  Non-linear electron screening corrections of stellar nuclear fusion rates are
calculated analytically in the framework of the Debye-Huckel model and compared
with the respective ones of Salpeter's weak screening approximation. In typical
solar conditions, the deviation from Salpeter's screening factor is less than
one percent, while for hotter stars such corrections turn out to be of the
order of one percent only over the limits of the Debye-Huckel model. Moreover,
an investigation of the impact of the derived non-linear screening effects on
the solar neutrino fluxes yields insignificant corrections for both the pp and
CNO chain reactions.
