在经典力学框架内, 把粒子在周期外场中的运动方程化为摆方程, 利用广义三角函数的Bessel展开讨论了系统存在高次谐波辐射的可能性, 并在固定力矩情况下讨论了系统的基本特征。用Jacobian椭圆函数和第一类椭圆积分解析地给出了无扰动系统的解和振动周期, 并用数值方法分析了系统的相平面特征和它的稳定性。结果表明:当外力矩为零时, 系统的接受度最大, 俘获的电子数最多, 辐射强度最强; 随着外力矩增加, 接受度降低; 当无量纲的外力矩为1时, 接受度为零, 系统处于临界状态。临界状态与系统参数有关, 只需适当调节参数, 可望输出强度比较大的高次谐波辐射。

In the classical mechanics frame, the particle motion equation in the periodic field is reduced to a pendulum equation, a possibility of the existence of a higher harmonic radiation is discussed by using Bessel function expansion of a generalized trigonometrical function, and the system basic characteristic in the fixing moment situation was discussed. Analytically going the equation solution and the period of vibration for the non-perturbed system by the Jacobian elliptic function and the first kind of elliptic integral, also analyzing the system phase plane characteristic and its stability with the numerical method.The result show that when the moment is zero, the system acceptance is maximum, the capture electronic number is the most, and the radiation intensity is the biggest. Increases along with the moment, acceptance reduces. When the value of dimensionless moment is 1, acceptance is the zero, the system is at the critical condition. Critical condition is related to system para-meter. Only obtaining the suitable adjustment parameter, it were hopeful to obtain higher harmonic radiation with the bigger intensity.