  We find a remarkably enhanced production rate in star clusters (relative to
the field) of very short period, massive double-white-dwarf stars and of
giant-white dwarf binaries. These results are based on N-body simulations
performed with the new GRAPE-6 special purpose hardware and are important in
identifying and characterizing the progenitors of type Ia supernovae. The high
incidence of very close double-white-dwarf systems is the result of dynamical
encounters between (mostly) primordial binaries and other cluster stars.
Orbital hardening rapidly drives these degenerate binaries to periods under ~10
hours. Gravitational radiation emission and mergers producing
supra-Chandrasekhar objects follow in less than a Hubble time. If most stars
are born in clusters then estimates of the double white dwarf merger rates in
galaxies (due to cluster dynamical interaction) must be increased more than
tenfold. A majority of the Roche lobe overflow giant-white dwarf binaries are
not primordial; they are produced in exchange reactions. Most cases resulted in
a common-envelope and formation of a double-white-dwarf binary rather than
Supersoft X-ray sources leading possibly to a type Ia supernova.
