Continuum Theory of Thomson Scattering

Abstract

The theory of incoherent (Thomson) scattering of electromagnetic waves by thermal fluctuations in a plasma is rederived using continuum equations instead of kinetic theory. Because of the inherent simplicity of this approach, it is possible to extend the theory by including the effect of density fluctuations of the neutral molecules upon the scattering. The following results are obtained from the continuum theory: (1) The total predicted scattered power is exactly the same as in the previous kinetic theories. (2) The frequency spectrum of the scattered signal when neutral fluctuations are neglected agrees very well with the spectrum obtained using kinetic theory (with the Bhatnagar-Gross-Krook model for collisions) whenever ${\ensuremath{\lambda}}_{\mathrm{in}}$, the ion-neutral mean free path, is smaller than ${\ensuremath{\lambda}}_{0}$, the wave number of the incident signal. (3) The major difference in the spectrum when the neutral fluctuations are included is the addition of two resonances shifted from the signal frequency by $\ifmmode\pm\else\textpm\fi{}k{U}_{n}$, where $k=\frac{4\ensuremath{\pi}}{{\ensuremath{\lambda}}_{0}}$, and ${U}_{n}$ is the neutral sound speed. For a weakly ionized gas, these resonances are found to be significant whenever ${\ensuremath{\lambda}}_{\mathrm{in}}<{r}^{\frac{1}{2}}{\ensuremath{\lambda}}_{0}$, with $r$ the ratio of the electron density to the neutral-atom density.