A statistical analysis of the low-energy geosynchronous plasma environment—I. Electrons

There has been a long-standing lack of detailed statistical information on the low-energy (1-eV–100-keV) geosynchronous plasma environment. In this paper, data on the electron environment between ～30 eV and 80 keV were analyzed from a statistical standpoint. Specifically, ～50 days of 10-min averages of the first 4 moments of the distribution function from the University of California at San Diego low-energy plasma detectors on the ATS-5 and ATS-6 geosynchronous satellites were analyzed in terms of: occurrence frequency, local time variations, K_p variations and variations at a given local time following injection. The 4 moments were intercompared and simple expressions capable of simulating their relationships empirically derived. In conjunction with this analysis, the accuracy of the 4-moment representation was tested and, for the electrons, found to be of value in specifying the background electron environment at geosynchronous orbit.     

A statistical analysis of the low-energy geosynchronous plasma environment—II. Ions

This is the second of two papers which together provide a detailed statistical analysis of the low-energy (1-eV–100-keV) geosynchronous plasma environment. In this paper, data on the ion environment between ～1 eV and 80 keV are statistically analysed. About 50 days of 10-min averages of the first 4 moments of the ion distribution function from the University of California at San Diego low-energy plasma detectors on the ATS-5 and ATS-6 geosynchronous satellites are studied in terms of: occurrence frequency, local time variations, K_p variations, injection events, and intercomparisons among the 4 moments. Variations in the 4 moments can be explained by assuming the existence of 2 dominant plasma populations (the plasmasphere and ring current) upon which are superimposed plasma injection events. In conjunction with this analysis, the accuracy of the 4-moment representation for ions was tested and, unlike that for electrons, found to be limited by the energy band-pass of the instrumentation and by a lack of knowledge of the angular anisotropies and ionic composition. Even so, these limitations are outweighed by the utility and compactness of the method. A technique for correcting the limited energy band-pass of the instrumentation is presented in the Appendix.     

Ground Pc3–Pc5 wave power distribution and response to solar wind velocity variations

We examine the magnetospheric wave power in the Pc3–Pc5 range in terms of its growth and decay characteristics and its distribution in L shell in response to the interplanetary plasma bulk velocity, V_SW. We use linear and nonlinear (rank-order) correlation and filtering methods to quantify the effective coupling of the wave power to V_SW variations. These methods are applied to measurements from 26 ground magnetometers of the IMAGE array and NOAA's GOES-10 spacecraft at geosynchronous orbit, taken over 2 years of solar-maximum activity (2002–2003). We find that the ground ULF wave power is structured in the range 3.5<L<6.4 and distributed uniformly in the range 6.4<L<15 (uncertainties in L are estimated to be ±0.5). The response of the wave power to the V_SW is characterized by an increase starting 3 days before the V_SW peak, intensifying several hours before the peak, and is followed by a fast decrease in the next 2 days. The rapid decay of ULF waves has two stages: one at τ=−6±2 h before the solar wind velocity reaches its peak, and one at the V_SW peak, τ=0. We suggest that the first one is brought about by wave–particle interaction with inner-magnetospheric populations while the second one is a dV_SW/dt effect. The correlation results are confirmed by calculating the finite-impulse response, which shows clearly the decay of the ULF waves after the V_SW peak. The response of the wave power at geosynchronous orbit is remarkably similar to that of the ground wave power at comparable L shells. The above findings characterize the inner-magnetospheric response to interplanetary high-speed streams, as opposed to the more short-lived, higher-amplitude response to CMEs.     

Magnetohydrodynamic simulation of the coronal transient associated with the solar limb flare of 1980, June 29, 18∶21 UT

Soft X-ray data from the XRP experiment on SMM are used to generate the temperature and density in the flaring region of the 1980, June 29 (18∶21 UT) solar flare. The temporal data (T _max ～- 20 × 10⁶ K and n _max ～- 4 × 10¹¹ cm^?3), together with an assumed velocity, are used to simulate mass injection as the input pulse for the MHD model of Wu et al. (1982a, 1983a). The spatial and temporal coronal response is compared with the ground-based, Mark III K-coronameter observations of the subsequent coronal transient. The simulation produces a spatially-wide, large amplitude, temporarily-steepened MHD wave for either of the two ‘canonical’ magnetic topologies (closed and open), but no shock wave. This result appears to be confirmed by the fact that a type II radio event was observed late in the event for only a few minutes, thereby indicating that a steepening wave with temporary, marginal shock formation, was indeed present. The density enhancements produced by the simulation move away from the Sun at the same velocity observed by the K-coronameter. However, the observation of the coronal transient included a rarefaction that does not appear in the simulation. A probable explanation for this discrepancy is the likelihood that the magnitude and temporal profile of the density of the soft X-ray emitting plasma should not have been used as part of the mass injection pulse. We believe that the temperature profile alone, as suggested by earlier simulations, might have been a necessary and sufficient condition to produce both the compression and rarefaction of the ambient corona as indicated by the K-coronameter data. Hence, the dense plasma observed by XRP was probably confined, for the most part, close to the Sun during the ～ 17 min duration of the observations.     

The necessity of fundamental emission in type III bursts

Observations of some type III radio bursts in the hectometer and kilometer wave range are compared with theoretical predictions. It is shown that the burst emission must be near the plasma frequency in the region between 10 R _⊙ and 50 R _⊙ in order to be consistent with the observed steep rise in brightness temperature for these bursts. The results of Fainberg, Malitson et al., and Haddock and Alvarez are discussed and compared with the interpretation of emission near the plasma frequency.     

Magnetospheric asymmetries associated with the y-component of the IMF

Observed magnetospheric asymmetries which occur in response to the y-component of the IMF are discussed in terms of the open model of the magnetosphere. The torque which the IMF exerts on the magnetosphere about the Earth-Sun axis results in asymmetric addition of open flux tubes to the tail lobes about the noon-midnight meridian. In response an IMF-associated B_y field appears across the tail lobes. The ratio between internal and external B_y fields will generally be same as the ratio between internal and external electric fields. If the tail flux asymmetry is related to an asymmetric distribution of the field normal to the tail magnetopause then an asymmetry in tail lobe electric field and plasma populations will immediately result, as observed. If the flux asymmetry is associated with a twist in the tail then the B_y field will appear but not necessary the electric field and plasma asymmetries. Generally both effects may occur together. Simple open tail lobe models are derived which demonstrate the asymmetry effects. These represent more physically satisfactory models of the tail and its plasma populations than available hitherto, but they remain somewhat unrealistic in a number of respects. Finally, it is shown that the observed asymmetry effects on closed (auroral zone) field lines may be at least qualitatively accounted for if the cross-magnetosphere IMF-associated B_y field pervades not only the open but also the closed field line regime, as may be generally expected.     

Instability of Electrons Trapped by the Coronal Magnetic Field and Its Evidence in the Fine Structure (Zebra Pattern) of Solar Radio Spectra

Solar radio emission is a significant source of information regarding coronal plasma parameters and the processes occurring in the solar atmosphere. High resolution frequency, space, and time observations together with the developed theory make it possible to retrieve physical conditions in the radiation source and recognize the radiation mechanisms responsible for various kinds of solar radio emission. In particular, the high brightness temperature of many bursts testifies to coherent radiation mechanisms, that is, to plasma instabilities in the corona. As an example, the fine structure of solar radio spectra looking like a set of quasi-harmonic stripes of enhanced and lowered radiation, which is observed against the type IV continuum at the post-flare phase of activity, is considered. It is shown that such emission arises from a trap-like source filled with a weakly anisotropic equilibrium plasma and a small addition of electrons which have a shortage of small velocities perpendicular to the magnetic field. For many recorded events with the mentioned fine spectral structure the instability processes responsible for the observed features are recognized. Namely, the background type IV continuum is due to the loss-cone instability of hot non-equilibrium electrons, and the enhanced striped radiation results from the double-plasma-resonance effect in the regions where the plasma frequency f _p coincides with the harmonics of electron gyrofrequency f _B ; f _p=sf _B . Estimations of the electron number density and magnetic field in the coronal magnetic traps, as well as the electron number density and velocities of hot electrons necessary to excite the radiation with the observed fine structure, are given. It is also shown that in some cases several ensembles of non-equilibrium electrons can coexist in magnetic traps during solar flares and that its radio signature sensitively depends on the parameters of the distribution functions of the various ensembles.     

Plasma properties in the dayside cusp region

A statistical study of the cusp plasma has been performed using mainly electron data from the LPS, Rome, plasma experiment flown onboard HEOS-2. We have located the cusp by means of 35–50 eV electrons, from 1.5 to 2.5R_E (south pole) and from 3R_E up to 11R_E (north pole) at 60–70° SM latitude within ±60° of SM longitude from the noon meridan plane. The average cusp thickness is 4.2° of invariant latitude. The location of the cusp in invariant latitude around the noon meridian plane depends on the IMF component B_zGSM according to the linear best fit: Λ = 78.7° + 0.48B_zGSM(γ). Away from the noon meridian plane the invariant latitude of the cusp decreases from 79–84° to 70–74° (at ±50° SM Longitude). At the equatorward edge of the north pole cusp, at all radial distances and at all SM longitudes, we have found a population of electrons with a harder energy spectrum than in the cusp itself. These electrons show a peak at 170–280 eV in our data. They are not the cusp (35–50 eV) electrons and are easily distinguishable from the 1 keV magnetospheric electrons. In the south pole auroral oval they are found at any SM longitude mainly poleward of the 1 keV electrons. The cusp electrons (35–50 eV) and protons have anisotropies that vary with radial distance and SM latitude, both flowing earthward more or less along the magnetic field.     

The effects of the polytropic coefficient on plasma sheath in two cases isothermal and adiabatic ion thermal flow

Recently it has been shown that for finite and small values of the electron Debye length, the ion polytropic coefficient is approached to some constant value in the plasma sheath region by decreasing the plasma density. In this paper, using a plasma multi fluid model, the effect of ion polytropic coefficient γ _i on the plasma sheath structure have been examined. The numerical calculations of the basic equation of the model show that the polytropic coefficient strongly affects on the plasma sheath characteristics. The results show that by transition from an isothermal flow (γ _i =1) to an adiabatic flow (γ _i =3), the net current to the wall and the electric potential distribution increase and the sheath width decreases in a thermal plasma sheath.     

A model for thinning of the plasma sheet

A one-dimensional model for thinning of the plasma sheet is developed on the basis of launching a fast mode MHD rarefaction wave propagating in the tailward direction along the plasma sheet. Behind the rarefaction wave the pressure is reduced, leading to thinning of the plasma sheet and also to an Earthward plasma flow with a speed on the order of the sound speed a₀. The plasma sheet thickness is reduced by a factor of 2 if an Earthward plasma flow speed of 0.8a₀ is induced. The predictions of the model are in reasonable agreement with observations.     

A study of the Bremsstrahlung of plasma at about 1 A.U. in times of quiet sun and flare activity

In space plasma, especially in the interior of plasma with weak magnetic field, Bremsstrahlung is the main mechanism of loss of the plasma energy. As shown by our calculations of the Bremsstrahlung of plasma at 1 A.U. in times of quiet sun and flare activity, the variation of intensity of plasma radiation I_f is directly related to the frequency of the electromagnetic wave. When the frequency f is close to that of plasma f_pe, the intensity of radiation is greatly enhanced. With increasing frequency, the enhancement of the radiation intensity with frequency exhibits a slow logarithmic decrease. The brightness temperature T_b is directly proportional to the electron temperature of plasma T_e and to the optical depth of medium. The overall tendencies of variations of T_b and I_f with frequency are identical. For the same frequency, the values of I_f and T_b are lower in time of quiet sun than in time of flare activity.     

Formation of the localized structures and the generation of turbulence by 3-dimensional kinetic Alfvén waves in solar wind plasmas

In the present paper, we have investigated nonlinear interaction of three dimensional kinetic Alfvén wave with perpendicularly propagating magnetosonic wave for intermediate β-plasma (m _e /m _i ?β?1). We have developed the set of dimensionless equations in the presence of ponderomotive nonlinearity due to three dimensional kinetic Alfvén wave in the dynamics of perpendicularly propagating magnetosonic wave. Numerical simulation has been carried out to study the effect of nonlinear coupling of three dimensional kinetic Alfvén wave with perpendicularly propagating magnetosonic wave on power spectrum for the plasma parameters applicable to solar wind around 1 AU. Relevance of the obtained results is pointed out with observation received by Cluster spacecraft for the solar wind around 1 AU.     

The effects of neutral air winds on the electron content of the mid-latitude ionosphere and protonosphere in summer

The effects of neutral air winds on the electron content (N_T) and other parameters of the mid-latitude ionosphere have been modelled by means of mathematical solutions of the time-dependent continuity and momentum equations for oxygen and hydrogen ions. The geometry is chosen to represent a propagation path between a geosynchronous satellite and a ground station, and the computations are compared with results from slant path observations of the ATS-6 radio beacon made at Lancaster (U.K.) and Boulder, Colorado (U.S.A.).It is demonstrated that the electron content responds markedly to the magnitude and phase of the neutral air winds and that the effect induced by the wind on the electron content shows a consistent quantitative relationship with the wind velocity, especially during daytime. Reasonable variations in the phase and magnitude of the wind produce a range of daily electron content patterns which encompass the range of daily variations observed.The computations show that the wind gives rise to enhanced filling of the protonosphere. This shows as a depressed value of the shape factor (F), which by definition means that a greater fraction of the ionization is at higher altitudes. The depression of F is enhanced by a poleward wind and is suppressed or even superseded by an equatorward wind through changes of the electron density distribution with altitude.     

Dynamical History of the Earth–Moon System

Differential equations describing the tidal evolution of the earth's rotation and of the lunar orbital motion are presented in a simple close form. The equations differ in form for orbits fixed to the terrestrial equator and for orbits with the nodes precessing along the ecliptic due to solar perturbations. Analytical considerations show that if the contemporary lunar orbit were equatorial the evolution would develop from an unstable geosynchronous orbit of the period about 4.42 h (in the past) to a stable geosynchronous orbit of the period about 44.8 days (in the future). It is also demonstrated that at the contemporary epoch the orbital plane of the fictitious equatorial moon would be unstable in the Liapunov's sense, being asymptotically stable at early stages of the evolution. Evolution of the currently near-ecliptical lunar orbit and of the terrestrial rotation is traced backward in time by numerical integration of the evolutional equations. It is confirmed that about 1.8 billion years ago a critical phase of the evolution took place when the equatorial inclination of the moon reached small values and the moon was in a near vicinity of the earth. Before the critical epoch t _cr two types of the evolution are possible, which at present cannot be unambiguously distinguished with the help of the purely dynamical considerations. In the scenario that seems to be the most realistic from the physical point of view, the evolution also has started from a geosynchronous equatorial lunar orbit of the period 4.19 h. At t < t _cr the lunar orbit has been fixed to the precessing terrestrial equator by strong perturbations from the earth's flattening and by tidal effects; at the critical epoch the solar perturbations begin to dominate and transfer the moon to its contemporary near-ecliptical orbit which evolves now to the stable geosynchronous state. Probably this scenario is in favour of the Darwin's hypothesis about originating the moon by its separation from the earth. Too much short time scale of the evolution in this model might be enlarged if the dissipative Q factor had somewhat larger values in the past than in the present epoch. Values of the length of day and the length of month, estimated from paleontological data, are confronted with the results of the developed model.     

Parametric study of near-wake structure of spherical and cylindrical bodies in the laboratory

Some aspects of the interaction between metal bodies and streaming rarefied plasmas were studied in a newly constructed Plasma Wind Tunnel as part of an attempt to investigate (via simulation) phenomena relevant to the spacecraft/space plasma interaction. Detailed near-wake ion current profiles for both spherical and cylindrical bodies at different body potentials (φ_S) and at different plasma flow parameters are presented. Various features of the profiles can be correlated, at least qualitatively, with both plasma and body characteristics. For example, the width of the wake zone appears proportional to the Debye length (λ_D) and depends on the potential of the target body although it appears to be relatively insensitive to the ratio $\text{S = V}{}_{\mathrm{<mtext>flow</mtext>}}\text{/(}\text{2kT}{}_{\mathrm{e}}\text{M}{}_{\mathrm{+}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. The amplitude of the ion current peak(s) also appears proportional to λ_D while, for fixed φ_S, the location of the peak is directly related to S and possibly dependent upon body geometry. The general importance of body geometry is qualitatively demonstrated. In addition, a discussion of the relevance of the above studies to previous in situ data obtained from the Ariel I and Gemini/Agena missions is given.     

Towards a theory for type III solar radio bursts

The mechanisms for the transformation of plasma waves into radiation near the fundamental and second harmonic of the plasma frequency are reviewed and equations are given for both the emission and absorption coefficients for these mechanisms. Near the fundamental the process is the scattering of plasma waves on the polarization clouds of ions and the absorption coefficient can be negative, i.e. the radiation can be amplified. Near the second harmonic the process is the combination of two excited plasma waves for which the absorption coefficient can only be positive. These results are applied to construct models of the radiation source for type III solar radio bursts both at high frequencies where the fundamental is dominant and at low frequencies where the second harmonic is dominant using two model plasma wave spectra, one being one-dimensional, the other isotropic. At high frequencies second harmonic radiation is used to determine the source area for a given energy density in plasma waves W _p . The source size and W _p are detrmined uniquely for a given plasma wave spectrum by tracing rays in a model source taking into account amplification of the fundamental. The results for a strong source at the 80 MHz plasma level with a ratio of emissivities of the fundamental to second harmonic P(ω _p )/P(2ω _p ) ≈ 10 are that the source with a one-dimensional plasma wave spectrum is about 14000 km in diameter and W _p = 10^?6.52 erg cm^?3, and the source with an isotropic distribution of plasma waves is about 200 km in diameter and W _p = 10^?6.3 erg cm^?3. It is shown that at low frequencies, where amplification of the fundamental is no longer possible, second harmonic radiation must be dominant and thus very little information about the source can obtained from the radiation.     

Nonlinear generation of ion loss-cone waves by electrostatic turbulence in the magnetosphere

Effects of plasma turbulence on the stability of electrostatic ion loss-cone waves are examined. The turbulence is assumed to be electrostatic with frequencies near 1.5 times the electron gyrofrequency and the frequencies of the generated waves are below the ion plasma frequency ω_pi>. A nonlinear growth rate of the order of 10^?2ω_pi may be obtained, when the amplitude of the turbulence is 20 mV/m. This is comparable to previously found growth rates of the linear ion loss-cone instability, in a plasma with large pitch angle anisotropy. Bounce averaged pitch angle diffusion coefficients are also presented for different models of the ion loss-cone wave spectrum.     

Characteristic of ion acoustic shock waves in a dissipative quantum pair plasma with dust particulates

The behavior of quantum dust ion-acoustic (QDIA) shocks in a plasma including inertialess quantum electrons and positrons, classical cold ions and stationary negative dust grains are studied, using a quantum hydrodynamic model (QHD). The effect of dissipation due to the viscosity of ions is taken into account. The propagation of small but finite amplitude QDIA shocks is governed by the Kortoweg-de Vries-Burgers (KdVB) equation. The existence regions of oscillatory and monotonic shocks will depend on the quantum diffraction parameter (H) and dust density (d) as well as dissipation parameter (η ₀). The effect of plasma parameters (d,H,η ₀), on these structures is investigated. Results indicate that the thickness and height of monotonic shocks; oscillation amplitude of the oscillatory shock wave and it’s wavelength effectively are affected by these parameters. Additionally, the possibility of propagation of both compressive and rarefactive shocks is investigated. It is found that depending on some critical value of dust density (d _c ), which is a function of H, compressive and rarefactive shock waves can’t propagate in model plasma. The present theory is applicable to analyze the formation of nonlinear structures at quantum scales in dense astrophysical objects.     

Two spacecraft observation of particle bursts at the distant magnetopause and in the magnetotail boundary layer

Bursts of energetic particles have been observed simultaneously by IMP-6 (≈ 24 R_E, R_p ? 0.21 MeV) and IMP-8 (≈ 29.7 R_E, E_p ? 0.29 MeV, E_e ? 0.22 MeV) in the distant magnetotail on Nov. 26, 1973 at a time when the auroral electrojet showed significant intensification. During one of the bursts IMP-6 was briefly in the duskside plasma sheet and IMP-8 was only a few R_E away at the magnetopause/boundary layer, as revealed from magnetic field and plasma measurements. The time behaviour of the proton intensities and anisotropies indicate that the particles have their origin in the plasma sheet. Measurements of the energy spectra during one of the bursts in the boundary layer/magnetosheath show significant variation of the differential exponent and suggest a rigidity-dependent escape of energetic particles from the plasma sheet into the magnetosheath. With the high temporal resolution of IMP-8 data intensity peaks of relativistic electrons and/or energetic protons could be detected at the magnetopause when Bx ≈ 0 γ. They appear superimposed on the general intensity time profile of the burst and last 2–3 min. It is concluded that some of the relativistic electrons can escape from the plasma sheet very fast and form a temporally-varying layer at the magnetopause.     

The electron-ion streaming instabilities driven by drift velocities of the order of electron thermal velocity in a nonmagnetized plasma

The kinetic Alfven waves are investigated using Maxwell-Boltzmann-Vlasov equation to evaluate the kinetic dispersion relation and growth/damping rate with magnetic field gradient, density gradient, temperature gradient and velocity gradient with inhomogeneous plasma. The effect of gradient terms is included in the analysis for both the regions k _⊥ ρ _i <1 and k _⊥ ρ _i >1, where k _⊥ is the perpendicular wave number and ρ _i is the ion gyroradius. This study elucidates a possible scenario to account for the particle acceleration and the wave dissipation in inhomogeneous plasmas. This model is able to explain many features observed in plasma sheet boundary layer as well as to evaluate the dispersion relation, growth rate, growth length and damping rate of kinetic Alfven wave. The applicability of this model is assumed for auroral acceleration region, plasma sheet boundary layer and cusp region.