  We calculate the abundances of electrons and ions in the hot (> 500 K), dusty
parts of protoplanetary disks, treating for the first time the effects of
thermionic and ion emission from the dust grains. High-temperature ionization
modeling has involved simply assuming that alkali elements such as potassium
occur as gas-phase atoms and are collisionally ionized following the Saha
equation. We show that the Saha equation often does not hold, because free
charges are produced by thermionic and ion emission and destroyed when they
stick to grain surfaces. This means the ionization state depends not on the
first ionization potential of the alkali atoms, but rather on the grains' work
functions. The charged species' abundances typically rise abruptly above about
800 K, with little qualitative dependence on the work function, gas density, or
dust-to-gas mass ratio. Applying our results, we find that protoplanetary
disks' dead zone, where high diffusivities stifle magnetorotational turbulence,
has its inner edge located where the temperature exceeds a threshold value
~1000 K. The threshold is set by ambipolar diffusion except at the highest
densities, where it is set by Ohmic resistivity. We find that the disk gas can
be diffusively loaded onto the stellar magnetosphere at temperatures below a
similar threshold. We investigate whether the "short-circuit" instability of
current sheets can operate in disks and find that it cannot, or works only in a
narrow range of conditions; it appears not to be the chondrule formation
mechanism. We also suggest that thermionic emission is important for
determining the rate of Ohmic heating in hot Jupiters.
