The acceleration dynamics of electrons in a laser wakefield
accelerator is discussed, in particular the coupling of longitudinal
and transverse motion. This coupling effect is important for electrons
injected with a velocity below the laser pulse group velocity. It is
found that the electron bunch is adiabatically focused during the
acceleration and that a finite bunch width contributes to bunch
lengthening and growth of energy spread. These results indicate the
importance of a small emittance for the injected electron bunch.
