D. T. Farley

A Theory of Incoherent Scattering of Radio Waves by a Plasma

A theory is developed which describes the scattering of radio waves by the random thermal fluctuations of electron density in a collision-free plasma. The frequency spectrum, as well as the amplitude, of the scattered radiation is calculated. Particular attention is paid to the part of the spectrum which corresponds to small Doppler shifts, this being the region of greatest significance in connexion with the phenomenon of incoherent scattering from the ionosphere. The calculations are based on a generalized version of Nyquist’s noise theorem, and they lead to the following conclusions: (1) The mean scattering cross-section for the ionosphere is equal to that which would exist if each of the electrons scattered independently with a cross-section of one-half the classical Thomson cross-section. (2) The mean Doppler broadening of the scattered signal corresponds roughly to the speed of the ions rather than to that of the electrons. (3) The spectral shape of this signal is not Gaussian. There is a mild maximum in the spectrum away from the central frequency, as can be seen in figure 1. (4) Plasma resonance effects contribute only negligibly to the scattering for frequencies currently of interest.

Theory of equatorial electrojet plasma waves: new developments and current status

Abstract There have been several important theoretical breakthroughs in the last few years that have substantially improved our understanding of the electrojet plasma instabilities. We now understand (1) the linear and nonlinear processes that control the longest wavelengths and probably also affect the electrojet current strength, (2) quite a bit about the two-dimensional turbulent cascade process that generates both the type 2 irregularities seen by radar and waves propagating even in the vertical direction, and (3) the anomalous diffusion process that limits the growth of the directly excited short wavelength type 1 waves and explains many of their properties. We finally really understand why type 1 and type 2 waves are different. In this paper we first briefly summarize the observed characteristics of the electrojet irregularities and then discuss the theory, devoting most of our attention to recent developments.

VHF radar and rocket observations of equatorial spread F on Kwajalein

VHF radar data from the Summer 1990 Equatorial Spread F campaign on Kwajalein are presented. The Cornell 50 MHz portable radar interferometer (CUPRI) operated concurrently with the Altair UHF incoherent scatter radar throughout July and August and supported two sounding rocket flights on July 30 and August 2. This experiment provided the first opportunity to simultaneously diagnose equatorial spread F using the three prime experimental techniques: VHF/UHF coherent scatter, incoherent scatter, and in situ probe measurements of electric field and density fluctuations. The intensity of the coherent echoes observed was consistent with typical Jicamarca spread F observations, but chains of periodic, large-scale plasma upwellings were observed more often and for much longer durations on Kwajalein than have been seen over Peru. CUPRI also measured Doppler frequencies in one upwelling corresponding to 1200-m/s plasma drift velocities. This measurement agrees with recent observations of supersonic drift rates at the magnetic equator by spacecraft. Near the most active localized plasma upwellings, interferometer data reveal that the zonal drift rate of plasma irregularities can vary sharply in space, as one would expect for two-dimensional incompressible flow. We introduce a semiempirical model of the three-dimensional spectrum of F region irregularities that is consistent with the one-dimensional spectra of density fluctuations observed by sounding rockets and with the axial ratio of irregularities determined recently. Normalized to data from one of the rocket flights on Kwajalein, the model predicts the 3-m scattering cross-section measured by CUPRI to within a few decibels.

Observations of auroral E-region plasma waves and electron heating with EISCAT and a VHF radar interferometer

Two radars were used simultaneously to study naturally occurring electron heating events in the auroral E-region ionosphere. During a joint campaign in March 1986 the Cornell University Portable Radar Interferometer (CUPRI) was positioned to look perpendicular to the magnetic field to observe unstable plasma waves over Tromso, Norway, while EISCAT measured the ambient conditions in the unstable region. On two nights EISCAT detected intense but short lived (< 1 min) electron heating events during which the temperature suddenly increased by a factor of 2–4 at altitudes near 108 km and the electron densities were less than 7 × 104 cm−3. On the second of these nights CUPRI was operating and detected strong plasma waves with very large phase velocities at precisely the altitudes and times at which the heating was observed. The altitudes, as well as one component of the irregularity drift velocity, were determined by interferometric techniques. From the observations and our analysis, we conclude that the electron temperature increases were caused by plasma wave heating and not by either Joule heating or particle precipitation.

Numerical simulations of large-scale plasma turbulence in the daytime equatorial electrojet

We present numerical simulations of the large-scale electron density irregularities in the daytime equatorial electrojet driven by the gradient drift instability. The nonlocal nonlinear two-fluid equations are integrated numerically with scales ranging from about 10 km to less than 100 m directly resolved on a 128×128 grid, while the effects of the smaller subgrid scales are included with the use of anomalous electron mobility and diffusion coefficients [Ronchi et al., 1990a]. The instability evolves to a state in which the perturbations propagate primarily in the east-west direction with a typical horizontal wavelength of about 2 km. The output of the numerical simulations does not indicate the presence of a significant anisotropy in the power spectrum of the irregularities in the plane perpendicular to the ambient magnetic field, in contrast to the marked differences observed in physical space between the vertical and horizontal dynamics. The one-dimensional integrated density and electric field power spectra have a power law dependence with a power index ranging between −2.5 and −1.2. The numerical results are compared with in situ rocket observations by probing the simulation region along different flight paths, following both eastward and westward trajectories. Electron vertical turbulent velocity distributions are computed from the code output and are contrasted with radar backscatter data. The features typical of the 3-m type 2 echoes (such as the broadening and asymmetry in the frequency power spectra) are also present in the computed distributions, indicating that during weak electrojet conditions the small-scale structures act as tracers of the large-scale electric field variations. A conclusion of particular note is that a purely linear nonlocal analysis (valid for wavelengths λ ≈ 1 km) leads to the result that all perturbations are eventually damped, either by shear and then diffusion or by recombination. The inclusion of nonlinear effects, however, restores the instability. In the strongly turbulent regime a nonsteady saturated state is reached, whereby the linear convection of energy via shear to high wavenumbers is countered by the nonlinear modification of the equilibrium density and electric field gradients and by mode coupling of shorter wavelengths back to long.

Early incoherent scatter observations at Jicamarca

Abstract We describe some of the highlights of the incoherent scatter observations made at Jicamarca in the 1960s. Some of the observations were then and are still now unique and worthy of further study. Of particular note are (1) a long series of electron density measurements extending to altitudes as high as 10,000 km on a few occasions, (2) density and temperature observations during a total solar eclipse, (3) temperature and composition measurements extending past the O+-H+ transition region, and (4) observations of the ion gyro resonance effect for protons.

High‐resolution radar observations of daytime kilometer‐scale wave structure in the equatorial electrojet

Using a new antenna configuration and new data processing hardware, the authors probed the electrojet with unprecedented spatial resolution in January 1991 at Jicamarca. The altitude resolution was 125 m, and the east-west antenna beamwidth was about 0.6[degrees], or about 1 km at electrojet altitudes. The high spatial resolution allowed them to observe, at certain altitudes and times, pronounced wavelike structures with vertical wavelengths of the order of 1 km and periods of tens of seconds. These observations closely resemble the predictions of recent nonlocal, nonlinear numerical simulations of large-scale turbulence in the equatorial electrojet. The comparison demonstrated the validity of the theory and confirmed the idea that the Doppler power spectra of type 2 echoes at 50 MHz (due to 3-m plasma waves generated by the gradient-drift instability and a nonlinear cascade of energy from long-wavelength modes to short) are controlled primarily by the large-scale dynamics and not by the nonlinear local growth and decay rates of the 3-m waves themselves. 16 refs., 7 figs.

High‐resolution radar measurements of turbulent structure in the equatorial electrojet

Observations of the equatorial electrojet were made with unprecedented altitude resolution at the Jicamarca Radio Observatory in January 1990. We obtained high-quality Doppler spectra with 250-m and sometimes better altitude resolution at heights from 95 to 120 km during the daytime and early evening with the large 50-MHz radar. This resolution and coverage revealed a richness of dynamics and structure not previously appreciated, a structure that is sometimes reminiscent of VHF radar maps of equatorial spread F, albeit at smaller primary scale sizes. Individual scattering centers sometimes appear to drift in large swirls over many kilometers in altitude, maintaining their identity for times occasionally as long as a minute or two. On the other hand, we also see rapid variations with altitude (a kilometer or less) and time (a few seconds or less) in the Doppler spectra and signal power.

Radar measurements of very small aspect angles in the equatorial ionosphere

Equatorial spread F (ESF) irregularities are very highly aligned with the geomagnetic field. In order to understand the physics of the irregularities, that is, the unstable plasma waves, it is important to measure this degree of alignment as accurately as possible. Measuring the angles with a radar is no easy task, however, since the angles in question, perhaps a few times 10−2 degrees or less, are much smaller than the radar beam widths available at any equatorial radar, and there are numerous potential sources of error that can make the angles appear larger than they really are. Nevertheless, the measurement can be done. At Jicamarca we have determined an upper limit on the rms deviations from perfect alignment that is often as small as 0.015°. This paper describes the measurement technique and presents a few illustrative examples of the data. The following companion paper [Hysell and Farley, this issue] discusses the theoretical implications of these measurements.

The E-region rocket/radar instability study (ERRRIS): scientific objectives and campaign overview

Abstract The E -region Rocket/Radar Instability Study (Project ERRRIS) investigated in detail the plasma instabilities in the low altitude ( E -region) auroral ionosphere and the sources of free energy that drive these waves. Three independent sets of experiments were launched on NASA sounding rockets from Esrange, Sweden, in 1988 and 1989, attaining apogees of 124, 129 and 176km. The lower apogee rockets were flown into the unstable auroral electrojet and encountered intense two-stream waves driven by d.c. electric fields that ranged from 35 to 115 mV/m. The higher apogee rocket returned fields and particle data from an active auroral arc, yet observed a remarkably quiescent electrojet region as the weak d.c. electric fields (~ 10–15 mV/m) there were below the threshold required to excite two-stream waves. The rocket instrumentation included electric field instruments (d.c. and wave), plasma density fluctuation ( δn / n ) receivers, d.c. fluxgate magnetometers, energetic particle detectors (ions and electrons), ion drift meters, and swept Langmuir probes to determine absolute plasma density and temperature. The wave experiments included spatially separated sensors to provide wave vector and phase velocity information. All three rockets were flown in conjunction with radar backscatter measurements taken by the 50MHz CUPRI system, which was the primary tool used to determine the launch conditions. Two of the rockets were flown in conjunction with plasma drift, density, and temperature measurements taken by the EISCAT incoherent scattar radar. The STARE radar also made measurements during this campaign. This paper describes the scientific objectives of these rocket/radar experiments, provides a summary of the geophysical conditions during each launch, and gives an overview of the principal rocket and radar observations.