The new planar-continuum potential, the sine-squared potential, is introduced to analyse the behaviour of particle motion in a planar channel, and particle motion equation is written by the well known pendulum; particle motion equation and oscillation period are solved exactly by Jacobi elliptic functions and the first kind of complete elliptic integrals; radiation intensity and spectral characteristics of Kumakhov radiation are further analyzed; The results show that it is possible to take Kumakhov radiation as a new y-ray laser.