Abstract
Abstract 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−i ω 0 t 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, t 0, when a wave front moving with radial component of wave group velocity from the poloidal surface (a magnetic surface where the source frequency ω 0 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.
Highlights
Among ultra low-frequency oscillations in the Earth’s magnetosphere, the azimuthally small-scale Alfven waves are distinguished, i.e., the waves with large azimuthal wave numbers m 1 (Takahashi, 1988; Anderson, 1993; Denton et al, 2003)
A new feature of impulse-generated high-m Alfven waves in a curved two-dimensionally inhomogeneous field is a gradual change of the field line oscillations frequency from the local poloidal frequency to the local toroidal frequency, found by Leonovich and Mazur (1998)
They gave the following interpretation of this phenomenon: a sudden impulse formally excites a continuous set of monochromatic waves instantaneously on all magnetic shells
Summary
Among ultra low-frequency oscillations in the Earth’s magnetosphere, the azimuthally small-scale Alfven waves are distinguished, i.e., the waves with large azimuthal wave numbers m 1 (Takahashi, 1988; Anderson, 1993; Denton et al, 2003). Opposite to the monochromatic case are the waves generated by the sudden impulse, which is the delta-function of time In this case, each field line oscillates with its own frequency (Hasegawa et al, 1983); the oscillations on neighboring magnetic shells rapidly acquire a significant phase difference (phase mixing), and the wave becomes strongly “indented” in radial coordinate with much smaller amplitude. A new feature of impulse-generated high-m Alfven waves in a curved two-dimensionally inhomogeneous field is a gradual change of the field line oscillations frequency from the local poloidal frequency to the local toroidal frequency, found by Leonovich and Mazur (1998) They gave the following interpretation of this phenomenon: a sudden impulse formally excites a continuous set of monochromatic waves instantaneously on all magnetic shells. All the basic results were obtained analytically using various asymptotic methods and illustrated by the graphics obtained numerically
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