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首先,详细推导了AVF型回旋加速器中束团粒子在曲线坐标系中的动力学方程(考虑和不考虑空间电荷相互作用力两种情况)。然后,在假定动力学方程中各参数值的前提条件下,用Lunge-Kutta方法对考虑空间电荷时的动力学方程进行了数值计算。结果表明,束晕的形成和发展同样也是强流回旋加速器中束流损失的一个主要原因。但束晕形成的机制不同于直线加速器的情况,它不是由共振和混沌引起,而是由于粒子的排斥运动和束团内粒子的涡流运动引起的。
First of all, the kinetic equations of bunch particles in the AVF cyclotron in the curvilinear coordinate system are deduced in detail (considering and not considering the space charge interaction force). Then, using the Lunge-Kutta method, the kinetic equation considering the space charge is numerically calculated on the premise of assuming the value of each parameter in the kinetic equation. The results show that the formation and development of halo are also one of the main causes of the beam loss in a strong-flow cyclotron. However, the mechanism of beam halo formation is different from linear accelerator in that it is not caused by resonance and chaos, but due to the particle’s repulsive motion and the particle’s vortex motion in the beam mass.