Proton Whistlers Research Articles

Linear wave conversion processes in the theory of the proton whistler

The linear coupling between the different kinds of waves propagating in a warm plasma inhomogeneous along thex direction is investigated in order to locate the regions (ω,k) space where two of the roots of the characteristic equation coalesce. Firstly, using the approximation of geometrical optics the differential equation is derived and wave propagation at fixed wave numberkz is studied in these special cases for which the characteristic equation reduces to a biquadratic. When the density gradient is parallel to the magnetic field, a detailed analysis of the different properties of the waves shows that the mechanism proposed by Gurnett and others to explain the characteristics of the proton whistler is unlikely to operate, even if a wave coupling occurs at the so called cross over frequency for small incidence angles. The only relevant process occurs when the density gradient is perpendicular to the magnetic field for waves propagating at small incidence angles. It is shown that, close to a coalescence point, but within the limit of the geometrical optics approximation, one of the WKB solutions is a mixed (transverse-longitudinal) mode which becomes purely longitudinal in the limit of large wave numbers. Consequently, as this wave has E almost parallel tok, coalescence implies that the waves are nearly longitudinal at the singular point, in agreement with other results. Next, application of the theory is made to some relevant space observations. It is shown that the proton whistler could be the result of a linear coupling between the extraordinary and the slow ion cyclotron waves close to the Buchsbaum resonance in ionospheric regions above 300 to 400 km where the H+ density begins to grow. Transformation conditions are given which favour the coupling mechanism in regions of strong latitudinal gradients. Finally, a comparison is made with experiment which confirms the principal features of the present theory.

Propagation of trans-equatorial deuteron whistlers in the low latitude topside ionosphere

The high latitude limit of trans-equatorial deuteron whistlers is found to occur at latitudes where B m = B 2 , in which B is the local magnetic field at the satellite and B m is the minimum magnetic field on the field line through the satellite. The high latitude limit of trans-equatorial proton whistlers, often extends to the latitude where B m = B 4 in the autumn and winter. Trans-equatorial deuteron whistlers have a constant time interval for an echo train. The damping rate of the cyclotron resonant interaction with rare deuteron is large enough to generate deuteron whistlers. Ray tracing results for non-ducted propagation of trans-equatorial deuteron whistlers show that rays are guided by the geomagnetic field within one degree in invariant latitude for several bounces between the two hemispheres. Although the non-ducted propagation mode is L-mode, waves are reflected in the R mode at a LHR frequency after frequency between the deuteron and helium gyrofrequency after the mode changes at the cross-over frequency.

Deuteron whistler and trans-equatorial propagation of the ion cyclotron whistler

New ion cyclotron whistlers which have the asymptotic frequency of one half the local proton gyrofrequency, G p 2 , and the minimum (or equatorial) proton gyrofrequency, G pm , along the geomagnetic field line passing through the satellite have been found in the low-latitude topside ionosphere from the spectrum analysis of ISIS VLF electric field data received at Kashima, Japan. Ion cyclotron whistlers with asymptotic frequency of G pm or G pm 2 are observed only in the region of B m > B 2 or rarely B m > B 4 , where B is the local magnetic field and B m is the mini magnetic field along the geomagnetic field line passing through the satellite. The particles with one half the proton gyrofrequency may be the deuteron or alpha particle. Theoretical spectrograms of the electron whistlers ( R-mode) and the ion cyclotron whistlers ( L-mode) propagating along the geomagnetic field lines are computed for the appropriate distributions of the electron density and the ionic composition, and compared with the observed spectrograms. The result shows that the ion cyclotron whistler with the asymptotic frequency of G p 2 is the deuteron whistler, and that the ion cyclotron whistlers with the asymptotic frequency of G pm or G pm 2 are caused by the trans-equatorial propagation of the proton or deuteron whistler from the other hemisphere.

Characteristics of electron-ion whistlers and their application to ionospheric probing

In this communication the effect of ion temperature on the propagation of electron-ion whistlers in the ionosphere is investigated. A general expression including the effect of ion temperature is derived for the group travel time for the electron-ion whistler as it travels from the base of the ionosphere to the satellite. A study of the dependence of the group travel time on ion temperature indicates that thermal effects contribute about 20% to the total group travel time for the proton whistlers. Further, from the expression for the group travel time including the effect of the ion temperature in conjunction with the generalized dispersion relation a relation for the cyclotron damping rate (both temporal and spatial) has been obtained. A detailed study of the cyclotron damping rate with travel time and ion temperature leads to the conclusion that the observed amplitude cutoff characteristics for the proton whistler can be explained on the basis of the mechanism of cyclotron damping. It is also shown that the knowledge of the group travel time of an electron-ion whistler can be used to estimate the ion temperature at the satellite.

Full‐wave analysis and coupling effects in a crossover region

The solution of the wave equation for a plane stratified medium is obtained by using a fourth‐order accurate numerical integration technique. The general solution thus obtained is described in terms of four characteristic waves, two upgoing and two downgoing. A compact expression for the coupling coefficients Γij(i ≠j), which is suitable for numerical calculation, is also derived. These techniques are then used in a quantitative study of transmission coefficients, coupling factors, and wave structures through the crossover region where the proton whistlers are generated. The negligible influence of collisions upon the transmitted energies in the two upgoing modes is discussed. The results are then compared with previous works in which the thin‐slab full‐wave method was used.

Group travel time for proton whistlers in the ionosphere

In this communication a theoretical relation is derived for the group travel time of the proton whistlers to reach the satellite from their place of occurrence. The expression for the group travel time contains two terms. The first term is the dominant term and is inversely proportional to (Ω - ω)1/2, where Ω and ω are the proton gyrofrequency and the wave frequency, respectively. The contribution from the second term, which is inversely proportional to (Ω - ω)7/2, is about 10% of the first term. It is shown that the group travel time is sensitive to the variation of temperature, gradient of proton gyrofrequency, and ion density along the path of a proton whistler. The effect of variation in each of the above parameters on the group travel time is discussed, and it is shown that an estimate of proton temperature can be made from the measured data on the proton whistlers.

Additional results from an Ogo 6 Experiment concerning ionospheric electric and electromagnetic fields in the range 20 Hz to 540 kHz

Ogo 6 was launched on June 5, 1969, into a polar orbit with a perigee of 400 km and an apogee of about 1100 km; normal Ogo 6 operations were terminated on June 28, 1971. Our experiment on the spacecraft yielded real time analog data in four 15-kHz bands (20 Hz to 15 kHz, 15–30 kHz, 92.5–107.5 kHz, and 280–295 kHz), and tape-recorded digital data in two 200-Hz bands (200 kHz and 540 kHz), and from a broad band intensity detector. The experiment sensor consisted of an electric dipole with a tip-to-tip length of about 24 meters. This paper summarizes those findings from the experiment that have not been published previously. These include the following: (1) an observation of emissions triggered by proton whistlers, (2) numerous clear examples of whistler-associated lower hybrid resonance (LHR) noise, (3) new results on the auroral hiss zone and on its relation to the high-altitude polar cusp, and (4) new results on emissions triggered by VLF stations, which point to a similarity between whistler precursors and triggered emissions, suggesting a similarity in the generation mechanisms.

Use of the three-dimensional covariance matrix in analyzing the polarization properties of plane waves

A technique for analyzing the polarization properties of plane waves that offers a number of advantages over methods currently used in the analysis of both ground and satellite observations of waves is developed. This technique reduces the computations required to find the wave normal vector, is less sensitive to common noise sources, and is amenable to analog implementation. The technique here is applied specifically to the analysis of a proton whistler, but it can also be used in most studies of ULF, ELF, and VLF magnetic-wave phenomena.

Measurement of the wave-normal vector of proton whistlers on Ogo 6

Description of the first experimental determination of the wave-normal vector of proton whistlers in the ionosphere. Between the crossover frequency and the proton gyrofrequency, both right-hand and left-hand modes of propagation can occur for upgoing waves. Theoretically, the amount of energy in the respective modes depends on theta, the angle between the wave normal and the magnetic field. For proton whistlers with only left-hand mode energy between the crossover and proton gyrofrequency, theta ranged from 36 to 51 deg. For proton whistlers with strong right-hand and left-hand mode signals, theta ranged from 24 to 29 deg. The result is in good agreement with Wang's (1971) collisionless mode-coupling model. The angle between the wave normal and the vertical is found to increase with increasing altitude.

Crossover frequencies in plasmas with two species in the presence of the Coriolis force

Points out that, in the presence of the Coriolis force, a crossover frequency can exist in a plasma with only two species and comments on the results with respect to proton whistlers. (see abstr. A67926 of 1970).

An experimental study of very-low-frequency mode coupling and polarization reversal

Electron and proton whistlers polarization reversal and mode coupling, explaining magnetic latitude dependence

Complex Ray Theory for Ion Cyclotron Whistlers

SINCE their discovery on VLF recordings from the Injun 3 and Alouette satellites in 1964 (ref. 1), proton whistlers and more recently helium whistlers2 have proved to be useful diagnostic probes for studying the constitution of the topside ionosphere3,4. An ion cyclotron whistler of either of these types is associated with a “fractional hop” whistler and appears on the spectrogram as a trace breaking away from the “electron whistler” trace at a “crossover” frequency and then approaching asymptotically the proton or helium gyrofrequency at the level of the observing satellite. The theory of these whistlers was given by Gurnett et al.5, who considered the effects of positive ions on electromagnetic waves in the topside ionosphere. As well as the usual electron whistler, polarized with a right handed sense in the northern hemisphere, it is possible at certain altitudes and for certain frequency ranges for the left hand polarized mode to propagate.

Irregularities in proton density deduced from cyclotron damping of proton whistlers

The damping of proton whistlers is found to be much more gradual than predicted by the cyclotron damping theory of Gurnett and Brice (1966) for an assumed homogeneous plasma with an isotropic Maxwellian proton velocity distribution. Several possible causes of the discrepancy are: nonlinear effects, anisotropy, a non-Maxwellian velocity distribution, and irregularities in proton density. It is concluded that plasma density irregularities are responsible for the observed gradual damping. When these effects are included, the deduced proton temperature increases significantly (about a factor of 2) and the magnitudes of the variations in proton plasma frequency estimated are about 15–20%.

Polarization of proton whistlers

An experiment that separates whistler-mode waves into characteristic right- and left-hand circularly polarized components on a broad-band basis has shown that electron whistlers are nearly right-hand polarized and proton whistlers are nearly left-hand polarized, as is predicted by whistler theories. The method has application to the study of broad-band phenomena such as hiss and chorus, and should allow improved accuracy of ion density as measured from proton whistlers.

Harmonic Ion Cyclotron Resonances observed by the OGO–4 Satellite

A NEW very low frequency phenomenon associated with the propagation of whistlers in the upper ionosphere has recently been found in the VLF recordings from the Injun 3 and Alouette satellites1. This phenomenon showed up on a frequency–time spectrogram as a rising tone which started immediately after the reception of a short fractional-hop whistler. The spectrogram showed a rapid rise in frequency with an asymptotic approach to the cyclotron frequency for the protons in the plasma surrounding the satellite. These signals have been called proton whistlers. Analysis has shown that they are excited because of mode coupling or conversion from the electron whistler mode with right-hand polarization to the ion cyclotron wave with left-hand polarization2. The frequency at which polarization reversal or coupling occurs has been called the crossover frequency, which is below the ion cyclotron frequency. More recently it was reported that the ion wave at a helium cyclotron frequency has been observed in addition to the proton whistler in one of the Alouette II records3.

VLF measurements of the Poynting Flux along the geomagnetic field with the Injun 5 satellite

Poynting flux direction for proton whistlers determined from Injun 5 observations, obtaining data on source region and propagation in ionosphere

The effect of the latitudinal variation of the terrestrial magnetic field strength on ion cyclotron whistlers

The propagation of a low frequency electromagnetic wave in a cold multicomponent plasma in which collisions between electrons, ions and neutral particles can occur, is discussed. The wave frequencies are of the order of the ion gyro-frequencies. When the angle θ between the wave normal and the magnetic field exceeds a critical value θ c , then the sense of rotation of the electric and magnetic field vectors of the wave can suffer reversal. This phenomena is discussed for a model night-time ionosphere, and it is shown that the value of θ c , and the height at which reversal occurs, depend on frequency. An ion cyclotron whistler has three frequencies associated with it, namely the ion gyro-frequency at the satellite, the crossover frequency at the satellite and the cut-off frequency. The cut-off frequencey is the greatest frequency that has suffered polarisation reversal in traversing the lower ionosphere. The main purpose of the present paper is to determine the effect of the latitudinal variation of the terrestrial magnetic field on the cut-off frequency of proton whistlers. It is assumed that the wave normal is refracted to become vertical on entering the lower ionosphere so that θ is related to magnetic latitude φ. Also considered is the effect of the magnetic field strength variation on the high latitude cut-off of proton whistlers.

Ion temperature in the ionosphere obtained from cyclotron damping of proton whistlers

In this paper we discuss a method of determining ion temperature in the ionosphere from cyclotron damping of proton whistlers. These whistlers are dispersed forms of lightning impulses, observed by satellites as propagating left-hand polarized (ion cyclotron) waves. It is found that the amplitude of the proton whistler decreases abruptly at a wave frequency slightly below the proton gyrofrequency at the satellite. Of several factors considered, it is found that only cyclotron damping can satisfactorily explain this abrupt cutoff. The theory of cyclotron damping of proton whistlers is developed, and the difference between the wave frequency at cutoff and the proton gyrofrequency at the satellite is related to the proton temperature. Sample proton temperatures in the ionosphere are determined, using proton whistlers observed by the Injun 3 and Alouette 1 satellites. The temperatures found are comparable to those obtained previously by other experimenters. The method of observing ion temperatures developed here has inherent advantages in that the parameters measured are independent of electron temperature and ion composition.

A Helium Whistler observed in the Canadian Satellite Alouette II

LIKE her sister Alouette I, the Alouette II satellite carries a broad band, very-low-frequency receiver, but the pass band has been extended to (0.05–30 kc/s) from (0.4–10 kc/s). The Alouette II orbit has almost the same inclination as that of Alouette I (∼ 80°), but is elliptical with a perigee of 501 km, and an apogee of 2,983 km, rather than the almost circular 1,000 km orbit of Alouette I. One of the significant discoveries made by analysis of very-low-frequency data recorded by the Alouette I satellite1 was that an atmospheric (an electromagnetic impulse originating from a lightning flash) that had propagated upwards to the satellite was often immediately followed by a novel type of very-low-frequency signal. Initially, the frequency of this signal rose rapidly; the rate of increase then gradually diminished until the frequency approached a nearly constant value. These signals have been termed proton whistlers, and analysis2 has shown that they are due to coupling of wave energy from the (electron) whistler mode into ion cyclotron waves. Such coupling is possible only at frequencies below the proton gyro-frequency. The coupling occurs over a range of heights below the satellite, with a given frequency component coupling most strongly at a height determined solely by the positive ion composition of the ionosphere. The resulting ion cyclotron waves propagate upwards to the satellite and suffer increasing time delay as their frequency approaches the local proton gyro-frequency. This interpretation explains the form of dispersion exhibited by proton whistler signals, and why such signals are observed only after the occurrence of a normal short fractional hop whistler as well as the manner in which the wave energy enters and propagates through the lower ionosphere.

Determination of hydrogen ion concentration, electron density, and proton gyrofrequency from the dispersion of proton whistlers

In this paper we discuss a method for determining H+ concentration, electron number density, and proton gyrofrequency in the vicinity of a satellite by measurements of the asymptotic frequency-time profile of a proton whistler near the proton gyrofrequency. This new technique is applied to proton whistlers received by the Injun 3 VLF receiver. The calculated values of H+ concentration and electron density are shown to be in good agreement with measurements by other experimenters at similar altitudes, latitudes, and local times. B values calculated from the proton gyrofrequency are compared with values calculated from the Jensen and Cain expansion for the geomagnetic field. It is shown that the wave energy of a proton whistler is guided very nearly along the geomagnetic field and that the parallel component of the group velocity is closely approximated by the group velocity for longitudinal propagation. It is found that for frequencies near the proton gyrofrequency at the satellite the kernel multiplying n(H+)½ in the travel-time integral is large only in the region near the satellite. Assuming that the H+ concentration is uniform within this region, an expression is derived for the travel time of a proton whistler near the proton gyrofrequency. The H+ concentration and proton gyrofrequency are obtained by fitting this theoretical frequency-time expression to observed proton whistler signals. By combining this method for determining n(H+) with the crossover frequency method for determining α1 = n(H+)/ne the electron density can also be determined.