We consider the quantum dynamics of a charged particle on the plane ${bf R}^2$ in the presence of a time-periodic magnetic field ${bf B}(t) = (0,0,B(t))$ with $B(t+T) =B(t)$ which is always perpendicular to this plane. Then the charged particle has the following three states accordingly to the mass of the particle, charge of the particle and $B(t)$; (I). For any $t$, the particle is in some compact region (bound state). (II). The particle goes to a distance with velocity $O(t)$. (III) The particle goes to a distance with velocity $O(e^{|t|})$. In this talk, we focus on the case (III) and see that the Hamiltonian of case (III) is closely related to so called homogeneous repulsive Hamiltonian. By using this similarity, we prove the Mourre estimate for the case (III).