Resonant magnetohydrodynamic waves in high-beta plasmas

Abstract

When a global magnetohydrodynamic (MHD) wave propagates in a weakly dissipative inhomogeneous plasma, the resonant interaction of this wave with either local Alfvén or slow MHD waves is possible. This interaction occurs at the resonant position where the phase velocity of the global wave coincides with the phase velocity of either Alfvén or slow MHD waves. As a result of this interaction a dissipative layer embracing the resonant position is formed, its thickness being proportional to R−1/3, where R⪢1 is the Reynolds number. The wave motion in the resonant layer is characterized by large amplitudes and large gradients. The presence of large gradients causes strong dissipation of the global wave even in very weakly dissipative plasmas. Very often the global wave motion is characterized by the presence of both Alfvén and slow resonances. In plasmas with small or moderate plasma beta β, the resonance positions corresponding to the Alfvén and slow resonances are well separated, so that the wave motion in the Alfvén and slow dissipative layers embracing the Alfvén and slow resonant positions, respectively, can be studied separately. However, when β≳R1/3, the two resonance positions are so close that the two dissipative layers overlap. In this case, instead of two dissipative layers, there is one mixed Alfvén-slow dissipative layer. In this paper the wave motion in such a mixed dissipative layer is studied. It is shown that this motion is a linear superposition of two motions, one corresponding to the Alfvén and the other to the slow dissipative layer. The jump of normal velocity across the mixed dissipative layer related to the energy dissipation rate is equal to the sum of two jumps, one that occurs across the Alfvén dissipative layer and the other across the slow dissipative layer.