Nonlinear Thomson Scattering In Laser-Plasma Interactions

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.