Low-frequency electric field fluctuations excited by ring current protons

Energetic protons haying ring type distributions are shown to generate low-frequency electrostatic waves, propagating nearly transverse to the geomagnetic field lines, in the ring current region by exciting Mode 1 arid Mode 2 nonresonant instabilities and a resonant instability. Mode 1 nonresonant instability has frequencies around ~4 Hz with transverse wavelengths of ~(8–80) km, and it is likely to occur in the region L = (7–8). Mode 2 nonresonant instability can generate frequencies ~(850–1450) Hz with transverse wavelengths ~(2–20) km. The typical frequencies and transverse wavelengths associated with the resonant instability are (950–1250) Hz and (30–65) km. Both the Mode 2 nonresonant instability and the resonant instability can occur in the ring current region with L = (4–6). The low-frequency modes driven by energetic protons could attain maximum saturation electric field amplitude varying from 0.8 mV/m to 70 mV/m. It is suggested that the turbulence produced by the low-frequency modes may cause pitch angle scattering of ring current protons in the region outside the plasmapause resulting in the ring current decay.     

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.     

Development of four magnetic storms in February 1972

Four magnetic storms were observed in February 1972, with instruments on the Explorer 45 satellite in the evening quadrant of the inner magnetosphere. The magnitude of the storms ranged from small, D_st ? ?40 γ, to moderate, D_st ? ?80 γ. During the development of the storms several substorms occurred. At the beginning of the substorms there was evidence of a partial ring current above L = 5. After the expansion phase of several substorms there was evidence of enhancement of a partial ring below L = 5. Distortions of the field in the east-west direction were observed, in conjunction with substorm expansions, that can be interpreted as due to field aligned currents flowing from the ionosphere. A substantial symmetric ring current, at L～4, developed during the largest storm. Very little additional ring current was contributed by the smallest storm. Relations between the magnetosphere inflation and ring current protons, plasmaspheric hiss, and ULF waves also measured on Explorer 45 were noted.     

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.     

Ring current protons in the upper atmosphere within the plasmasphere

keV protons observed by the ESRO 1A satellite in the upper atmosphere equatorward of the main precipitation zone are described and discussed. The protons are highly anisotropic (empty loss cone) between the low-latitude boundary of the main precipitation zone and approximately L=4 during quiet and moderately disturbed conditions (K_p=0?4). Between L=4 and L=2.7 the proton flux is generally enhanced compared to that at L values somewhat above 4 and only moderately anisotropic. Substorms push the outer main precipitation zone equatorwards, but the boundaries of the innermost, moderately anisotropic region (at L=2.7 and L=4) move only when strong magnetic storms compress the plasmasphere to within L=4. It is suggested that the moderately anisotropic zone is caused by the ion-cyclotron instability for which the growth rate may have a broad maximum between about L=2.7 and L=4. For proton energies in the keV range the instability is excited only in regions with cold plasma densities above several hundred ions per cubic centimeter. It is finally concluded that the observations of low-latitude proton precipitation lend further support to the mechanism of ion-cyclotron instability as the cause of proton pitch angle diffusion, as proposed by Cornwall et al. (1970).     

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.     

The role of charge-exchange cross-section for pickup protons and neutrals in the inner heliosheath

The process of deceleration of the solar wind downstream of the termination shock is studied on the basis of a one-dimensional multi-component model. It is assumed that the solar wind consists of thermal protons, electrons and interstellar pickup protons. The protons interact with interstellar hydrogen atoms by charge-exchange. Two cases are considered. In the first one, the charge-exchange cross-section for thermal protons and hydrogen atoms is the same as for pickup protons and atoms. Under this condition, there is a strong dependence of the solar wind velocity on the downstream temperature of pickup protons. When the proton temperature is close to 10 keV, the change in the velocity with the distance from the termination shock is similar to that measured on the Voyager 1 spacecraft: linear velocity decrease is accompanied by an extended transition region with near-zero velocity. However, with a more careful approach to the choice of the charge-exchange cross-section, the situation changes dramatically. The strong dependence of the solar wind speed on the pickup proton temperature disappears and the transition region in the heliosheath disappears as well, at least at reasonable distances from the TS.     

Nonconvective ion cyclotron instability

The electromagnetic ion cyclotron instability is shown to be nonconvective for a wide range of plasma β's and ring current proton anisotropies A. The addition of cold plasma to the ring current enlarges the region of the β-A parameter space for nonconvective instability. Thus, despite the high Alfvén speed outside the plasmasphere, ion cyclotron wave amplitudes could grow to appreciable levels and contribute to the pitch-angle and energy diffusion of ring current protons.     

Transport,charge exchange and loss of energetic heavy ions in the earth's radiation belts: Applicability and limitations of theory

Ions in the trapping region of the earth's magnetosphere are subject to physical and chemical interactions which control their absolute and relative abundances. Charge exchange reactions act to establish a distribution of ionic states that is largely determined by the chemical properties of the individual species. Convection (“drift”) mechanisms and cross-L diffusion cause ions to be distributed over the entire trapping region with flux intensities determined by the nature and strength of the ion source, transport and loss mechanisms which in general are dependent on energy, mass and charge. Current theories describe ion transport through path tracing for individual particles or by radial diffusion for a population as a whole based on stochastic analysis; a comprehensive treatment of the combined convection and diffusion for trapped and non-trapped ions is yet to be developed. Even in studies where diffusion is the sole transport mechanism considered, only equatorially mirroring particles ($\text{α}{}_0\text{=}\text{π}\text{2}$) have been theoretically treated. There are clearly both upper and lower bounds on the ion energy beyond which diffusion theory ceases to be valid: at high energies where the ion gyroradius becomes too large for the adiabatic approximations to be valid and at low energies where convective drift is a dominant process. In spite of the known shortcomings of the diffusion theory and associated modeling, intriguing theoretical predictions of the relative ionic composition of the radiation belts have been made and some of them are now confirmed by direct observation. Among them is the predicted importance of ions heavier than protons at ring current energies of tens of keV which follows from the charge exchange chemistry.     

Induced proton flow in a collapsing post-sunset ionosphere and protonosphere

The effect of the onset of post-sunset conditions on thermal proton flow is examined for mid-latitudes by numerical solution of the equations of continuity, momentum and energy balance for H⁺ and O⁺. Results are calculated for a dipole magnetic field tube situated at L = 4 and acceleration terms are included in the momentum equations. Proton flow into the ionosphere results from decay of the F2-layer. Changes in temperatures and temperature gradients following sunset may not enhance the H⁺ flow. Under extreme conditions the H⁺ flow remains subsonic. It seems unlikely that an interhemispheric flux of protons can directly maintain the nighttime F2-layer.     

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.     

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.     

Advanced method to derive the IMF direction near Mars from cycloidal proton distributions

In a previous paper, we showed a method for deriving the interplanetary magnetic field (IMF) orientation from the velocity distribution of ring-like distributed ions as measured by the Ion Mass Analyser (IMA) on board Mars Express (MEX). This method has been improved so that one can derive the IMF orientation from a very limited portion of the ring distributions, i.e., only the highest energy portion of the ring distribution. This method uses the maximum variance direction L instead of the minimum variance direction N, which are derived from manually selected ring data. Because IMA's count rate for a semi-persistent ring distribution is nearly proportional to energy squire, L is most likely aligned to the tangential direction of the ring distribution at its highest energy, and this tangential direction is parallel or anti-parallel to the electric field. A vector product of L and the solar wind direction (X) gives the IMF orientation projected to the Y-Z plane. The tilt angle of IMF toward the X direction from the Y-Z plane is the same as the angle between the X direction and the ring plane, and is obtained from two methods when the initial speed of the ring ions is estimated to be much smaller than the solar wind speed: (1) angle between the velocity of ring's maximum energy portion and the solar wind vector, and (2) energy ratio between the solar wind and the maximum energy of the ring. The present method is applied to the IMA data from 3 June 2005 (0605-0640 UT) when the Mars Global Surveyor (MGS) magnetometer data are available. Using these data, we also tried to determine the sign of the IMF direction by estimating the evolution direction of the ring ions.     

Steady-state observations of geomagnetically trapped energetic heavy ions and their implications for theory

Measurements of energetic heavy ions using the Explorer 45 and ATS-6 satellites are reviewed and the resulting implications for theory are evaluated. The measured ions are basically protons and helium ions in the energy range from 0.1 to 1 MeV/nucleon. The equatorial energetic ion distributions inside L = 4.5 are found to be very stable for extended periods of time. These ions are very closely confined to the equatorial plane and are sharply peaked as a function of L around a value designated as L_max. Beyond L = 5.0 the fluxes of these ions are more variable with order of magnitude variations being observed at L = 6.6 on the time scales of minutes, hours, or days. The region inside L = 4.5 appears to be well described by radial diffusive transport driven by fluctuations in the geomagnetic field coupled with losses due to charge exchange and Coulomb interactions with ambient hydrogen geocorona and terrestrial plasma environment. From an analysis relating the position in L-value of the maximum intensity, L_max, observed for a given ion species and energy, it is argued that the influence of fluctuations in the convection electric field as discussed by Cornwall (1972) are not effective in radially diffusing in L ions with energies greater than a few hundred kiloelectron volts per nucleon. The source of these ions remains basically undetermined and its determination must await further measurements.     

Ring current energy injection rate and solar wind-magnetosphere energy coupling

Assuming that the formation of the ring current belt is a direct consequence of an enhanced convection of plasma sheet protons, the expression for the energy injection rate U_R is formulated as a function of the cross-tail potential drop φ_CT for a simple electric field-magnetic field model. It is shown that an approximate expression for U_R thus formulated consists of two parts: (i) the first part U_R1, which is linearly proportional to φ_CT, is supplied by the corotation electric field and (ii) the second part U_R>2, which is proportional to φ²_CT, is supplied by the solar wind energy input to the magnetosphere. The second part U_R2 dominates the ring current energy input when the cross-tail potential drop φ_CT is greater than ～ 95 keV, namely during disturbed periods. An important finding is that the second part U_R2 of the ring current energy input is shown to be proportional to the solar wind-magnetosphere energy coupling function ?, recovering the observationally established relationship. Therefore, the present study verifies that an enhanced convection is the cause of the ring current formation.     

Observations of Pg pulsations in the Northern Auroral zone and at lower latitude conjugate regions

An analysis is made of giant pulsation (Pg) data recorded at ground stations in the Northern Auroral Zone in Scandanavia (mainly at Tromsø, L = 6.4 and Kiruna, L = 5.5) during the period September 1976 to December 1977. They are shown to have a meridional variation of amplitude and polarization consistent with a field line resonance structure and their vertical component behaviour suggests that they also have a rapid azimuthal phase variation. Limited data from conjugate stations at L = 4.4 are used to show that Pg's are odd mode oscillations of the field line. Pg's are equated to the observation of a unique compressional wave in space at synchronous orbit and it is suggested that they result from the drift wave instability of the compressional Alfven wave at the outer edge of the quiet time ring current.     

Formation of the lunar atmosphere

Measurements of⁴⁰Ar and helium made by the Apollo 17 lunar surface mass-spectrometer are used in the synthesis of atmospheric supply and loss mechanisms. The argon data indicate that about 8% of the⁴⁰Ar produced in the Moon due to decay of⁴⁰K is released to the atmosphere and subsequently lost. Variability of the atmospheric abundance of argon requires that the source be localized, probably in an unfractionated, partially molten core. If so, the radiogenic helium released with the argon amounts to 10% of the atmospheric helium supply. The total rate of helium escape from the Moon accounts for only 60% of the solar windα particle influx. This seems to require a nonthermal escape mechanism for trapped solar-wind gases, probably involving weathering of exposed soil grain surfaces by solar wind protons.     

Excitation of magnetosonic waves with discrete spectrum in the equatorial vicinity of the plasmapause

There is a magnetosonic waveguide under the arch of the plasmasphere. This channel, in the form of a ring with radius L～4, surrounds the Earth. It is shown that in this region of the magnetosphere the flute-like electromagnetic disturbances (k6 = 0) with frequencies ω = sω_p can be excited by energetic protons, with non-monotonic dependence on transverse energy ($\text{??/?ε}{}_{\mathrm{\perp }}\text{> 0}$). The interpretation of magnetic pulsations which have been observed in the equatorial vicinity of the plasmapause on the satellite OGO-3 in the frequency range ～10² cps (Russell et al., 1970) is given. In particular the origin of discrete structure of the observed spectra (narrow band spikes for a rather broad range of frequency) is discussed.     

Proton observations supporting the ion cyclotron wave heating theory of SAR arc formation

Low altitude satellite observations of precipitated and locally mirroring protons during periods of ground-based SAR arc observations are presented. The SAR arcs are found to be located in a region with significantly enhanced proton pitch angle scattering and enhanced electron temperature, but inside the plasmapause where the proton pitch angle distribution is anisotropic. The increase in the pitch angle scattering takes place in a localized region having a width of a few tenths of a L-value. The observations can favourably be accounted for by the Cornwall et al. (1971) theory for the SAR arc formation. Using observed proton fluxes and typical energy spectra, the expected Hβ intensity in the SAR arc region is estimated to be a few Rayleighs, and the energy flux from precipitated protons above a few keV to be 10^?2?10^?1erg/cm²s. These estimates are in reasonable agreement with previously published theoretical and experimental values. Simultaneous groundbased observations of Hα emissions were found in the region of intense, isotropic proton precipitation located outside the plasmapause.