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This paper develops a unified linear theory of local cross-field plasmainstabilities, such as the Farley-Buneman, electron thermal, and ion thermalinstabilities, in collisional plasmas with fully or partially unmagnetizedmulti-species ions. Collisional lasma instabilities in low-ionized, highlydissipative, weakly magnetized plasmas play an important role in the lowerEarth's ionosphere and may be of importance in other planet ionospheres, staratmospheres, cometary tails, molecular clouds, accretion disks, etc. In thesolar chromosphere, macroscopic effects of collisional plasma instabilities maycontribute into significant heating -- an effect originally suggested fromspectroscopic observations and relevant modeling. Based on a simplified5-moment multi-fluid model, the theoretical analysis produces the generallinear dispersion relation for the combined Thermal-Farley-Buneman Instability(TFBI). Important limiting cases are analyzed in detail. The analysisdemonstrates acceptable applicability of this model for the rocesses understudy. Fluid-model simulations usually require much less computer resourcesthan do more accurate kinetic simulations, so that the apparent success of thisapproach to the linear theory of collisional plasma instabilities makes itpossible to investigate the TFBI (along with its possible macroscopic effects)using global fluid codes originally developed for large-scale modeling of thesolar and planetary atmospheres.

Unified fluid-model theory of $\mathbf{E}\times\mathbf{B}$ instabilities  in low-ionized collisional plasmas with arbitrarily magnetized multi-species  ions