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In the framework of an axisymmetricmagnetospheric model, we have constructed a theory for broad-band standingAlfvén waves with large azimuthal wave number <i>m</i> » 1 excited by astochastic source. External currents in the ionosphere are taken as theoscillation source. The source with statistical properties of "whitenoise" is considered at length. It is shown that such a source drivesoscillations which also have the "white noise" properties. Thespectrum of such oscillations for each harmonic of standing Alfvén waves hastwo maxima: near the poloidal and toroidal eigenfrequencies of the magneticshell of the observation. In the case of a small attenuation in the ionospherethe maximum near the toroidal frequency is dominated, and the oscillations arenearly toroidally polarized. With a large attenuation, a maximum is dominantnear the poloidal frequency, and the oscillations are nearly poloidallypolarized.<  <b>Key words. </b>Ionosphere-magnetosphere interaction · Wavepropagation · Magnetospheric physics · MHD waves and instabilitie

Standing Alfvén waves with m ≫ 1 in an axisymmetric magnetosphere excited by a stochastic source