Stability and convection in compressible partially ionized plasma layers: nonlinear and linear analysis

Abstract The thermal convection of compressible, partially ionized plasma has been investigated using nonlinear and linear analyses across three boundary configurations. Nonlinear analysis was carried out via the energy method, while linear analysis was assessed using the normal mode method. For free-free boundaries, exact solutions were obtained, whereas, for rigid-rigid and rigid-free boundaries, the higher-order Galerkin-weighted residual method was employed for numerical results. The critical Rayleigh numbers for both analyses coincide, indicating global stability and confirming the absence of subcritical regions. The impact of collisional frequency on energy decay was quantified, revealing a significant effect on the decay rate, although it does not affect the Rayleigh number. The principle of exchange of stabilities was confirmed in the linear analysis. Compressibility delays the onset of convection. The critical Rayleigh numbers were computed as 986.267, 2,561.64, and 1,650.97 for the free–free, rigid–rigid, and rigid–free cases, respectively, demonstrating that plasma confined between rigid–rigid surfaces exhibits the highest thermal stability.