Magnetic field dragging in accretion discs

We consider a thin accretion disc of half-thickness H, vertically threaded by a magnetic field. The field is due to contributions from both the disc current and an external current (giving rise to a uniform external field). We derive an integro-differential equation for the evolution of the magnetic field, subject to magnetic diffusivity η and disc accretion with radial velocity νr. The evolution equation is solved numerically, and a steady state is reached. The evolution equation depends upon a single, dimensionless parameter |D=2/ (3H\ |ᵣ|) = (R/H (/) |⁠, where the latter equality holds for a viscous disc having viscosity ν. At the disc surface, field lines are bent by angle i from the vertical, such that tan |i=1. 52D^-1|⁠. For values of D somewhat less than unity, the field is strongly concentrated towards the disc centre, because the field lines are dragged substantially inwards.