Azimuthally small-scale Alfvén waves in magnetosphere excited by the source of finite duration

In this paper the spatial structure of azimuthally small-scale Alfvén waves in magnetosphere excited by the impulse source is studied. The source is suddenly switched on at a definite moment and works as e^-iω0t during the finite time interval. The influence of factors which lead to the difference of toroidal and poloidal eigenfrequencies (like curvature of field lines and finite plasma pressure) is taken into account. Due to these factors, a radial component of the group velocity of Alfvén wave appears. An important value is the time moment, t₀, when a wave front moving with radial component of wave group velocity from the poloidal surface (a magnetic surface where the source frequency ω₀ coincides with the poloidal frequency) passes the given magnetic shell with the radial coordinate x. The temporal evolution at all the points, where the front has not come yet, is determined by the phase mixing of the initial disturbance. At the points through which the wave front has already passed, the wave field structure almost coincides with the structure of monochromatic wave. The region where the front propagates is bounded by the interval between the poloidal surface and the toroidal one (that is, the Alfvén resonance surface). For this reason, outside this region the evolution is always determined by the phase mixing, which leads to much smaller amplitudes than between poloidal and toroidal surfaces. After the source turned off, a back wave front is formed, which comes through the given point in direction from the poloidal surface to the toroidal one. After the back front has come, the monochromatic wave structure disappears and there is only a weak disturbance, which steadily disappears because of the phase mixing and the final conductivity of ionosphere.