  The magnetohydrodynamics (MHD) of protoplanetary disks are strongly subject
to the non-ideal MHD effects arising from the low ionization fraction of the
disk gas. A strong electric field induced by gas motions can heat ionized gas
particles and can thereby affect the ionization balance in the disks. Our
previous studies revealed that in dusty protoplanetary disks, the Ohmic
conductivity decreases with increasing electric field strength until the
electrical breakdown of the disk gas occurs. In this study, we extend our
previous work to more general cases where both electric and magnetic fields
affect the motion of plasma particles, allowing us to study the impacts of
plasma heating on all non-ideal MHD effects: Ohmic, Hall, and ambipolar
diffusion. We find that the upper limit on the electric current we previously
derived applies even in the presence of magnetic fields. Although the Hall and
ambipolar resistivities can either increase or decrease with electric field
strength depending on the abundance of charged dust grains, the Ohmic
resistivity always increases with electric field strength. An
order-of-magnitude estimate suggests that a large-scale electric current
generated by gas motions in the inner part of protoplanetary disks could exceed
the upper limit. This implies that MHD motions of the inner disk, such as the
motion driven by the Hall-shear instability, could either get suppressed or
trigger electrical breakdown (lightning discharge). This may have important
implications for gas accretion and chondrule formation in the inner part of
protoplanetary disks.
