It seems to be widely accepted that the dark spots on Jupiter caused b
y the impacting fragments of comet Shoemaker-Levy 9 are due to dust pa
rticles which have formed immediately after the impacts. However, the
actual nature and origin of these grains is still uncertain. We propos
e that they may consist of amorphous carbon and have calculated the ti
me-dependent formation and growth of such dust particles assuming an e
xponential pressure decrease in an adiabatic fireball. The resulting p
roperties of the grains, e.g. their sizes, are consistent with observa
tions, The question whether carbon or silicate grains will form depend
s critically on the chemical composition of the Jovian atmosphere. If
a carbon-rich environment exists at the impact sites our model demonst
rates that there is enough time to grow amorphous carbon grains in the
fireballs rising immediately after the impacts.