  We explore the hypothesis that the magnetic fields of neutron stars are of
fossil origin. For parametrised models of the distribution of magnetic flux on
the Main Sequence and of the birth spin period of the neutron stars, we
calculate the expected properties of isolated radio pulsars in the Galaxy using
as our starting point the initial mass function and star formation rate as a
function of galacto-centric radius. We then use the 1374 MHz Parkes Multi-Beam
Survey of isolated radio pulsars to constrain the parameters in our model and
to deduce the required distribution of magnetic fields on the main sequence. We
find agreement with observations for a model with a star formation rate that
corresponds to a supernova rate of 2 per century in the Galaxy from stars with
masses in the range 8 - 45 solar masses and predict 447,000 active pulsars in
the Galaxy with luminosities greater than 0.19 mJy kpc^2. The progenitor OB
stars have a field distribution which peaks near 46 Gauss with about 8 percent
of stars having fields in excess of 1,000 Gauss. The higher field progenitors
yield a population of 24 neutron stars with fields in excess of 10^14 Gauss,
periods ranging from 5 to 12 seconds, and ages of up to 100,000 years, which we
identify as the dominant component of the magnetars. We also predict that high
field neutron stars (log B>13.5) originate preferentially from higher mass
progenitors and have a mean mass of 1.6 solar masses, which is significantly
above the mean mass of 1.4 solar masses calculated for the overall population
of radio pulsars.
