Fast methods for tracking grain coagulation and ionization

Thermal ionization is a critical process at temperatures T > 10 3 K, particularly during star formation. An increase in leads to decrease nonideal magnetohydrodynamics (MHD) resistivities, which has significant impact on protoplanetary disks and protostar We developed an extension of the fast computational method presented our recent paper include thermal ionization. The model can be used inexpensively calculate density ions electrons electric charge each size grains for arbitrary distribution. This tool should useful self-consistent calculation MHD resistivities multidimensional simulations, especially protostellar collapse disks.