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We investigated the classical nonlinear Thomson scattering (TS), from a single relativistic electron, generated by either: (a) an incoming plane wave monochromatic laser radiation and general elliptical polarization or (b) incoming radiations with intrinsic orbital angular momentum (OAM). Both (a) and (b) propagate along the z direction, with wave vector k0, frequency ω0, and initial phase φ0≠0 and have any intensity. Item (a) enables obtaining general electron TS Doppler frequencies and other quantities, for fusion plasmas. We explored the possibility of approximating nonlinear TS with OAM beams (Item (b)) by means of nonlinear TS with plane wave beams (Item (a)). For Item (a), a general explicit solution of the Lorentz relativistic equation and the subsequent TS are given in terms of ζ=ω0t−k0z (t denoting time). In particular, it includes the cases for linear and circular polarizations and φ0≠0 for fusion plasmas, thereby extending previous studies for φ0=0. The explicit solutions give rise to very efficient computations of electron TS Doppler frequencies, periods of trajectories, and drift velocities, and the comparisons with ab initio numerical solutions (for Item (a)) yield an excellent match. The approximate approach, using explicit solutions for Item (a), towards TS OAM (employing ab initio numerical computations for Item (b)), extending previously reported ones) yields a quite satisfactory agreement over time spans including several optical cycles, for a wide range of laser intensities, polarizations, and electron energies. The role of φ0≠0 was analyzed. A simple quantitative criterion to predict whether the agreement between the two approaches (a) and (b) would be observed over a given time span is discussed.

Electron Dynamics and Thomson Scattering for Ultra-Intense Lasers: Elliptically Polarized and OAM Beams