Abstract
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.
Highlights
The scattering of electromagnetic radiation by free charges is a standard diagnostic of their distribution functions and for the diagnosis of intense or ultra-intense laser beams
The parametric representation of dynamics obtained in the previous subsection allows for an analytical computation of several quantities of interest associated with the trajectory in a rather straightforward manner, namely the fundamental period/frequency of the trajectory, the fundamental period/frequency at detector position, the drift velocity, the extremal values for the momentum components and the γ factor
The input beam field was chosen to be an electromagnetic wave in vacuum that propagates along the z axis, from −∞ towards +∞, and corresponds to a Gauss–Laguerre mode in the (x, y)-plane and, so, having some given orbital angular momentum (OAM)
Summary
The scattering of electromagnetic radiation by free charges is a standard diagnostic of their distribution functions (see for example [1,2] for applications in fusion plasmas) and for the diagnosis of intense or ultra-intense laser beams. Another reason to study such plane-wave solutions is to compute TS quantities (Doppler frequencies, spectral or spatial intensity distribution, etc.), with potential interest for fusion plasmas/laser beam diagnostics. The classical equations of motion for a relativistic electron subject to an incoming (non-necessarily monochromatic) electromagnetic plane wave have been solved exactly in an analytical ( implicit) way [27], which provided the basis for subsequent approximate studies of incoherent TS [28,29,30,31,32,33], by using the asymptotic Liénard–Wiechert retarded radiated fields [34]. In the above approximation scheme, the effect of the radiation reaction (becoming increasingly appreciable, for a near-infrared intense laser pulse, beyond 1023 W/cm2) and the controversial possibility of runaway solutions (a feature associated with the Abraham–Lorentz equation) [27,34,37] were disregarded from the outset
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