The transverse oscillatory motion of trapped electrons under the influence of the laser fields trailing the temporally-asymmetric driving laser pulse was investigated with a theoretical model of the quasi-steady state solution of trapped electron dynamics in the cavity. Our studies show that the transverse oscillation of electrons accelerated in the ion cavity can increase drastically due to the resonance with the laser field of the tail of the temporally-asymmetric pulse. The motion of the accelerated electrons can be represented by a forced harmonic oscillation and it was confirmed by 2D particle-in-cell simulations. These transverse oscillations of beams lead to micro-bunching as well, which can be used for generation of femtosecond coherent radiations of keV range photon energies. (C) 2012 Elsevier B.V. All rights reserved.