Localized electrostatic wave packets in the frequency region of lower hybrid waves have been detected by the instruments on the FREJA satellite. These waves are often associated with local density depletions indicating that the structures can be interpreted as wave filled cavities. The basic features of the observations are discussed. On the basis of simple statistical arguments it is attempted to present some characteristics which have to be accommodated within an ultimate theory describing the observed wave phenomena. An interpretation in terms of collapse of nonlinear lower hybrid waves is discussed in particular. It is argued that such a model seems inapplicable, at least in its simplest form, by providing a timescale and a length scale which are not in agreement with observations. Alternatives to this model are presented.1.

Abstract. Low-frequency electrostatic¯uctuations in the ionospheric E region were detected by instruments on the ROSE rockets. The phase velocity and dispersion of plasma waves in the ionospheric E region are determined by band-pass ®ltering and cross-correlating data of the electric-®eld¯uctuations detected by the probes on the ROSE F4 rocket. The results were con®rmed by a dierent method of analysis of the same data. The results show that the waves propagate in the Hall-current direction with a velocity somewhat below the ion sound speed obtained for ionospheric conditions during the¯ight. It is also found that the waves are dispersive, with the longest wavelengths propagating with the lowest velocity.

Sparsely sampled irregular arrays and random arrays have been used or proposed in several fields such as radar, sonar, ultrasound imaging, and seismics. We start with an introduction to array processing and then consider the combinatorial problem of finding the best layout of elements in sparse 1-D and 2-D arrays. The optimization criteria are then reviewed: creation of beampatterns with low mainlobe width and low sidelobes, or as uniform as possible coarray. The latter case is shown here to be nearly equivalent to finding a beampattern with minimal peak sidelobes.We have applied several optimization methods to the layout problem, including linear programming, genetic algorithms and simulated annealing. The examples given here are both for 1-D and 2-D arrays. The largest problem considered is the selection of K = 500 elements in an aperture of 50 by 50 elements. Based on these examples we propose that an estimate of the achievable peak level in an algorithmically optimized array is inverse proportional to K and is close to the estimate of the average level in a random array.Active array systems use both a transmitter and receiver aperture and they need not necessarily be the same. This gives additional freedom in design of the thinning patterns, and favorable solutions can be found by using periodic patterns with different periodicity for the two apertures, or a periodic pattern in combination with an algorithmically optimized pattern with the condition that there be no overlap between transmitter and receiver elements. With the methods given here one has the freedom to choose a design method for a sparse array system using either the same elements for the receiver and the transmitter, no overlap between the receiver and transmitter or partial overlap as in periodic arrays.

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