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
v2Te/c2,
as it is for the case in the absence of collective effects, but of the
order
ω2pe/ω2
times less –
which, for example in the solar interior, where
ω2pe/ω2
is of the order of
v2Te/c2,
is then
of the order of v4Te/c4.