Calculation of the nonlinear relativistic Thomson scattering fields and Its application to electron distribution function diagnostic

Abstract

Analytical results obtained recently of the ab-initio classical incoherent Thomson Scattering (TS) spectrum from a single-electron (Alvarez-Estrada et al 2012 Phys. Plasmas 19 062302) have been numerically implemented in a paralelized code to efficiently compute the TS emission from a given electron distribution function, irrespective of its characteristics and/or the intensity of the incoming radiation. These analytical results display certain differences, when compared with other authors, in the general case of incoming linearly and circularly polarized radiation and electrons with arbitrary initial directions. We regard such discrepancies and the ubiquitous interest in TS as motivations for this work. Here, we implement some analytical advances (like generalized Bessel functions for incoming linearly polarized radiation) in TS. The bulk of this work reports on the efficient computation of TS spectra (based upon our analytical approach), for an electron population having an essentially arbitrary distribution function and for both incoming linearly and circularly polarized radiation. A detailed comparison between the present approach and a previous Monte Carlo one (Pastor et al 2011 Nuclear Fusion 51 043011), dealing with the ab-initio computation of TS spectra, is reported. Both approaches are shown to fully agree with each other. As key computational improvements, the analytical technique yields a × 30 to × 100 gain in computation time and is a very flexible tool to compute the scattered spectrum and eventually the scattered electromagnetic fields in the time domain. The latter are computed explicitly here for the first time, as far as we know. Scaling laws for the power integrated over frequency versus initial kinetic energy are studied for the case of isotropic and monoenergetic electron distribution functions and their potential application as diagnostic tools for high-energy populations is briefly discussed. Finally, we discuss the application of these techniques to the obtention and interpretation of TS spectra in fusion plasmas and the inverse problem, i.e. the construction of the electron distribution function that best fits experimentally obtained TS data.

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].…”

“…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,…”