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This paper is concerned with the spatial structure and temporal evolution of the azimuthally small scale Alfvén wave generated by a sudden impulse concentrated on a given magnetic shell. At the outset, both poloidal and toroidal components are present in the wave's magnetic field. The oscillation in the poloidal component on a given magnetic shell is a superposition of two monochromatic oscillations, one with the local resonance frequency on this shell, and the other with the frequency corresponding to the resonance frequency on the source surface. The superposition of these two oscillations leads to beating. Due to phase mixing, the poloidal component of the oscillation decreases with time down to zero, transferring its energy to the toroidal component. Beating in the toroidal component is less pronounced. As time elapses, energy concentration near the source magnetic shell occurs with the frequency of the oscillation corresponding to the Alfvénic resonance frequency on this surface. Outside this thin region wave amplitudes become rather small at oscillation frequencies corresponding to the local resonance frequency of the respective magnetic shell

Spatio-temporal structure of Alfvén waves excited by a sudden impulse localized on an L-shell