Pergamon zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA J. Quant. Spectrosc. Radiat. Transfer Vol. 55, No. 6, pp. 809-813, 1996 Copyright 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved S0022-4073(% )00049-0 0022~4073/96 $15.00 + 0.00 STIMULATED SCATTERING AND FREQUENCY DIFFUSION OF PHOTONS IN PLASMAS V. N. TSYTOVICH,“t R. BINGHAM,” U. DE ANGELIS,’ and A. FORLANI* “Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX1 1 OQX, U.K. and bDepartment of Physical Sciences, University of Naples, Italy (Received 7 September 1995) Abstract-Stimulated scattering on electrons and frequency diffusion in the transport equation for photons in plasmas are considered including the collective plasma effects. The results are applied to the solar interior (where collective plasma effects are not negligible for a wide range of frequencies) to find the effect on the solar opacity. Copyright 0 1996 Elsevier Science Ltd 1. INTRODUCTION This is the third in a series of papers dealing with relativistic corrections to scattering of photons in plasmas and their effects on the solar opacity. In the first two papers in the series’,* the corrections to spontaneous scattering were found. Here we consider the induced scattering of photons by the plasma electrons and the effect of frequency diffusion taking into account the collective plasma effects. The transport equation for the distribution function Nk of photons of wavenumber zyxwvutsrqponm k and frequency wk = zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA w (k) can be written, in the quasi-classical approximation, as’ _ + Nk s -‘- af $1 d’p d’k ’ Nk' Wj$h(k - &‘).-- 8P W I6 where and $= C&$, 2 E(O)= l-2 ( 1 (1) is the group velocity, ape = J4ne*n,/m, is the plasma frequency, _P@) is the electrons’ (a = e) or ions’ (LX = i) distribution function in the plasma and Wpl, is the probability of scattering on electrons or ions, respectively. The first two terms on the rhs of (1) represent the spontaneous processes and the last term gives the contribution of stimulated scattering on electrons (we neglect stimulated scattering on ions which is smaller by the factor m,/mi). tpermanent address: General Physics Institute, Russian Academy of Sciences, Moscow, Russia. 809