A charged particle moving along the direction of the low crystal face index can penetrates through the crystal as easily as it does through a channel. This phenomenon is so-called channeling effect. The classical physics points out that an accelerated charged particle radiates energy continuously when moving in an electromagnetic field. The analogous situation occurs in crystal channel. When a charged particle moves in an accelerated way through a lattice field

the radiation energy can be produced. It is such an extremely strong lattice field that results in the rather higher radiation energy. For a positron with the energy of 10MeV

the radiation energy can reach keV in order of magnitude. The motion behavior of the channeling particle is governed by the interaction potential between the particle and the crystal. The potential

which we generally use

is Lindhard potential

Moliere potential

and sine-squared potential. Because the motion behavior of the channeling particle is most similar with that of a free electron moving in a Wiggler

it is expected that the channeling radiation can be changed as X-laser or γ-laser to pretend new high energy laser source. In 4

th

-order Lindhard potential approximation

the particle motion equation can be reduced to a second order nonlinear differential equation with a cubic term under the frame of the classical mechanics. By employing both the Jaco-bian ell iptic function and the first kind complete elliptic integral

the solution of the equation is derived and the channeling radiation frequency is obtained in an analytical expression. Besides

the instantaneous radiation intensity

the average radiation intensity and the maximum radiation frequency of positrons are also obtained. As an application of channeling radiation of positrons

the average intensity and the maximum frequency of single crystal silicon are calculated. The results indicate that it is possible to make channeling radiation as γ-laser.