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Thermal ionization is a critical process at temperatures T > 10 3 K,particularly during star formation. An increase in ionization leads to adecrease in nonideal magnetohydrodynamics (MHD) resistivities, which has asignificant impact on protoplanetary disks and protostar formation. Wedeveloped an extension of the fast computational ionization method presented inour recent paper to include thermal ionization. The model can be used toinexpensively calculate the density of ions and electrons and the electriccharge of each size of grains for an arbitrary size distribution. This toolshould be particularly useful for the self-consistent calculation of nonidealMHD resistivities in multidimensional simulations, especially of protostellarcollapse and protoplanetary disks.

Fast methods to track grain coagulation and ionization. II. Extension to thermal ionization