Amplification of compressional magnetohydrodynamic waves in systems with forced entropy oscillations

The propagation of compressional MHD waves is studied for an externally driven system. It is assumed that the combined action of the external sources and sinks of the entropy results in the harmonic oscillation of the entropy (and temperature) in the system. It is found that with the appropriate resonant conditions fast and slow waves get amplified due to the phenomenon of parametric resonance. In addition, it is shown that the considered waves are mutually coupled as a consequence of the nonequilibrium state of the background medium. The coupling is strongest when the plasma $\beta \approx 1$. The proposed formalism is sufficiently general and can be applied to many dynamical systems, both under terrestrial and astrophysical conditions.

Figure 1

$X_F$ (solid lines) and $X_S$ (dotted lines) plotted against time $\tau$.

Figure 2

As in Fig. 1 for $\xi \ll 1$.

Figure 3

As in Fig. 1 for $\xi =1$. $K_x=0.00005$.

Figure 4

As in Fig. 1 for $\xi =1$. $K_x=0.5$.