Changes in the auroral zone current system are often accompanied by magnetic pulsations with periods of about 1 s. These so-called bursts of irregular pulsations (PiB) have been observed both on ground magnetograms and with in situ satellite observations. These pulsations can be understood as excitations of a resonant cavity in the topside ionosphere, where the Alfven speed has a strong gradient due to the exponential decrease of density above the ionosphere divided by the ionospheric scale height. For a pure exponential Alfven speed profile, the mode frequencies are related to zeroes of the zeroth-order Bessel function. For other profiles of the density, and therefore Alfven speed, the frequencies are not exactly given by the simple theory, but the frequency and mode structure are similar provided the Alfven speed sharply increases above the ionosphere. ¿ American Geophysical Union 1988