寻找新光源, 特别是短波长激光光源引起了人们的广泛兴趣。在时空周期场中运动的带电粒子表现出了预期的行为。指出了置于外场中的超晶格是典型的时空周期场。假设掺杂超晶格的导带底是周期调制的, 在经典力学框架内, 将非相对论粒子在时空周期场中的运动方程化为带有阻尼项和受迫项的摆方程。在无阻尼情况下, 利用摄动法导出了系统的一阶近似解, 讨论了高次谐波辐射和辐射强度; 用Hamiltonian原理和相平面方法讨论了系统的稳定性。在阻尼情况下, 利用Melnikov方法讨论了系统的临界特征和混沌行为。结果表明, 非相对论粒子的高次谐波辐射存在局部极大, 可望作为短波长激光光源。由于系统的稳定性与它的参数有关, 只需适当调节这些参数, 系统的稳定性就能得到保证。

Looking for a new light source, especially short wavelength laser light source, has attracted widespread attention. The charged particles in a space-time periodic field show the expected behaviors. It is pointed out the superlattice in the external field is the typical space-time periodic field. It assumes that the conduction band of the doping superlattice is periodically modulated, the motion equation of the non-relativistic particle in a space-time periodic field is reduced to a generalized pendulum equation with a damping term and a forced term in the classical mechanics. In the absence of damping, first order approximate solution of the system is derived by perturbation method, the higher-order harmonic radiation and radiation intensity are discussed; and the stability of the system is discussed by using Hamiltonian principles and phase plane methods. In the damping case the critical properties and a chaotic behaours for the system are analyzed by Melnikov method. The results show that the local maximum of higher-order harmonic radiation for non-relativistic particle exists and it is expected as a short-wavelength laser source. Because the stability of the system relates to its parameters, its stability can be guaranteed only by appropriately adjusting these parameters.