  Type Ia Supernovae (SNe Ia) may originate from a wide variety of explosion
scenarios and progenitor channels. They exhibit a factor of about 10 difference
in brightness and, thus, a differentiation in the mass of 56Ni->56Co->56 Fe. We
present a study on the fate of positrons within SNe Ia in order to evaluate
their escape fractions and energy spectra. Our detailed Monte Carlo transport
simulations for positrons and gamma-rays include both beta + decay of 56 Co and
pair production. We simulate a wide variety of explosion scenarios, including
the explosion of white dwarfs (WD) close to the Chandrasekhar mass, M(Ch),
He-triggered explosions of sub-M Ch WDs, and dynamical mergers of two WDs. For
each model, we study the influence of the size and morphology of the progenitor
magnetic field between 1 and 1E13 G. Population synthesis based on the observed
brightness distribution of SNe Ia was used to estimate the overall
contributions to Galactic positrons due to escape from SN Ia. We find that this
is dominated by normal-bright SNe Ia, where variations in the distribution of
emitted positrons are small. We estimate a total SNe Ia contribution to the
Galactic positrons of < 2% and, depending on the magnetic field morphology,
less than 6...20% for M(Ch) and sub-M(Ch), respectively.
