  The collapse and fragmentation of initially prolate and oblate, magnetic
molecular clouds is calculated in three dimensions with a gravitational,
radiative hydrodynamics code. The code includes magnetic field effects in an
approximate manner: magnetic pressure, tension, braking, and ambipolar
diffusion are all modelled. The parameters varied for both the initially
prolate and oblate clouds are the initial degree of central concentration of
the radial density profile, the initial angular velocity, and the efficiency of
magnetic braking (represented by a factor $f_{mb} = 10^{-4}$ or $10^{-3}$). The
oblate cores all collapse to form rings that might be susceptible to
fragmentation into multiple systems. The outcome of the collapse of the prolate
cores depends strongly on the initial density profile. Prolate cores with
central densities 20 times higher than their boundary densities collapse and
fragment into binary or quadruple systems, whereas cores with central densities
100 times higher collapse to form single protostars embedded in bars. The
inclusion of magnetic braking is able to stifle protostellar fragmentation in
the latter set of models, as when identical models were calculated without
magnetic braking (Boss 2002), those cores fragmented into binary protostars.
These models demonstrate the importance of including magnetic fields in studies
of protostellar collapse and fragmentation, and suggest that even when magnetic
fields are included, fragmentation into binary and multiple systems remains as
a possible outcome of protostellar collapse.
