Influence of a sudden compression of the magnetosphere on outer zone electron fluxes measured at arbitrary pitch-angle

Analytical laws of motion of individual particles are used to evaluate the effects of a sudden compression on the outer radiation zone. A modulation of fluxes can be detected by synchronous satellites. Its intensity increases with the pitch-angle of the particles and the inward convection of field lines.     

Electron precipitation in a non-uniform glow aurora

Electron intensities at 5 keV >18 keV and >45 keV, were measured on a Petrel rocket flown from Kiruna, Sweden, into a non-uniform glow aurora during the recovery phase of a magnetic bay. The intensities depend on pitch-angle in a way that is consistent with the precipitation being caused by pitch-angle diffusion from reservoirs of geomagnetically-trapped electrons. The scattering process that causes pitch-angle diffusion, and leads to three regions of relatively high intensity, appears to have properties different from the scattering process that leads to two intervening regions of low intensity. A spatial structure in electron reservoir intensity, is attributed mainly to variations in the rate of erosion by pitch-angle diffusion of an initially nearly-uniform reservoir intensity. An expression is derived for the minimum lifetime of trapped electrons undergoing strong pitch-angle diffusion.     

磁重联电流片的参数变化对电子加速的影响

通过采用试验粒子的方法,研究了在有引导磁场Bz存在的磁重联电流片中,电子被super-Dreicer电场Ez加速后的运动特征.首先,考虑了引导磁场恒定且与电场有不同方向时对粒子加速的影响.在这种情况下,Bz方向的改变直接改变了电子的运动轨迹,使其沿着不同的路径离开电流片.在Bz和Ez同向时,高能电子的pitch-angle接近于180°.然而,当2者反向时,高能电子的pitch-angle接近0°.引导磁场的取向只是使电场有选择地对不同区域的电子进行加速,不会最终影响电子的能量分布,最终得到的能谱是普遍的幂率谱E-γ.在典型的日冕条件下, γ大约等于2.9.进一步的研究表明γ的大小依赖于引导磁场及磁重联电场的强弱,以及电流片的尺度.随后,也研究了包含多个X-点和O-点电流片中被加速粒子的运动特征.结果表明X-点和O-点的存在使得粒子被束缚在加速区并获得最大的加速,而且最终的能谱具有多幂率谱的特征.     

Precipitation of charged particles by a parallel electric field

A time-dependent model of the effect of a parallel electric field on particle precipitation from a closed field-line has been constructed and the results are presented. A pattern of field-aligned pitch-angle distributions and energy peaks develops rapidly and then persists unchanged in shape while the intensity decreases for a time of the order of the bounce period of the energetic particles. It is shown that the structures in velocity space are created by the juxtaposition of particles from different source populations. Four sources are found to be sufficient to reproduce the principal features observed frequently by rockets and satellites. They are, a trapped plasma sheet distribution, a loss-cone partially filled by pitch-angle diffusion at the equator, cold ionospheric plasma which has flowed outward along the field line and particles backscattered from the precipitation into the atmosphere.The model develops density gradients and discontinuities far sharper than any observed, so that any parallel electric field actually occurring in an aurora must be accompanied by strong wave-particle interactions either as part of the accelerating mechanism or as a result of the density gradients produced by it.     

On the convective mechanism for formation of the plasma sheet in the magnetospheric tail

Calculation of stationary distributions of the most important plasma parameters (particle energy, density, field-aligned and transversal pressure) is performed for a model magnetotail plasma sheet which is formed by convecting plasma mantle particles injected into the closed geomagnetic field line tubes. Computations have been done for two convection models: (i) a model of completely adiabatic particle motion with conservation of the first two invariants and (ii) a model with a strong pitch-angle diffusion which maintains isotropy. It is found that in both cases the heating and compression of the plasma are somewhat more effective than is necessary to account for the observed gradients of magnetic field in the magnetospheric tail. A leakage of accelerated particles through the dawn and dusk edges of the plasma sheet is proposed as a possible mechanism for maintenance of stationary convection in the magnetotail. The question of the dependence of the stationary magnetotail parameters on the solar wind state is discussed briefly.     

Large-scale transport of plasma in the Earth's plasma sheet: comparative analysis for adiabatic and non-adiabatic cases

A system of multi-fluid MHD-equations is used to compare adiabatic and non-adiabatic transport of the energetic particles in the magnetospheric plasma sheet. A “slow-flow” approximation is considered to study large-scale transport of the anisotropic plasma consisting of energetic electrons and protons. Non-adiabatic transport of the energetic plasma is caused by scattering of the particles in the presence of both wave turbulence and arbitrary time-varying electric fields penetrating from the solar wind into the magnetosphere. The plasma components are devided into particle populations defined by their given initial effective values of the magnetic moment per particle. The spatial scales are also given to estimate the non-uniformity of the geomagnetic field along the chosen mean path of a particle. The latters are used to integrate approximately the system of MHD-equations along each of these paths. The behaviour of the magnetic moment mentioned above and of the parameter which characterizes the pitch-angle distribution of the particles are studied self-consistently in dependence on the intensity of non-adiabatic scattering of the particles. It is shown that, in the inner magnetosphere, this scattering influences the particles in the same manner as pitch-angle diffusion does. It reduces the pitch-angle anisotropy in the plasa. The state of the plasma may be unstable in the current sheet of the magnetotail. If the initial state of the plasma does not correspond to the equilibrium one, then, in this case, scattering influences the particles so as to remove the plasma further from the equilibrium state. The coefficient of the particle diffusion across the geomagnetic field lines is evaluated. This is done by employing the Langevin approach to take the stochastic electric forces acting on the energetic particles in the turbulent plasma into account. The behaviour of the energy density of electrostatic fluctuations in the magnetosphere is estimated.     

Initial pitch-angle of narrowly beamed electrons injected into a magnetic mirror,formation of trapped and precipitating electron distribution,and asymmetry of hard X-ray and microwave footpoint emissions

A new kind of static distribution function for trapped and precipitating electrons is derived by solving a time-independent Fokker–Planck equation in a magnetic mirror, with injection of initially narrow-beamed electrons at an arbitrary initial pitch-angle. There are two independent parameters to determine the ratio of trapped and precipitating electrons, as well as their emissions, i.e., the mirror ratio and the initial pitch-angle, which is helpful for understanding some new features of asymmetrical hard X-ray and microwave footpoint emissions in solar observations.     

Nonlinear boussinesq convective model for large scale solar circulations

We present extensive numerical calculations for a model of thermal convection of a Boussinesq fluid in an equatorial annulus of a rotating spherical shell. The convection induces and maintains differential rotation and meridian circulation. The model is solved for an effective Prandtl number P = 1, with effective Taylor number T in the range 10² <T <10⁶, and effective Rayleigh number R between the critical value for onset of convection, and a few times that value. With = 2.6 × 10^–6 s^–1, d = 1.4 × 10¹⁰ cm (roughly the depth of the solar convection zone) the range of Taylor number is equivalent to kinematic viscosities between 10¹⁴ and 10¹² cm² s^–1, which encompasses eddy viscosities estimated from mixing length theory applied to the Sun.The convection does generally make equatorial regions rotate faster, the more so as T is increased, but local equatorial deceleration near the surface is also produced at intermediate T for large enough R above critical. The differential rotation is maintained primarily through momentum transport in the cells up the gradient, rather than by meridian circulation. Differential rotation energy increases relative to cell energy with increasing T, surpassing it near T = 3 × 10⁴. The differential rotation tends to stretch out the convective cells, analogously to what is thought to happen to solar magnetic regions. Differential rotation and meridian circulation energies are nearly equal for T = 10³, but the meridian circulation energy falls off relative to differential rotation like T ^–1 for larger T. The meridian circulation is always toward the poles near the surface, contrary to models of Kippenhahn, Cocke, Köhler, and Durney and Roxburgh. The radial shear produced in the differential rotation is almost always positive, as in the Köhler model, but contrary to the assumptions made by Leighton for his random walk solar cycle model.Solutions in the neighborhood of T = 3 × 10⁴ seem to compare best with various solar observations including differential rotation amplitude, cell wavelength, tilted structure, horizontal momentum transport, and weak meridian circulation. The local equatorial deceleration (equatorward of 10–15°) has not been observed, although the techniques of data analysis may not have been sensitive to it. The most important deficiency of the model is that all the solutions with T 10³ show the vertical heat transport a rather strong function of latitude, with a maximum at the equator, no evidence of which is seen at the solar surface.The National Center for Atmospheric Research is sponsored by The National Science Foundation.     

The relationship of pc 5 micropulsation activity in the morning sector to the auroral westward electrojet

Data from a line of magnetometers stretching along a corrected geomagnetic meridian ～ 302°E through western Canada are used to study the relationship between the convection westward electrojet and Pc 5 micropulsations in the morning sector. It was found that the dominant spectral bands in the Pc 5 range occur within the same latitudinal range occupied by the electrojet. The intensity contours and the character of the polarization parameters clearly show that the Pc 5 activity tracks the westward convection electrojet. The Pc 5 activity is found to be enhanced in conjunction with rapid reconfigurations of the electrojet. Evidence of spatial oscillations of the borders of the electrojet and variations in the intensity of the electrojet is presented. It is concluded from our study that the Pc 5 activity in the morning sector is closely related to the convection westward electrojet and its associated three-dimensional current system.     

Effects on the plasmasphere of a time-varying convection electric field

The time evolution of the plasmasphere has been investigated theoretically, using simple computational models. The magnetic field is assumed to be dipolar and time-independent, but the convection electric field is allowed to vary in time. For purposes of comparison, various spatial distributions of the magnetospheric electric field are considered. Plasmasphere flux tubes are assumed to be filled by diffusion of plasma upwards from the dayside ionosphere. Following a reduction in the convection field, the bulge of the original plasmasphere develops into a long tail that gradually wraps itself around the main plasmasphere. Periodic gusts in a spatially uniform convection field produce extremely complicated fine structure that depends strongly on both local time and universal time. Each large gust produces a distinct tail of cold plasma that stretches from the main body of the plasmasphere to the magnetopause, and causes a peak in density, outside the main plasmapause; similar features have been observed by OGO satellites. The calculations indicate that a periodic gusty field has a major effect on the size of the plasmasphere if the field has large Fourier components close to the drift period of cold plasma near the plasmapause. Gusts occurring randomly, at an average rate of several a day, can also cause substantial reduction in the size of the plasmasphere. The assumption that the convection field is spatially uniform, but gusty, leads to better agreement with the observed average shape of the plasmasphere than the assumption of a constant, uniform electric field. The theory indicates that the thickness of the plasmasphere boundary should be inversely correlated with magnetic activity, in general agreement with OGO 5 observations.     

On the energy dependence of the ring current proton precipitation

Low altitude satellite measurements of protons in the 1–100 keV range indicate two energy dependent proton precipitation boundaries. At low invariant latitudes mostly below 60° there is a region of moderately weak proton precipitation. The poleward boundary of this region tends to be at higher latitudes for the high energy protons than for the low energy protons. At high invariant latitudes there is a region where both the low and high energy protons precipitate with an isotropic pitch-angle distribution. The equatorward boundary of this region tends to be at lower latitudes for protons with energy more than 100 keV than for those in the 1–6 keV range. This region with isotropic pitch-angle distribution is located well outside the plasmapause both for the 1–6 and 100-keV protons.Between these two precipitation zones there is a region where the proton pitch-angle distribution is highly anisotropic with almost no protons in the loss cone. This region tends to be wider and more pronounced in the 1–6 than in the 100-keV protons.These findings lend further support to the mechanism of ion-cyclotron instability as the cause of proton pitch-angle diffusion in the low and intermediate regions. The process responsible for the strong diffusion at auroral latitudes has not yet been identified.     

The role of plasma interchange motion for the formation of a plasmapause

Mcllwain's electric and magnetic field distributions (E3H and M2) have been used to calculate the drift path of plasma density irregularities taking into account plasma interchange motion driven by the gravitational and inertial forces acting on the whole mass of the plasma elements.It has been shown that there is a region in the magnetosphere which is unstable with respect to the interchange motion of the cold plasma element. Any plasma hole in the background density drifts ultimately toward an asymptotic trajectory. Along this trajectory the inward gravitational force is balanced by the outward inertial force averaged over one revolution around the Earth. This asymptotic trajectory, along which all plasma holes ultimately accumulate, is identified with the equatorial plasmapause. The maximum velocity for the interchange motion is proportional to the excess (or defect) of density in the plasma element, and inversely proportional to the integrated Pedersen conductivity. Plasma detachment is shown to occur preferentially in the post-midnight sector.     

Magnetospheric tail dynamics and a concept of combined action of viscous drag and magnetic merging

Characteristic features of the two solar wind-magnetosphere interaction mechanisms, i.e. the viscous drag and magnetic merging, are discussed in the paper. The main difference between them is that the viscous drag acts mainly near the equatorial cross-section of the magnetopause, whereas the magnetic merging acts near the noon-midnight meridian cross-section. Energy input to the tail due to viscous drag action decreases as the magnetic flux in the tail lobes increases, whereas the energy input due to magnetic merging does not depend on the magnetotail flux. A concept is developed that a combined action of these two mechanisms is intimately related to substorm occurrence. In this paper large scale cross-tail electric fields and their relation to energy conversion processes in the tail are analysed qualitatively and interpreted. An induced part of the tail electric fields is taken into account and the relationship between polar cap electric fields and energy conversions in the tail is discussed.     

Quiet auroral arcs: Ionosphere effect of magnetospheric convection stratification

A detailed study of the mechanism of electromagnetic stratification of the large-scale stationary magnetospheric convection due to a friction of the convective flow in the ionosphere layer was performed. Magnetosphere-ionosphere interaction was taken into account by means of the effective boundary conditions on the ionosphere top and bottom boundaries including the actual height profile of charge particles velocity in the ionosphere. It has been shown that the magnetospheric convection is stratified into small-scale current sheets which are respective in the linear approximation to an oblique Alfvén wave. The dispersion equation was deduced for the Alfvén mode and its solution obtained determining the space-time scales and the increment of instability. The maximum increment is realized for the disturbances stretched along the convection velocity that is correspondent to the actual orientation of the auroral arcs. In the conditions of rapid growth of Alfvén velocity above the maximum of the ionosphere F layer, it was shown that small-scale disturbances with the transverse scales l_⊥ ? 1 km are localized at the altitudes up to several thousand kilometers whereas the large-scale stratification penetrate into the equatorial plane of the magnetosphere. A mechanism is proposed to intensify the parallel electric field acting at that stratification stage when the field-aligned currents in the Alfvén wave are sufficient to form abnormal resistance along geomagnetic lines of force.     

High temporal and spatial resolution observations of low energy electrons by a mother-daughter rocket in the vicinity of two quiescent auroral arcs

Low energy precipitated electrons have been measured with high time resolution through an auroral display by a series of high geometrical factor particle counters on a ‘mother-daughter’ sounding rocket, launched during wintertime near 2100 LT from Andenes, Norway.The observations show that the 0·5–3 keV electron fluxes are anisotropically distributed, with a maximum in a direction parallel to the local geomagnetic field vector at all latitudes covered by the rocket, except within the visual auroral forms where the pitch-angle distributions are isotropic or slightly peaked in a direction normal to the geomagnetic field. The 1 and 3 keV electron fluxes are weakly anticorrelated in the vicinity of the arcs, where also the 3 keV electron flux displays a more structured variation than the 0.5 and 1 keV electron fluxes.     

Can oscillations grow in a sunspot umbra?

Umbral flashes and running penumbral waves have been attributed by Moore (1972) to overstable oscillations in the umbra. His numerical results were derived by inserting physical conditions at two particular depths beneath the umbral surface. Seven variables must be specified at each point. We have extended Moore's analysis to examine the depth-dependence of overstable oscillations in a recently computed umbral model. Electrical conductivity is evaluated taking full account of partial ionization and magnetic fields. In the surface layers, within 250 km of the top of the umbral convection zone, the conductivity is so low that Joule dissipation is more rapid than the growth rate of oscillations. In these layers, Moore's results are therefore not applicable. At greater depths, oscillations can grow and we agree with Moore that both umbral flashes and penumbral waves may be due to overstable oscillations. However, we suggest that both phenomena can arise at the same depth in the spot, and not in two layers, as Moore suggests.The umbral model we used is based on Öpik's cellular convection model. The interaction between the vertical magnetic field and convection is included by varying the diameter of the cell, and not its height. The diameter is assumed to be proportional to the distance that gas diffuses relative to the field during its upward convection.Work supported by NASA Contract NGR-39-005-066.     

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.     

On the divergence of the ionospheric electric field around the westward travelling surge

The pattern of the ionospheric electric field around the westward travelling surge (WTS) is theoretically studied. This is obtained by solving the current continuity equation at the ionospheric altitude for temporal and spatial development of the field-aligned current density modelled as the WTS phenomenon. The results show that the divergence of the ionospheric electric field is significantly changed depending on the dawn-to-dusk convection electric field E₀ because of non-uniformity in the ionospheric conductivity: the ionospheric electric field diverges in the upward current region (around the head of the WTS) when a westward electric field E₀ of 10 mV m⁻¹ is uniformly applied. On the other hand, the ionospheric electric field converges without E₀. From the observational inference that the ionospheric electric field converges around the head of the WTS, it is suggested that the WTS phenomenon may not be accounted for by the discharging process in the presence of the enhanced dawn-to-dusk convection electric field and non-uniform conductivity as was studied by previous authors.     

Gyrosynchrotron Emission from Anisotropic Pitch-Angle Distribution of Electrons in 3-D Solar Flare Sources

We present calculations, made for the first time, of the gyrosynchrotron emission by mildly relativistic electrons with anisotropic pitch-angle distribution using a realistic magnetic loop model in three dimensions. We investigated the intensity, spectral index of the optically thin region of the spectrum, the spatial morphology and the dependency on the source position on the solar disk. The method to describe a three-dimensional source and the procedure to perform the calculations are presented. We have modified the Ramaty’s gyrosynchrotron code to allow the evaluation of anisotropic pitch-angle electron distributions, as described in the complete formalism. We found that anisotropic electron distributions affect the intensity of the radiation, spatial morphology and spectrum of spatially resolved sources. However, the spatially integrated spectrum of the emission seems to be insensitive to the electron pitch-angle distribution, as the magnetic field inhomogeneity smooths out the effects of the anisotropic distribution in the produced radiation, in contrast to homogeneous sources.