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 spontaneously 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. The behaviours of the charged particles moved in a crystal channel are controlled by the interaction potential between a charged particles and the crystal. Usual interaction potential is Lindhad potential

Moliere potential and Sine-squared potential. The channeling radiation is described analytically by using the sine-squared potential. The bend of the crystal is equivalent to constant moment. Thus in a framework of the classical mechanics the motion equation of a particles in a bent crystal is reduced to pendulum equation with a constant moment by using the sine-squared potential.The phase planar properties of the system are analyzed by the numerical method.In the small amplitude approximation the motion equation of a particles is reduced to the equation for the hard spring-oscillator.The solution of the equation and the period of the particle motion are expressed exactly by means of Jacobian elliptic function and 1st kind elliptic integral.The properties of the radiation spectrum is discussed.It pointed out it is possible to take channeling radiation as a new γ-Laser.As example

maximum radiation frequence

deflective angle ψ of a positron in the carbon crystal are calculated.The result is coincident basically with other work.