It is generally accepted that protoplanetary discs have a dead zone at the mid-plane - a region of low turbulence (Gammie 1996). There is a critical level of ionisation required for the MRI to drive turbulence. Below this level, the gas is not well coupled to the magnetic field. The innermost parts of the hot enough to be thermally ionised. Further out, the dominant sources of ionisation are cosmic rays and X-rays from the central star (Glassgold et al. 2004). These may ionise the surface layers and allow the MRI to operate there. In the outer most parts of the disc, because the surface density declines with radius, the rays may penetrate all the way to mid-plane.

The critical surface density that is ionised by cosmic rays or X-rays is still not well understood. There have been recent attempts to calculate the detailed ionisation balance of the disc due to external sources of ionisation and subject to processes such as ambipolar diffusion and the presence of dust that tend to suppress the ionisation (e.g. Bai & Goodman 2009, Perez-Becker & Chiang 2011). When applied to protostellar discs, these calculations result in accretion rates much smaller than those observed in T Tauri stars. This discrepancy is as yet unresolved.