摘要
利用哈密顿-雅科比方法,完整求解了平面电磁波中的电子运动方程。并对于给定的矢势,给出电子运动方程的精确解。利用电子运动方程的精确解,在电子平均静止坐标系求得谐波辐射平均功率的角分布。得到谐波振幅的生成函数f(ρ0,ρ,ψ,t),其按照变量t的罗朗展开的系数αm(ρ0,p,ψ)是谐波振幅的基本组成部分。αm(ρ0,ρ,ψ)被表示为激光强度和偏振以及观测方向等物理量的函数,在数学上是一类新的特殊函数。系统分析了函数αm(ρ0,ρ,ψ)的表示和性质以及各类特殊无穷求和中的整体性质和行为。计算得到在电子初始静止系和电子与激光场对撞的实验室系内谐波辐射功率的角分布。在其他条件保持不变,偏振度变化时,讨论了背向Thomson散射谐波功率的极值问题。对最重要的基频背向Thomson散射情形,证明了其最大值为圆偏振入射场,最小值为线偏振入射场,并给出其表示。运用相对论和规范变换等方法,系统讨论了经典电磁场理论的对称性,指出某些文献中方法与结论之错误。
The equations of motion for an electron in plane wave electromagnetic fields are solved by applying the Hamilton-Jacobi technique. And the exact solutions of the electron motion are given under the given vector potentials. The average power per unit solid angle of the harmonic radiation is caculated using the solution of the electron motion in the frame where the electron is on the average at rest. The generating function f(ρ0,ρ,ψ,t) for the harmonic radiation amplitudes is found and its coefficient of Laurent expantion according to the variable t denoted by am(ρ0,ρ,ψ) is fundamental element of the harmonic radiation amplitude. The function am(ρ0,ρ,ψ) which is a new sort of advanced function in mathematics is expressed by the physical variables such as the intensity of the laser field, the degree of elliptical polarization and the observation direction. The representations and properties of the function am(ρ0,ρ,ψ), and the global characters and behaviors of the infinite summations related to am(ρ0,ρ,ψ) in the special cases are analyzed systematically. The average power per unit solid angle of the harmonic radiation in the frame where the electron is initially at rest and in the laboratory frame where the laser and the electron meet in a collinear geometry is calculated. Keeping all the other situations the same while varying the degree of elliptical polarization, the extremum property of the backscattered radiation power of the nonlinear Thomson scattering is discussed. It is found that the circular polarization reaches maximum while the linear polarization minimum at the same situations in the fundamental backscattered radiation which is the most important case. The symmetry of classical electromagnetic theory is discussed systematically by the methods of special relativity and guage transformations. And the wrong methods and conclusions made in some references are pointed out.
引文
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