VOLUME 43, NUMBER 26 PHYSICAL REVIEW LETTERS 24 DxcEMBKR 1979 Nonlinear Steepening of the Electrostatic Ion Cyclotron Wave M. Temerin, M. Woldorff, and F. S. Mozer Space Sciences Laboratory, Unicersity of California, Berkeley, Ca/ifornia 94720 (Received ll September 1979) Electrostatic ion cyclotron waves observed in space at altitudes between 5000 and 8000 km often have a sinusoidal form. Occasionally, however, wave forms having a spiky or sawtooth form indicative of steepening are observed. The nonlinear fluid equations which characterize the electrostatic ion cyclotron wave have traveling-wave solutions with sinusoidal, spiky, and sawtooth forms Th. e wave form depends on the amplitude and phase velocity of the wave. We report the observation of the nonlinear steepening of the electrostatic hydrogen cyclotron wave at altitudes between 5000 and 8000 km above the auroral regions of Earth's ionosphere. The observed waves are shown to have a form similar to the nonlinear propagating-wave solutions of the fluid equations which describe the electrostatic ion cyclotron wave. The electrostatic ion cyclotron wave is one of the low-frequency eigenmodes of a magnetized plasma. "' Such waves may be unstable to cur- rent-driven instabilities in the auroral magneto- sphere at altitudes above 1000 km, ' and have often been observed by S3-3 satellite at altitudes be- tween 5000 km and the maximum altitude of the satellite, 8000 km. 4 These waves are usually as- sociated with beams of 0. 5- to 16-keV H' and 0' ions flowing out of the auroral regions along mag- netic field lines and with the observations of mag- netic fluctuations indicative of currents flowing parallel to the magnetic fields. ' The S3-3 satellite was equipped with three or- thogonally oriented pairs of spheres which made three-component measurements of the electric field. The spheres on two of the pairs were sepa- rated by 37 m while the third pair was separated by 6 m. Data from one of these pairs of detectors from three separate hydrogen cyclotron-wave events are shown in Fig. 1. The potential differ- ence has been divided by the separation distance to give the electric field in millivolts per meter. The top part of Fig. 1 shows the usual wave form of the electrostatic hydrogen cyclotron wave. As is clear from the data there was a narrow spec- tral peak at 140 Hz which, as is expected from the theory of electrostatic ion cyclotron waves, ' was above the hydrogen cyclotron frequency of 116 Hz. The middle and bottom parts of Fig. 1 also display hydrogen cyclotron waves. Here, however, the hydrogen cyclotron waves are steep- ened. The data in the middle part of Fig. 1 have a sawtooth from while in the bottom part the wave has steepened into a series of double spikes re- 5mV/m U U I .05 I I I .IO .20 .25 RELATIVE TIME, SEC. I .30 .35 FIG. 1. Three examples of electrostatic ion cyclotron waves observed by the S3-3 satellite. The orbital pa- rameters are given in Table I. peating at frequencies of those hydrogen cyclotron waves at the same altitude which show little non- linear steepening. The orbital parameters corre- sponding to the times of these measurements are given in Table I. In each case the electrostatic- ion-cyclotron-wave events lasted for a time less than the 9 to 18 sec that it took to determine the complete pitch-angle distribution of the particles. In the top example the ion detector was fortuitous- ly pointing along the magnetic field downward to- ward Earth and saw ions with energies between 0.09 and 1.4 keV flowing up. The detector has eight energy steps between 0.09 and 3.9 keV. We now show that these nonsinusoidal wave forms resemble the traveling-wave solutions of the nonlinear fluid plasma equations describing the electrostatic ion cyclotron wave. It has been shown that traveling-wave solutions for the ion cyclotron wave may have a sawtooth form. ' Our 1979 The American Physical Society 1941