Cosmic-Ray-driven Thermal Modes in Partially Ionized Viscous Plasma with Hall Current

Abstract This research investigates the dynamics of cosmic-ray-driven thermal modes within a partially ionized plasma permeated by a magnetic field. A two-fluid model is adopted to capture the intricate physics arising from the presence of neutral dynamics. The ion–cosmic fluid is described using a nonideal magnetohydrodynamic framework, incorporating ion and neutral viscosities, the Hall current, and ion–neutral collisions. Neutral dynamics are characterized by neutral viscosity, pressure, and collisional interactions. The derived general dispersion relation reveals two dominant modes: a collisional neutral thermal viscous mode and a Hall-modified cosmic magnetothermal viscous mode. The domains of instability for the neutral thermal viscous mode are determined, while the stability of the ion–cosmic thermal viscous mode is assessed using the Routh–Hurwitz criterion, yielding critical lengths for isochoric, isobaric, and isentropic modes. In the collisional regime, a seventh-order dispersion relation is derived and analyzed numerically. Next, the second dominant mode of the general dispersion relation is further analyzed in both transverse and longitudinal directions relative to the magnetic field. In the transverse direction, a seventh-order collisional cosmic magnetothermal viscous mode is obtained, influenced by ion and neutral viscosities, the diffusion coefficient, collisions, and the cosmic and ion acoustic speeds. This mode is further investigated analytically and numerically. Numerical estimates demonstrate that the diffusion coefficient and cosmic pressure enhance the growth rate of thermal modes. The critical wavelength of the magnetothermal cosmic mode is calculated. In the longitudinal direction, the obtained modes exhibit no substantial cosmic influence, but instead represent Hall-modified collisional Alfvén waves.