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Abstract. The perpendicular scale of electron phase-space holes is investigated using electric field data from the Po-

[1] We present Polar Plasma Wave Instrument (PWI) measurements of electrostatic solitary waves in the high-altitude polar magnetosphere. These waves are electrostatic pulses that move parallel (and antiparallel) to the geomagnetic field and are similar to waves detected in many regions of the magnetosphere by other spacecraft. The PWI instantaneous dynamic range was 72 dB with an added 30 dB obtained by changing gain states. This large dynamic range enables the study of amplitude-size relations up to a maximum electric field of 44 mV/m in the lowest gain state as well as enabling the investigation of small-amplitude waves (<0.1 mV/m). The Polar PWI data indicate that these small-amplitude solitary waves have typical scale sizes the order of the Debye length, velocities the order of the electron thermal speed, and electrostatic potentials that are small compared with the electron thermal energy per charge (f ( k B T e /e). Statistical distributions of the wave properties are presented, and the properties are compared with theoretical predictions of electron phase-space holes and electron-acoustic solitons. BGK-type analysis of electron holes predicts a relationship between the minimum allowed scale size and the amplitude and velocity. The observed solitary waves are consistent with these predictions.

[1] Electron phase space holes are analyzed in terms of solitary-wave solutions to the nonlinear Vlasov-Poisson equations in a collisionless plasma. Width-amplitude relations for one-dimensional and three-dimensional electron holes are derived to be inequalities that allow existence of the holes in regions to one side of a bound. The theoretical origin of the width-amplitude inequality is elucidated to show that the inequality nature is independent of specific functional forms of the solitary potential and ambient plasma distribution functions. Ion dynamics and effects of finite hole velocity and finite perpendicular size are subsequently included. Finally, we show that the electron holes reported by Franz et al. (2005) populate an allowed region in the solution space that is significantly away from the bounding curve. These electron holes evidence the accessibility of electron holes whose widths and amplitudes are only loosely constrained and open up the possibility of spontaneous generation of phase-space holes in turbulent fluctuations.

Abstract. To determine the wavelength of waves within a random, isotropic wave field, we introduce the observable of wave coherency measured with plasma wave interferometers. We show generally that within a random direction wave field, wavelengths large compared to the interferometer length produce large coherency (nearly 1), but wavelengths the order of a few times the interferometer length, or smaller, produce small coherency (close to zero). We apply this principle first to examining auroral hiss and lower hybrid waves measured by the Physics of Auroral Zone Electrons (PHAZE) 2 and Topside Probe of the Auroral Zone (TOPAZ) 3 experiments and show that the implied wavelengths are consistent with the expected dispersion relations and with other, different estimates of wavelength for these modes. Next, we apply the principle to broadband extra low frequency (BB-ELF) electric fields observed in both experiments and conclude that the wavelengths are small. In one case we calculate the coherency of BB-ELF electric fields, using an ensemble average of 7889 data samples, and demonstrate that the coherency near the oxygen gyrofrequency is very small (=0.15), corresponding to wavelengths of 10 m and the order of the ion gyroradius. We conclude that because of the short wavelengths, previous satellite measurements of BB-ELF electric fields may have underestimated the electric field amplitudes, unless ion gyroradii are substantially larger than the case for these rocket measurements. Although the wavelengths and frequencies of BB-ELF electric fields are now known, we are unable to assign the wave to a known, normal mode of homogeneous plasmas. This suggests that inhomogeneities may be essential for describing BB-ELF electric fields.