  The ionization-induced injection in laser wakefield acceleration has been
recently demonstrated to be a promising injection scheme. However, the energy
spread controlling in this mechanism remains a challenge because continuous
injection in a mixed gas target is usually inevitable. Here we propose that by
use of certain initially unmatched laser pulses, the electron injection can be
constrained to the very front region of the mixed gas target, typically in a
length of a few hundreds micro meters determined by laser-driven bubble
deformation. Under some optimized conditions, the injection region is well
limited within $200\rm \mu m$ and the electron beam with central energy of 383
MeV, energy spread of 3.33% in FWHM, normalized emittance of 3.12 mm mrad and
charge of 14.58 pC can be obtained according to particle-in-cell simulations.
Both multi-dimensional simulations and theoretical analysis illustrate the
effectiveness of this scheme.
