Numerical computation of Thomson scattering spectra for non-Maxwellian or anisotropic electron distribution functions

Abstract

Monte Carlo techniques applied to Thomson scattering (TS) power spectrum computation have been extended so as to include non-Maxwellian and anisotropic electron distribution functions (EDFs). First, a simple model has been selected for the spatial (angular) anisotropy of electron velocities (uniformly distributed around an axis of angular symmetry on a cone of semiaperture θ anis), while the energies are distributed according to a lower-hybrid-like model function. Spectra have been computed, and their dependence with the EDF model parameters has been given. The most noticeable changes in the spectrum with respect to the isotropic Maxwellian are the broadening and blue-shift of the spectrum due to suprathermal electrons, and the presence of satellite or additional maxima (that can be either red-shifted or blue-shifted with respect to the thermal Maxwellian maximum) coming from the anisotropy of the EDF. Also, extensive numerical computations have been carried out on angularly non-separable EDFs (meaning that the sampling of the distribution function cannot be done independently on angle and energy variables), like the relativistic bi-Maxwellian (with or without drift). The connection of these results with some recent TS measurements reported by Yamada et al (2010 Rev. Sci. Instrum. 81 10D522) and more generally, with the possibility of detecting non-Maxwellian or anisotropic EDF features with TS, has been discussed.

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

“…As a further development (also in section 2), the explicit temporal evolution of the scattered electromagnetic fields at the detector position is given, as it is employed to benchmark the new software against its Monte Carlo counterpart and to provide a precise and quantitative measure of the agreement between both approaches. The results of some detailed algebraic comparisons among Doppler frequencies and power spectra reported by other authors and in our preceding works [19][20][21] and the present one are summarized in subsection 2.8: such comparisons are important (albeit, recognizedly, somewhat technical) because, in particular, Doppler frequencies have a critical influence on the power spectra. Section 3 contains the bulk of our work.…”

“…The present paper implements new numerical procedures for computing the TS power spectra (and the scattered electromagnetic fields involved) for an arbitrary electron distribution function. It is based on the analytical treatment in [20] and compares its efficiency with the results of the Monte Carlo codes in [19,21]. The analytical formulae used in this work are critically compared with results obtained from other authors and it is shown that they represent a generalization in the case of incoming circularly polarised light, due to the general geometrical set-up considered for the electron-wave interaction.…”

“…In previous papers [19][20][21], we developed Monte Carlo and analytical methods for the ab-initio computation of TS spectra under very general conditions with respect to the distribution function of the electrons, as well as the intensity and the polarization of the incoming laser radiation. In particular, reference [19] was devoted to the Monte Carlo computation of the electron trajectories, i.e.…”

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].…”

“…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,…”