Ambipolar diffusion regulated collapse of filaments threaded by   perpendicular magnetic fields
  We numerically reproduce the density profiles for filaments that are in magnetohydrostatic and pressure equilibrium with their surroundings obtained in Tomisaka (2014) and show that these equilibria are dynamically stable. If the effect of ambipolar diffusion is considered, these filaments lose magnetic support initiating cloud collapse. The filaments do not lose magnetic flux. Rather the magnetic flux is redistributed within the filament from the centre towards the envelope.   The rate of the collapse is inversely proportional to the fractional ionisation and two gravitationally-driven ambipolar diffusion regimes for the collapse are observed as predicted in Mouschovias & Morton (1991). For high values of the ionisation coefficient, that is $X \geq 10^{-7}$, the gas is strongly coupled to the magnetic field and the Jeans length is larger than the ambipolar diffusion length scale. Then the collapse is governed by magnetically-regulated ambipolar diffusion. For $X \lesssim 10^{-8}$, the gas is weakly coupled to the magnetic field and the magnetic support is removed by gravitationally-dominated ambipolar diffusion. Here, neutrals and ions only collide sporadically, that is the ambipolar diffusion length scale is larger than the Jeans length.   When decaying turbulence is included, additional support is provided to the filament. This slows down the collapse of the filament even in the absence of a magnetic field. When a magnetic field is present, the collapse rate increases by a ratio smaller than for the non-magnetic case. This is because of a speed-up of the ambipolar diffusion due to larger magnetic field gradients generated by the turbulence and because the ambipolar diffusion aids the dissipation of turbulence below the ambipolar diffusion length scale. The highest increase in the rate is observed for the lowest ionisation coefficient and the highest turbulent intensity. 
C. A. Burge, S. Van Loo, S. A. E. G. Falle and T. W. Hartquist
astro-ph.GA