On the ring current energy injection rate

Assuming that the formation of the ring current belt is a direct consequence of an enhanced crosstail electric field and hence of an enhanced convection, we calculate the total ring current kinetic energy (K_R) and the ring current energy injection rate (U_R) as a function of the cross-tail electric field (E_CT); the cross-tail electric field is assumed to have a step function-like increase. The loss of ring current particles due to recombination and charge-exchange is assumed to be distributed over the whole ring current region. It is found that: (1) the steady-state ring current energy K_R is approximately linearly proportional to E_CT; (2) the characteristic time t_c for K_R to reach the saturation level is 3–4 h; (3) the injection rate U_R is proportional to E_CT^β where β ? 1.33?1.52; and (4) the characteristic time t_p for U_R to reach the peak value is 1–2 h and the peak U_R value is 50% higher than the steady-state value. Since β is now determined specifically for an enhanced convection, an observational determination of the relationship between E_CT(or φ_CT) and U_R is essential to a better understanding of ring current formation processes. If the observed β is greater than 1.5, additional processes (e.g. an injection of heavy ions from the ionosphere to the plasma sheet and subsequently to the ring current region) may be required.     

Pitch angle dependence of the charge-exchange lifetime of ring current ions

Previous work has parameterized the pitch angle dependence of the charge-exchange lifetime τ of ring current ions in terms of γ, the power of the cosine of the mirror latitude λ_m of the particles, such that $\text{τ(λ}{}_{\mathrm{m}}\text{)}\text{τ(0) ≌}\text{cos}{}^{\mathrm{\gamma }}\text{λ}{}_{\mathrm{m}}$ at given L. Using the atomic hydrogen density model of Johnson and Fish, previous authors have suggested values of γ = 5 or 6. We here evaluate γ as a function of λ_m and L using the more recent Chamberlain density models, and show that γ = 3?4 is more appropriate over most of the pitch angle and L range. Consequently, ion distributions in the ring current decay phase are expected to become rather less anisotropic in pitch angle due to chargeexchange than previously believed. We have also investigated the use of several other simple approximate analytic forms for $\text{τ(λ}{}_{\mathrm{m}}\text{)}\text{τ(0)}$, one of which gives far better agreement with the numerical results than the cos^γ λ_m, variation, and should hence be used in future studies.     

On the high energy proton spectrum measurements

The steepening of the proton spectrum beyond 1000 GeV and the rise in inelastic cross sections between 20 and 600 GeV observed by the PROTON 1-2-3 satellite experiments may be explained by systematic effects of energy dependent albedo (back-scatter) from the calorimeter.

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Résumé L'accroissement avec l'énergie de l'albedo dû au calorimètre peut expliquer l'augmentation de la pente du spectre primaire de protons au-delà de 1000 GeV et la croissance des sections efficaces inélastiques entre 20 et 600 GeV observés lors des expériences en satellite PROTON 1, 2 et 3.

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On sabbatical leave at Goddard Space Flight Center, Greenbelt, Md.     

Pc5 pulsations associated with ring current proton drifts: Stare radar observations

Detailed properties of a Pc5 pulsation with large azimuthal wavenumber observed using the STARE radar have recently been reported. A further four examples of this type of pulsation are presented, and it is shown that their properties are generally similar to those of the first example. However, there are some differences, the most important being that the variation of azimuthal phase velocity with latitude is significantly different for different time intervals during individual events, so that a mean phase velocity for a given latitude cannot be defined.When mapped to the equatorial plane in a dipole geomagnetic field, the variation of azimuthal phase velocity with L resembles the gradient-curvature drift of energetic protons in only a few time intervals within the events. The results are interpreted in terms of current theories of drift and bounce resonance of energetic particles with hydromagnetic waves. It is found that no single theory explains all aspects of the observations.     

Some implications of low altitude observations of isotropic precipitation of ring current protons beyond the plasmapause

The precipitation patterns of 6 keV protons at 10° and 80° pitch angles have been mapped at altitudes <1500 km from the ESRO 1A and 1B spacecraft. Equatorward of the trapping boundary, a region of isotropic precipitation, bounded on its equatorward border by a region of anisotropic (depleted loss cone) precipitation, is always observed. The latitudinal location of this transition appears to be nearly spatially coincident with the plasmapause. Similar precipitation patterns are shown to exist for higher energy protons. The general absence of enhanced precipitation at the plasmapause suggests that the inner boundary of the ring current is not usually produced by an enhanced proton pitch angle diffusion process. The isotropic precipitation observed beyond the plasmapause is most consistent with the occurence of an electrostatic instability throughout the ring current zone. It is doubtful whether the proposed cold Li plasma seeding experiments beyond the plasmapause could significantly increase the observed natural proton precipitation rates.     

Radiation production and energy deposition by ring current protons precipitated into the mid-latitude upper atmosphere

In the present paper the radiation production and energy deposition by ring current protons precipitated along magnetic field lines into the mid-latitude upper atmosphere is investigated. Specifically, we are interested in protons lost from the ring current by plasma instabilities. We first determine the magnitude and sharpness of the atmospheric loss cone. We then study the behavior of the precipitated hydrogen particles in the denser atmosphere using a Monte Carlo calculation. It is found that the energy deposition and radiation production will critically depend on how far the ring current protons diffuse into the loss cone before being neutralized in the atmosphere; this in turn will depend on the strength of the plasma turbulence in the ring current belt region.     

A note on the lifetime of the ring current particles

Characteristics of the time variations of Dst during magnetic storms are discussed in the context of several energizing and loss processes thought to be important for the production and decay of the storm time ring current. The energy input rate U_R may be more accurately evaluated if the predominant lifetime for ring current particle loss is taken as a few hours during main phase energizations, and a few tens of hours for particles remaining during recovery phases, and allowing for populations with a range of lifetimes during recurrent episodes of energization.     

The solar longitude dependence of proton event delay time

The relationship between heliographic longitude and the delay between flare occurrence and solar proton observation is studied using results obtained aboard HEOS A1 during 1969. The result obtained differs from previous findings. We ascribe this to the formation of a long-lived magnetic field configuration close to the Sun associated with a particular group of active regions.CNRS.     

Localised compressional hydromagnetic waves in the magnetospheric ring current

It is shown that the field line resonance phenomenon that occurs for quasi-transverse signals in a non-uniform cold plasma generally occurs for disturbances with a compressional magnetic component in a hot plasma like the ring current. The equations describing such localised signals are derived and discussed in various limits. It is pointed out that recent observations of low frequency compressional oscillations on spacecraft may be an example of such localised signals.     

Decay of the magnetic storm ring current by the charge-exchange mechanism

Equatorial charge-exchange lifetimes of ring current protons are recalculated, and the decay of a collection of ring current protons trapped on an L-shell by the charge-exchange mechanism is determined using recent models of the hydrogen geocorona. Observational results pertaining to the decay of ring current energy are briefly discussed, as are a number of competing loss mechanisms. Since charge exchange is a simple physical process which is very efficient in removing ring current energy from L-shells near to the Earth (say, L < 4), it is suggested that it may well be the dominant loss mechanism in this region.     

Growth rate and decay of magnetospheric ring current

The rate of energy input to the ring current is studied as a function of solar wind parameters. The ring current dissipation rate is also examined. The decay constant τ in the main phase of a storm has been shown to be independent of its intensity and to equal (4 ± 2) h. In the recovery phase τ rises with increasing storm intensity.     

Inductive electric field of a time-dependent ring current

The inductive electric field generated by a time-dependent symmetric ring current has been investigated. The symmetric ring current was modelled by a population of protons drifting in a magnetic dipole field. The interaction of these protons with ion-cyclotron waves was assumed to be the dominant energy loss process for the ring current protons, at least under certain conditions. The calculation, with spectral densities for the ion-cyclotron waves that are based on experimental data, showed that an azimuthal inductive electric field of as much as 0.25 mV/m can be produced by this mechanism. Furthermore there is evidence that if the spectral density of the waves is substantially larger than the one adopted here, the electric field might increase to the order of 1.0 mV/m or more.     

440 keV proton precipitation at middle latitudes during the recovery phase of magnetic storms

Quasitrapped (H_min < 100 km) protons with energies E > 440 keV have been detected during magnetic storms by the IK-5 satellite in a narrow zone with a center at L = 3.0−3.2; this zone is well separated from the region of Isotropie fluxes at L > 4. Data for five moderate storms have been analysed in detail. It was found that the quasitrapped proton peaks appear during the recovery phase of magnetic storms and that the scattering of protons toward low mirror points takes place in all local time sectors. The relation between the observed precipitation of the E > 440 keV protons and the intraplasmaspheric precipitation of low-energy protons has been discussed in the light of the theory of generation of ion-cyclotron waves by the ring current and the theory of parasitic interaction of these waves with the radiation belt protons. A series of arguments indicates that the phenomenon under study is connected with the magnetopheric process which generates the SAR arcs.     

Bastille Day storm: Global response of the terrestrial ring current

Global images of the Earth's inner magnetosphere and its response to the coronal mass ejection (CME) on the 15 July 2000 were obtained by the IMAGE spacecraft. The images were taken in energetic neutral atoms (ENA) by the High-Energy Neutral Atom (HENA) imager. ENAs are produced by charge exchange between the hot ion population of the magnetosphere and the cold neutral hydrogen geocorona. The ENA images show how plasma is injected into the nightside magnetosphere as the interplanetary magnetic field (IMF) turns strongly southward. As the IMF B _z increases and the storm intensity decreases, the ENA images show that the ring current becomes closed and symmetric as IMF B _z reaches positive values.     

Evidence of energy dependent mechanisms for the precipitation of auroral electrons

This paper discusses the experimental results on electron precipitation in a diffuse aurora obtained by a sounding rocket launched from ANDENES (L ～ 6·2) on 3 November 1968. A considerable increase in the intensity of low energy electrons, E_e ? 5 keV, followed a large precipitation of more energetic electrons E_e ? 5 keV. From the observation of angular distributions and an estimate of the diffusion coefficient (D_α ? 10^?3 (sec)^?2), it is suggested that this higher energy precipitation is induced by gyroresonant interactions of magnetospheric electrons with radiation in the whistler mode. The lower energy precipitation separated in time and/or space, shows quasi-periodic modulations in the 5–15 sec range with periods close to the bounce period. It is suggested that this precipitation is the result of bounce-resonance interactions with electrostatic waves in the equatorial plane. Finally, from a comparison between the experimental energy spectra and plasma sheet spectra it can be concluded that these electrons are injected from the plasma sheet during a substorm and are then diffused and precipitated by energy dependent mechanisms.     

The energy of electric current sheets

Solar Physics - The free energy associated with current sheets formed by displacing magnetic dipoles in a highly conducting medium is discussed. Specific models are illustrated, based on the idea...     

The energy of electric current sheets

This paper treats two problems on the formation of electric current sheets in the highly electrically conducting solar atmosphere. The first problem concerns a vertical current sheet formed by decreasing the distance between a pair of parallel magnetic line-dipoles lying on the photosphere. The solution to this problem was given previously by Priest and Raadu. With an interest in the flare phenomenon, they derived a formula for the energy stored through the presence of the current sheet. We show that this formula is incorrect. Firstly, there is an error of sign in the derivation of Priest and Raadu, so that, when corrected, the formula gives a negative value for the stored energy. Secondly, the formula is shown to refer to an energy quite different from the free energy associated with the current sheet. To calculate for the current free energy, it is important to account for the frozen-in condition in the highly conducting photosphere.The second problem of the paper concerns the current sheet formed by increasing the distance between the pair of line-dipoles. A different field configuration results, with a curved current sheet lying transverse to the vertical. An analysis of the energy properties is given, to compare with the properties of the Priest-Raadu model.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

VLF-emissions associated with ring current electrons: Off-equatorial observations

The combination of a small inclination of the orbit (～4°) with the tilt angle (～11°) of the Earth's magnetic dipole axis enabled the S³-A satellite (Explorer 45) to make simultaneous observations of magnetospheric VLF-emissions and the associated enhancement of ring current electrons not only at the magnetic equator but also up to 15° geomagnetic latitudes. Microdensitometer scanning of the wideband data of these emissions reveals that the band of missing emission in the off-equatorial whistler mode emissions (chorus) appears at $\text{f}{}_{\mathrm{<mtext>Ho</mtext>}}\text{2}$ and that the intensities of the off-equatorial emission above $\text{f}{}_{\mathrm{<mtext>Ho</mtext>}}\text{2}$ are very weak in contrast to those of the near equatorial emissions, where $\text{f}{}_{\mathrm{<mtext>Ho</mtext>}}\text{2}$ is the equatorial electron gyrofrequency corresponding to the local gyrofrequency f_H at the satellite. Ray-tracing of whistler mode waves produced by the enhanced ring-current electrons at the geomagnetic equator just outside of the plasmapause has shown that some of these waves are reflected from high latitudes back to the Equator inside the source region. This process had been previously speculated to explain the formation of the bimodal intensity distribution with a gap at half the gyrofrequency (the two-band chorus) in the equatorial emission data. The intensities of those reflected waves, however, are shown to be insufficient to explain the observed emissions below $\text{f}{}_{\mathrm{<mtext>Ho</mtext>}}\text{2}$ at the Equator. These results indicate that the superposition of two types of emissions produced by the same processes but from different locations is not the main mechanism for the formation of the two-band chorus and that the dominant sources of these choruses are located around ± 5° geomagnetic latitude.