  Slow magnetoacoustic waves are omnipresent in both natural and laboratory
plasma systems. The wave-induced misbalance between plasma cooling and heating
processes causes the amplification or attenuation, and also dispersion, of slow
magnetoacoustic waves. The wave dispersion could be attributed to the presence
of characteristic time scales in the system, connected with the plasma heating
or cooling due to the competition of the heating and cooling processes in the
vicinity of the thermal equilibrium. We analysed linear slow magnetoacoustic
waves in a plasma in a thermal equilibrium formed by a balance of optically
thin radiative losses, field-align thermal conduction, and an unspecified
heating. The dispersion is manifested by the dependence of the effective
adiabatic index of the wave on the wave frequency, making the phase and group
speeds frequency-dependent. The mutual effect of the wave amplification and
dispersion is shown to result into the occurrence of an oscillatory pattern in
an initially broadband slow wave, with the characteristic period determined by
the thermal misbalance time scales, i.e. by the derivatives of the combined
radiation loss and heating function with respect to the density and
temperature, evaluated at the equilibrium. This effect is illustrated by
estimating the characteristic period of the oscillatory pattern, appearing
because of thermal misbalance in the plasma of the solar corona. It is found
that by an order of magnitude the period is about the typical periods of slow
magnetoacoustic oscillations detected in the corona.
