  A new self-injection scheme is proposed for the laser wakefield accelerator
in the nonlinear (cavity) regime using a pair of matched, copropagating laser
pulses which yields a pC electron bunch. By tuning their relative delay and
intensity, the subsequent betatron radiation energy can be considerably
$(\times 3)$ enhanced compared to the single pulse scheme for the same total
energy. A new condition for the optimal bubble size is derived and verified by
particle-in-cell simulations, demonstrating the advantages of the double-pulse
scheme for self-injection.
