser pulses.

Carrier-envelope phase effects during the interaction of relativistically intense few-cycle laser pulses with a plasma are studied in the ''bubble'' regime when an electron cavity (bubble) is formed behind the pulse. We show that for few-cycle laser pulses the cavity shape becomes asymmetric and depends strongly on the carrier-envelope phase. The carrier-envelope phase varies when the laser pulse propagates in plasma, which causes transverse oscillations of the cavity. Furthermore, the beam of electrons trapped by the cavity becomes modulated in the polarization plane. To describe these effects we derive an analytical model extended beyond the ponderomotive approximation. The degree of plasma cavity asymmetry as a function of the laser-plasma parameters is calculated. The obtained results are verified by particle-in-cell simulations.