  The ion sphere model introduced long ago by Salpeter is placed in a rigorous
theoretical setting. The leading corrections to this model for very highly
charged but dilute ions in thermal equilibrium with a weakly coupled,
one-component background plasma are explicitly computed, and the subleading
corrections are shown to be negligibly small. Such analytic results for very
strong coupling are rarely available, and they can serve as benchmarks for
testing computer models in this limit.
