用Jacobian椭圆函数求解了一维晶化束的非线性动力学方程,并用第一类全椭圆积分表示了粒子振动周期.在经典物理学框架内,讨论了储存环中作相对论运动的带电粒子的辐射能损,以及由于辐射能损导致的束流冷却.结果表明, 由于辐射损失束流将进一步冷却.

Suppose only the focussing and the Coulomb force act on an ion, where the focussing force is linear and the Coulomb force is nonlinear. When the two forces are balanced, the critical spacing between ions can be obtained. In this paper the radiation energy loss and the cooling of the onedimensional crystallization beam are discussed. The coherent transverse equation of particle motion has been reduced to Duffing equation with the hardspring properties in the frame of Newton mechanics. This nonlinear equation has been solved exactly by a Jacobian elliptical function, and the motion period of a particle has been expressed exactly by the firstkind complete elliptical integral. The energy loss and the beam cooling by the electromagnetic radiation of a charged particle in a storage ring have been discussed in a superrelativistic case. It is that the radiation energy loss of the onedimensional crystallization beam will result further in the beam cooling.