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The magnetohydrodynamics (MHD) of protoplanetary disks are strongly subjectto the non-ideal MHD effects arising from the low ionization fraction of thedisk gas. A strong electric field induced by gas motions can heat ionized gasparticles and can thereby affect the ionization balance in the disks. Ourprevious studies revealed that in dusty protoplanetary disks, the Ohmicconductivity decreases with increasing electric field strength until theelectrical breakdown of the disk gas occurs. In this study, we extend ourprevious work to more general cases where both electric and magnetic fieldsaffect the motion of plasma particles, allowing us to study the impacts ofplasma heating on all non-ideal MHD effects: Ohmic, Hall, and ambipolardiffusion. We find that the upper limit on the electric current we previouslyderived applies even in the presence of magnetic fields. Although the Hall andambipolar resistivities can either increase or decrease with electric fieldstrength depending on the abundance of charged dust grains, the Ohmicresistivity always increases with electric field strength. Anorder-of-magnitude estimate suggests that a large-scale electric currentgenerated by gas motions in the inner part of protoplanetary disks could exceedthe upper limit. This implies that MHD motions of the inner disk, such as themotion driven by the Hall-shear instability, could either get suppressed ortrigger electrical breakdown (lightning discharge). This may have importantimplications for gas accretion and chondrule formation in the inner part ofprotoplanetary disks.

The Generalized Nonlinear Ohm's Law: How a Strong Electric Field Influences Non-ideal MHD Effects in Dusty Protoplanetary Disks