Laser-electron interaction from classical electrodynamics

2 Laser-electron interaction from classical electrodynamics 

Salamin and Faisal (1996,1997) analysed harmonic generation and the ponderomotive scattering of electrons in intense laser fields based on a classical relativistic 

Here a denotes the maximum field amplitude, rj is the ellipticity together with the pulse-shape function g(rj), which depends on the phase rj = (ot — k r. The laser beam is characterized by the frequency co and the wave vector k with ck = co. The transversality condition implies k A — 0. For a charged point particle interacting with this external electromagnetic field, the Hamilton-Jacobi equation reads 

The constant vector s and the constant are determined by the initial conditions. Insertion of this ansatz into (1.2) together with the transversality condition for the vector potential allows for the solution (Sarachik and Schappert 1970) 

The initial conditions for the electron motion mentioned above are consistent with the choice s — yo me fio and = — yomc, respectively (Salamin and Faisal 1996). Given this result for S the energy of the electron can be derived via E(rj) = —3S/dt. Subtracting the rest energy the kinetic energy of the electron can be expressed as 

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