Monte Carlo approach to Thomson scattering in relativistic fusion plasmas with allowance for ultraintense laser radiation

Abstract

Thomson scattering (TS) of electromagnetic radiation by relativistic electrons is of great interest as an electron distribution diagnostics in high temperature plasma devices. A Monte Carlo approach to TS simulation has been implemented. It is based on first principles, i.e. on the integration of electron trajectories and on the computation and averaging of radiated Liénard–Wiechert fields. The treatment is relativistic. Nonlinear effects, arising from ultraintense lasers (both linear and circular polarizations having been considered) and/or from highly energetic electrons, are included from the outset. TS spectra from isotropic monoenergetic electron distribution functions and from the relativistic Maxwellian distribution have been extensively studied, both for low-intensity and for ultraintense incoming laser. A particularly simple quadratic dependence of S 2(ω) on ω has been found in the case of monoenergetic distributions. Numerical results are checked against known analytical results for low-intensity lasers, and found to be in agreement with them. For high-intensity lasers, new effects on scattered spectra arise, like an overall red-shift or the appearance of higher harmonics. The numerical methods developed in this work are general enough to deal with anisotropic and/or non-Maxwellian distribution functions.

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

“…2 We remind that 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 (although implicit) way, 12 which provided the basis for subsequent approximate studies of incoherent TS, [13][14][15][16][17][18] by using the Liénard-Wiechert radiated fields. 19 Recently, 20 the present authors extended those researches. We shall remind in this section some basic ingredients for Ref.…”

“…In our previous work, 20 the resulting solution for x(t) obtained from the numerical integration of Eq. (5) (also shown there to fully agree with the analytical solution 12 ) was used (with t replaced by t 0 ) to evaluate the dynamical electromagnetic field radiated by the particle, by plugging the former directly into the standard E rr;1 and B rr;1 .…”

“…We consider that a tiny spectrally flat (ideal) detector, placed at y and perpendicular to n, receives and measures the time average of 0 cEðy; tÞ 2 rr;1 (referred to in Ref. 20 as mean power or scattered power spectrum of the radiated field in a, perhaps, loosely way). It is understood that such an expression for the time average includes the sum over the two possible orthogonal polarizations of the radiated field, but they can be accounted for separately if needed.…”

“…We shall remind in this section some basic ingredients for Ref. 20, which will also be essential here: the mathematical set-up for the incoming laser beam, the classical equations of motion for the electron subject to the former, a very short quantitative reminder of the exact solution for an incoming, non-necessarily monochromatic, plane wave radiation 12 (to be amplified in Appendix A, later), and the Liénard-Wiechert radiated fields 19 as the basis for an approximate application to incoherent TS. The results of Ref.…”

“…Further reference to Ref. 20 will be made when absolutely necessary in the main text and, when several detailed aspects and generalizations thereof be required, in Appendix A. …”