Reply to ‘Comment on “Collective effects in bremsstrahlung in plasmas” ’

Abstract

We reply here to a criticism of our paper (Tsytovich et al. 1996) by Iglesias (1997).

In our paper we present a very general formulation of collective effects in bremsstrahlung that is valid for any non-equilibrium non-Maxwellian particle distribution. This result is given in (2.20) early in the paper. The standard treatments of bremsstrahlung found in books like Bekefi (1966) are only for thermal plasmas, where the fluctuation–dissipation theorem is valid. Note that the fluctuation–dissipation theorem cannot be used for non-thermal or non-dipole fields, and in this respect the method we use is more general. Our method is the more complex of the approaches used, but, as stated, it can handle situations that cannot be treated by the standard approach. Our main result is the formula (2.20), which is valid for any non-equilibrium non-Maxwellian particle distribution, and which cannot be found anywhere else in the literature. Furthermore, we find new qualitative effects indicating that the ion–ion bremsstrahlung (which is always neglected in the literature) is not small in the case where the collective effects are taken into account, and is in fact, for certain frequencies, of the order of the electron–electron bremsstrahlung. The other qualitatively new result is that, where collective effects are important, the electron–electron bremsstrahlung is not of the order v²_Te/c², as it is for the case in the absence of collective effects, but of the order ω²_pe/ω² times less – which, for example in the solar interior, where ω²_pe/ω² is of the order of v²_Te/c², is then of the order of v⁴_Te/c⁴.