The factors which govern the distribution of electrons and ions in a planet's exosphere under diffusive equilibrium are discussed. The theory takes into account the effect of the electric field that arises from charge separation, the centrifugal force arising from the rotation of the planet, and the effect of the planet's gravitational field. It is assumed that the charged particles are constrained to move only along the direction of the planet's magnetic lines of force. The modifications that result in the electron and ion distributions when a temperature variation is assumed along a line of force are also considered. The results predicted by the theory are compared with actual experimental observations of the electron density distribution in the earth's exospheric plasma which have been obtained in recent years from whistler data and from topside ionograms made by the Alouette satellite.

The OGO 1 satellite has yielded evidence for both ducted and nonducted modes of whistler propagation in the magnetosphere. Two new types of nonducted whistlers have been identified: the ‘magnetospherically reflected’ whistler and the ‘Nu’ whistler. These whistlers have never been observed on the ground. Their unique properties result in part from the presence of ions that permit reflection of whistler‐mode energy in the magnetosphere. These phenomena provide a new tool for study of the distribution of ionization in the magnetosphere. Ducted whistlers from OGO 1 have provided the first in situ observations of whistler ducts. Near L = 3, the equatorial separations between ducts ranged from 50 to 500 km, and the equatorial thicknesses were about 400 km. The analysis yielded independent experimental support for the diffusive equilibrium model of distribution of ionization along the field lines in the plasmasphere. Some evidence was found of distortion of the magnetic field on the nightside at L ∼ 3, possibly due to oblique incidence of the solar wind on the earth's field.

While the great majority of ground whistlers are interpreted as indirect evidence of magnetospheric ducts, the first direct evidence of ducts was obtained from the Stanford University broadband VLF experiments on Ogo 1 and Ogo 3. Five discrete whistler ducts were encountered by Ogo 3 on the inbound pass of June 15, 1966, between L = 4.7 and 4.1. Each duct was characterized by reception at the satellite of ducted whistlers with a distinct spectral shape, and of the high‐frequency portions of whistlers (leakages) that propagated inward from outer ducts. The data were interpreted in detail by ray tracing in a model magnetosphere that includes ducts of enhanced ionization. The following conclusions resulted: (1) the L shell thicknesses of the observed ducts ranged between 0.035 and 0.070 earth radii, and the interduct separations ranged between 0.017 and 0.18 earth radii; (2) the dimension of the ducts in longitude was estimated to be of the order of 4°, or 0.3 earth radii at the equator, which is a factor of ∼4–8 greater than the L shell dimension; (3) the whistler ducts are much more likely to be enhancements than troughs; (4) the minimum enhancement factors needed to trap frequencies up to half the equatorial electron gyrofrequency are on the order of 8%, with smaller values producing upper cutoffs at lower frequencies; (5) the limited spreading of the calculated leaked rays is in general agreement with the corresponding regions of observation and relative signal amplitudes; (6) the low cutoffs of leaked signals are probably due to accessibility; (7) cyclotron and Landau interactions are likely to play a role in upper cutoffs of leaked signals; (8) the upper cutoff of ground whistlers near fH0/2 is a trapping (rather than absorption) effect; (9) the hydrostatic type of distribution of ionization along the field lines is applicable in the plasmasphere; and (10) the travel times (and frequency of minimum delay) of ducted whistlers can be calculated with good accuracy by assuming purely longitudinal propagation.

A study has been made of electron density and total electron content in tubes of force near the knee in magnetospheric ionization. It was based on whistler observations made at Eights, Antarctica, in July and August 1963, under conditions of steady, moderate geomagnetic agitation (Kp = 2-4). During the period 0100-0400 LT, the electron density near the equatorial plane at a geocentric distance of 4 Rr drops a factor of 30-100 within a distance of less than 0.15 Rr. The corresponding change in tube content above 1 cm 2 at 1000 km is • factor of about 10 within less than a degree of latitude. The afternoon profiles are gen-erMly similar to the postmidnight results. In the afternoon the profiles are often well defined outside the knee, falling smoothly to about 1 el/cm 8 at 7 RE. Both the equatorial and tube content profiles show a definite repeatability between observations at a given local time and under conditions of moderate, steady geomagnetic agitation. DiurnM effects are evident, with amplitude differing from point to point on the profiles. The problem of the field-line distribution of ionization has been studied with a view to minimizing error in the profiles. Experimental and theoretical support has been found for using a diffusive-equilibrium distribution along the field lines inside the knee and a 'collisionless' model, behaving approximately as N• o: R -4, along the field lines outside the knee. A study of error shows that the uncertainty in individual points on the knee profiles is evewwhere less than a factor of ñ2, and on the content profiles less than • factor of ñ1.5. •On leave from Escola Polit•cnica, Universidade de S•o Paulo, Brasil.Reference profile. As a reference for the results on the knee, we have calculated equatorialdensity and total-tube-content profiles corresponding to the whistler shown on the upper record in Figure 1. This event was recorded at about 0150 LT during extremely quiet planetary magnetic conditions, when the equatorial distance to the knee is expected to be large (see K-l). Thus the many components in the whistler represent a broad range of field-line paths inside the knee. Figure 2 shows the calculated equatorial profile of electron density; Figure 3, the corresponding profile of total electron content in a tube of force versus dipole latitude at 1000 km. The latter profile is calculated for a tube with cross section of 1 cm -ø at 1000 km altitude and extending from 1000 km to the equatorial plane.In Figures 2 and 3, and in many of the following figures, there are three types of data symbol, corresponding to three levels of precision in the measurements. The solid symbols represent highest precision; isolated open sym- 711

Evidence for nonducted VLF propagation between conjugate hemispheres has been found in records from the broadband VLF receivers aboard the polar satellites OGO 2 (419–1521 km) and OGO 4 (412–908 km). The nonducted signals described here are received in the ionosphere between 47° and 56° invariant latitude. They have never been observed on the ground and include natural whistlers and fixed‐frequency signals (10.2–12.5 kHz) from the U.S. Navy Omega transmitters. In a time‐frequency spectrogram, these nonducted whistlers appear as rising tones with a lower cutoff frequency in the approximate range of 5 to 8 kHz. They have been named ‘walking‐trace’ (WT) whistlers, since a rapid increase in travel time as a function of satellite latitude causes successive examples of the rising trace to ‘walk through’ other whistlers having equal dispersions and produced by the same sequence of lightning sources. A train of WT whistlers exhibits a nearly constant lower cutoff frequency that is equal to the maximum value of the lower hybrid resonance (LHR) frequency above the satellite and an upper cutoff frequency that decreases with increasing satellite latitude. Reflected waves following a WT whistler can also be received if the LHR frequency below the satellite reaches values greater than above it. Observed spectral shapes of such whistlers resemble a fishhook. Fixed‐frequency Omega signals observed by OGO 4 in the hemisphere conjugate to the transmitter frequently have characteristics smiliar to those of the WT whistlers. The Omega signals exhibit two features that are not apparent in the natural whistlers: an enhancement of signal strength and a Doppler shift that increases with latitude and may reach hundreds of hertz. The main characteristics of the above phenomena are explained by tracing nonducted rays between conjugate hemispheres in a model magnetosphere. An equatorial electron concentration profile is derived from the WT whistlers.