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We study the role of dust–dust collisional charging in protoplanetary discs. We show that dust–dust collisional charging becomes an important process in determining the charge state of dust and gas if there is dust enhancement and/or dust is fluffy, so that dust surface area per disc volume is locally increased. We solve the charge equilibrium equations for various disc environments and dust number density η, using general purpose graphic processor units andcuda programming language. We found that as the dust number density η increases, the charge distribution experiences four phases. In one of these phases, the electrostatic field E caused by dust motion increases as . As a result, macroscopic electric discharge takes place, for example at (in units of minimum-mass solar nebula values, considering two groups of fluffy dust with radii of 10−2 and ). We present a model that describes the charge-exchange processes in the discs as an electric circuit. We derive analytical formulae of critical dust number density for lightning, as functions of dust parameters. We estimate the total energy, intensity and event ratio of such discharges (‘lightning’). We discuss the possibility of observing lightning and sprite discharges in protoplanetary discs by astronomically low frequency waves, infrared images, ultraviolet lines and high energy gamma rays. We also discuss the effects of lightning on chondrule heating, planetesimal growth and magnetorotational instability of the disc. [ABSTRACT FROM AUTHOR]

We study how the magnetorotational instability (MRI) in protoplanetary disks is affected by the electric discharge caused by the electric field in the resistive magnetohydrodynamic. We performed three-dimensional shearing box simulations with various values of plasma beta and electrical breakdown models. We find that the MRI is self-sustaining in spite of the high resistivity. The instability gives rise to the large electric field that causes the electrical breakdown, and the breakdown maintains the high degree of ionization required for the instability. The condition for this self-sustained MRI is set by the balance between the energy supply from the shearing motion and the energy consumed by ohmic dissipation. We apply the condition to various disk models and study where the active, self-sustained, and dead zones of MRI are located. In the fiducial minimum-mass solar-nebula model, the newly found sustained zone occupies only a limited volume of the disk. In the late-phase gas-depleted disk models, however, the sustained zone occupies a larger volume of the disk. [ABSTRACT FROM AUTHOR]