  Sedimentation of the neutron rich isotope $^{22}$Ne may be an important
source of gravitational energy during the cooling of white dwarf stars. This
depends on the diffusion constant for $^{22}$Ne in strongly coupled plasma
mixtures. We calculate self-diffusion constants $D_i$ from molecular dynamics
simulations of carbon, oxygen, and neon mixtures. We find that $D_i$ in a
mixture does not differ greatly from earlier one component plasma results. For
strong coupling (coulomb parameter $\Gamma>$ few), $D_i$ has a modest
dependence on the charge $Z_i$ of the ion species, $D_i \propto Z_i^{-2/3}$.
However $D_i$ depends more strongly on $Z_i$ for weak coupling (smaller
$\Gamma$). We conclude that the self-diffusion constant $D_{\rm Ne}$ for
$^{22}$Ne in carbon, oxygen, and neon plasma mixtures is accurately known so
that uncertainties in $D_{\rm Ne}$ should be unimportant for simulations of
white dwarf cooling.
