  We develop models for the self-similar collapse of magnetized isothermal
cylinders. We find solutions for the case of a fluid with a constant toroidal
flux-to-mass ratio (Gamma_phi=constant) and the case of a fluid with a constant
gas to magnetic pressure ratio (beta=constant). In both cases, we find that a
low magnetization results in density profiles that behave as rho ~ r^{-4} at
large radii, and at high magnetization we find density profiles that behave as
rho ~ r^{-2}. This density behaviour is the same as for hydrostatic filamentary
structures, suggesting that density measurements alone cannot distinguish
between hydrostatic and collapsing filaments--velocity measurements are
required. Our solutions show that the self-similar radial velocity behaves as
v_r ~ r during the collapse phase, and that unlike collapsing self-similar
spheres, there is no subsequent accretion (i.e. expansion-wave) phase. We also
examine the fragmentation properties of these cylinders, and find that in both
cases, the presence of a toroidal field acts to strengthen the cylinder against
fragmentation. Finally, the collapse time scales in our models are shorter than
the fragmentation time scales. Thus, we anticipate that highly collapsed
filaments can form before they are broken into pieces by gravitational
fragmentation.
