Nonlinear relativistic single-electron Thomson scattering power spectrum for incoming laser of arbitrary intensity

Abstract

The classical nonlinear incoherent Thomson scattering power spectrum from a single relativistic electron with incoming laser radiation of any intensity, investigated numerically by the present authors in a previous publication, displayed both an approximate quadratic behavior in frequency and a redshift of the power spectrum for high intensity incoming radiation. The present work is devoted to justify, in a more general setup, those numerical findings. Those justifications are reinforced by extending suitably analytical approaches, as developed by other authors. Moreover, our analytical treatment exhibits differences between the Doppler-like frequencies for linear and circular polarization of the incoming radiation. Those differences depend nonlinearly on the laser intensity and on the electron initial velocity and do not appear to have been displayed by previous authors. Those Doppler-like frequencies and their differences are validated by new Monte Carlo computations beyond our previuos ones and reported here.

On the similarity between Thomson scattering from high-intensity circularly polarised lasers and synchrotron radiation

“…In this section the mathematical formalism used to compare both phenomena in the frequency-domain is presented; it will provide the basis for the comparison in the time-domain in section 3. The steps to be taken closely follow the results for TS in [24][25][26][27]. Excellent monographs on classical electrodynamics and SR exist, which have been instrumental at the starting level of the present research: see, for example, [29,30,35,36].…”

“…x x x x = + + ( ) ( )ˆ( )ˆ( )ˆis the solution of the dynamical equations of motion for the incoming circularly polarized monochromatic plane wave and t x c 3 x x = ¢ -( ) , t′ being the 'radiation' time for the electron; p(ξ) is the momentum of the radiating electron, also following from those dynamical equations [24,25]. x 1 (ξ), x 2 (ξ), x 3 (ξ) and p(ξ) are collected in appendix C. The quantities γ 1 , f 1 and f 2 , employed below, are integration constants of the dynamical equations of motion [24,25]. Λ (ξ) C can be recast as:…”

“…Notice that ω 0 ξ is dimensionless and that we have approximated exp[iω((R/c)+(g 0,C /ω 0 ))];exp[iω(R/c)] in the quadratures given in equations (25) and (26),…”

“…To the best of our knowledge, no attempt has been made to probe fusion plasmas with ultra-intense circularly polarised lasers, either with diagnostic purposes, or to obtain from them a light source with the special properties predicted from the nonlinear effects. Numerical work presented by the authors in [24,25,27] suggest that using an ultra-intense laser could shift the emitted spectrum to the red, and hence spectral zones that are normally unaccessible due to practical considerations, like the one around the laser wavelength, could now be directly observed, increasing the diagnostic capability. The predicted harmonics to the (bulk) scattered spectrum would also be of potential diagnostic use.…”

“…In previous papers the authors have developed Monte Carlo and analytical methods for the ab-initio computation (in a classical framework, disregarding quantum effects) of TS spectra under very general conditions regarding the electron distribution function, as well as the intensity and the polarization of the incoming laser radiation, for plasma fusion diagnostic applications [24][25][26][27][28]. In the course of these investigations,…”