''Giant'' undulations on the equatorward boundary of the evening diffuse aurora, occasionally observed during a substorm, are numerically simulated. A ''giant'' undulation is defined as a waveform having the crest-to-trough amplitude comparable to the wavelength. The two-dimensional particle code is used for studying the motion of magnetospheric plasma perpendicular to the geomagnetic field. Based on the observational facts, it is assumed that in the auroral magnetosphere there exist azimuthally aligned sheets of enhanced density, which are called arc sheets. (Arc sheets inside the inverted-V structure can actually be responsible for discrete arcs.) The simulation model for giant undulations assumes the presence of an arc sheet equatorward of the proton diffuse aurora. Anomalous cross-field diffusion of the arc sheet protons leads to polarization of the arc sheet. The polarized arc sheet is such that a negative charge sheet is sandwiched between two positive charge sheets. The polarized arc sheet is subject to a Kelvin-Helmholtz (K-H) instability due to a velocity shear generated in the arc sheet. The K-H waves associated with the arc sheet can spatially modulate the equatorward boundary of the proton diffuse aurora.

In the actual simulation, the temporal evolution of the diffuse auroral pattern, as displayed in photographs from the satellites, can be visualized by following the cluster of the energetic protons. The outstanding indentations characteristic of observed giant undulations are successfully reproduced. There have been a few examples of the satellite measurements of electric fields, field-aligned currents, and fluxes of precipitating particles around the undulating diffuse auroral boundaries. The distributions of electric fields and space charges obtained from the simulation are found to be consistent with these observations. Therefore, giant undulations on the equatorward diffuse auroral boundary can be identified with spatial modulation of the energetic protons by the K-H waves arising from the polarized arc sheet. ¿ American Geophysical Union 1993