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指出了对周期介质加上周期变化的电场,可望获得时空周期变化的周期场;在这种场中运动的带电粒子表现出了人们预期的行为。对这种情况下的电磁辐射进行了讨论,并以掺杂超晶格为例进行具体分析。首先,在经典力学框架内和偶极近似下,把粒子的纵向运动方程化为广义摆方程;在小振幅近似下,把无扰动系统的摆方程进一步化为Duffing方程。用Jacobian椭圆函数和第一类椭圆积分严格地给出了粒子运动轨道和它的运动周期;讨论了粒子的辐射能量和辐射强度。结果表明,当超晶格的势阱深度为1eV,为λp=100nm,γ=104时,电子的辐射频率为8.85×1019,位于X-能区。
Pointed out that the periodic medium plus periodic changes in the electric field is expected to obtain periodic changes in space-time field; moving particles in this field showed the expected behavior. Electromagnetic radiation in this case is discussed, and doped superlattice as an example for specific analysis. First, the equations of longitudinal motion of particles are generalized pendulum equations in the framework of classical mechanics and dipole approximation. The pendulum equations of undisturbed systems are further reduced to Duffing equations under small amplitude approximation. The Jacobian elliptic function and the elliptic integral of the first kind are used to give the trajectory of the particle and its moving period strictly. The radiation energy and the radiation intensity of the particle are discussed. The results show that when the trap depth of the superlattice is 1eV, λp = 100nm, γ = 104, the electron radiation frequency is 8.85 × 1019, which is located in the X-ray region.