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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 physical mechanisms that cause the heating of the solar corona are still far from being completely understood. However, recent highly resolved observations with the current solar missions have shown clear evidence of frequent and very localized heating events near the chromosphere that may be responsible for the observable high temperatures of the coronal plasma. In this paper, we perform one-dimensional hydrodynamic simulations of the evolution of a hypothetical loop model undergoing impulsive heating through the release of localized Gaussian energy pulses near the loop's footpoints. We find that when a discrete number of randomly spaced pulses is released, loops of length L ¼ 5 and 10 Mm heat up and stay at coronal temperatures for the whole duration of the impulsive heating stage, provided that the elapsed time between successive heat injections is P175 and P215 s, respectively. The precise value of the critical elapsed time is sensitive to the loop length. In particular, we find that for increased loop lengths of 20 and 30 Mm, the critical elapsed time rises to about 240 and 263 s, respectively. For elapsed times longer than these critical values, coronal temperatures can no longer be maintained at the loop apex in spite of continued impulsive heating. As a result, the loop apex undergoes runaway cooling well below the initial state, reaching chromospheric temperatures ($10 4 K) and leading to the typical hot-cool temperature profile characteristic of a cool condensation. For a large number of pulses (up to $1000) having a fully random spatiotemporal distribution, the variation of the temperature along the loop is highly sensitive to the spatial distribution of the heating. As long as the heating concentrates more and more at the loop's footpoints, the temperature variation is seen to make a transition from that of a uniformly heated loop to a flat, isothermal profile along the loop length. Concentration of the heating at the footpoints also results in a more frequent appearance of rapid and significant depressions of the apex temperature during the loop evolution, most of them ranging from $1:5 ; 10 6 to $10 4 K and lasting from about 3 to 10 minutes. This behavior bears a tight relation with the strong variability of coronal loops inferred from SOHO observations in active regions of the solar atmosphere.