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Astron. Astrophys. 342, 300-310 (1999)

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7. Conclusions

1. A numerical code has been developed to study the propagation of nonlinear MHD body and surface waves along magnetic interfaces and slabs. Both longitudinal and transverse MHD waves have been simulated.

2. Since an initial value problem for linear surface waves propagating along a single magnetic interface embedded in an incompressible medium has full analytical solutions, our numerical code has been tested against these solutions. A good agreement between analytical and numerical results has been found.

3. The problem of propagation of linear surface waves along a single magnetic interface embedded in a compressible medium has also been tested by comparing our results with those obtained by Wu et. al. (1996), who utilized a different numerical scheme. Again, good agreement has been found between the results obtained by the two different numerical codes.

4. Our numerical code has been used to investigate the behavior of nonlinear MHD surface waves propagating along a magnetic slab and both longitudinal and transverse velocity perturbations with finite amplitudes were excited. The resulting wave patterns and nonlinear features have been shown and discussed.

5. The process of wave energy leakage from a magnetic slab to the field-free external medium has been studied. The obtained results show that [FORMULA] of the energy carried by transverse slab waves leaks to the external medium within two wave periods. This means that the efficiency of the energy transfer by these waves along the slab is significantly reduced.

6. The process of excitation of MHD waves in two adjacent magnetic slabs by large amplitude external acoustic waves has also been investigated. It is found that only [FORMULA] of the energy carried by these acoustic waves is transferred to the slabs, and that the efficiency of this process strongly depends on the location of the slabs relative to the source of acoustic waves and on the amplitude of these waves.

7. The leakage rates found are important for the problem of heating of magnetically structured regions in the solar and stellar atmospheres.

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© European Southern Observatory (ESO) 1999

Online publication: December 22, 1998