The evolution of quasi-isentropic magnetohydrodynamic waves of small but finite amplitude in an optically thin plasma is analyzed. The plasma is assumed to be initially homogeneous, in thermal equilibrium and with a straight and homogeneous magnetic field frozen in. Depending on the particular form of the heating/cooling function, the plasma may act as a dissipative or active medium for magnetoacoustic waves, while Alfvén waves are not directly affected. An evolutionary equation for fast and slow magnetoacoustic waves in the single wave limit, has been derived and solved, allowing us to analyse the wave modification by competition of weakly nonlinear and quasiisentropic effects. It was shown that the sign of the quasi-isentropic term determines the scenario of the evolution, either dissipative or active. In the dissipative case, when the plasma is first order isentropically stable the magnetoacoustic waves are damped and the time for shock wave formation is delayed. However, in the active case when the plasma is isentropically overstable, the wave amplitude grows, the strength of the shock increases and the breaking time decreases. The magnitude of the above effects depends upon the angle between the wave vector and the magnetic field. For hot (T > 10 4 K) atomic plasmas with solar abundances either in the interstellar medium or in the solar atmosphere, as well as for the cold (T < 10 3 K) ISM molecular gas, the range of temperature where the plasma is isentropically unstable and the corresponding time and length-scale for wave breaking have been found.

The dynamics of linear perturbations in a radiatively cooling dusty plasma is considered, with the charge of both dust (Z d ) and plasma (Z p ) components being allowed to vary with their densities. It is shown that in the longwavelength limit corresponding to the characteristic cooling length, when the plasma can be treated as quasineutral, the presence of dust particles changes the criteria for radiation instability, regardless the charging process of the dust particles. In particular, the condensation (isobaric) mode is shown to be stabilized (destabilized) if in the equilibrium, the relation between densities of the dust n d and plasma n under the quasineutrality condition, (d ln n d /d ln n) q < 1 (> 1) is satisfied, while the isentropic mode is stabilized (destabilized) when the opposite inequalities take place; the isochoric mode is unaltered. Numerical estimates show that these effects can be important in hot phases (T ∼ 10 6 K) of the interstellar plasma, and in tokamak plasma near the walls.

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The effects of the second viscosity on sound waves propagating in plasmas at thermochemical equilibrium are analyzed. It is found that this viscosity can be more important than the dynamical viscosity as well as than the thermometric conductivity, in particular, in photoionized plasmas with arbitrary metallicity Z. The strongest damping per unit wavelength always occurs for sound waves with a period of the order of the ionization relaxation time. Additionally, such a damping is more efficient for plasmas with solar abundances ͑Z =1͒ than for primordial plasmas ͑Z =0͒. In collisionally heated pure hydrogen plasmas the second viscosity becomes zero.

The nonlinear stability and time evolution of thermal structures constituted by optically thin plasmas are analyzed. The structure has been assumed to be heated at a rate ∼Tm, cooled by the standard cooling function for plasmas with solar abundances and with an anisotropic thermal conduction coefficient. Second-order analytical results are obtained for the thermal equilibrium solutions. For nonhomogeneous solutions and strong disturbances, a numerical analysis is carried out. The angle between the temperature gradient and the magnetic field is a crucial parameter in determining the stability of structures close to the marginal state. A central overheating may occur for large enough amplitudes of the initial disturbance imposed on stable steady-state thermal structures. Implications of the above results in the formation of cool structures in the solar atmosphere and in the interstellar medium are outlined.