On the role of the motion of the photospheric footpoints of the magnetic field lines

By means of a simple relation between the velocity v of the fluid particle and the velocity v_f of the photospheric footpoint of the magnetic field line v_z and B_z being respectively the components of v and the magnetic field B normal to the photospheric surface, it is shown formally that through the phtospheric surface the transport of all the quantities attributed to the magnetic field, such as the magnetic flux, the magnetic energy and the helicity, is independent of v_z, and v_f is the only kinematical quantity on which the transport depends. In addition, in the neighborhood of the neutral line the velocity v_l of the moving curve of constant B_z is found to be equal approximately to the component of v or v_f in the direction of v_l. Since v_l can be measured or extimated, so can the components of v and v_f near the neutral line.     

Effect of field-aligned currents in the polar cap at the recovery phase of a magnetic storm

Unusually great fluctuations in the ΔB module of the geomagnetic field have been observed in the polar cap from the satellite Cosmos-321. They are explained by small-scale two-sheet field-aligned current systems which exist during the periods when magnetic fields having a considerable northward B_z(B_z 10 nT) component are observed in interplanetary space.     

Seasonal dependences of geomagnetic variations in the polar region in connection with large-amplitude annual Z-variation at the geomagnetic pole

A noticeable depression of the vertical component Z of the geomagnetic field is observed in the polar cap in summer. From the statistical analysis of the equivalent overhead current patterns for daily geomagnetic variations in the summer and winter polar regions for three different conditions of IMF (interplanetary magnetic field), it was concluded that the annual variation of geomagnetic Z in the vicinity of the geomagnetic pole is attributed to the relative spatial shift of the twin-vortex current patterns over the polar cap from summer to winter. In winterthe clockwise current vortex in the dawn sector extends almost over the entire polar cap (except for the periods when the B_z component of IMF has a large positive value), and this will result in the positive variation of the Z-value at the geomagnetic pole. In summer the counter-clockwise current vortex in the dusk sector always extends over the whole polar cap even when B_z of IMF is positiveso that the variation of Z becomes negative. The persistent existence of current vortex in the dawn sector is important for the further study of magnetospheric convection when B_z is positive.     

Kp index correlations with solar-wind parameters during the first and second stages of a recurrent geomagnetic storm

The dependence of geomagnetic activity during a recurrent magnetic storm on the solar-wind magnetic field and plasma parameters has been studied. According to variations of solar-wind magnetic field strength B, a recurrent magnetic storm is divided into two stages: the first proceeding during the peak of B, and the second proceeding after the return of B to quiet level. The K_p index vs solar-wind parameters scattering diagrams for stages I and II differ significantly. In particular, the random scattering for stage I is much larger than for stage II. It was found that for stage I the K_p index correlates with B, with the sign and value of northsouth field component B_z and with the magnitude ΔB of field fluctuations, the situation being similar to that during sporadic magnetic storms, though the scale of the event is smaller. For stage II, the K_p index does not correlate with B, but strongly correlates with ΔB and weaker—with B_z. So geomagnetic activity at stage II is supported mainly by solar-wind magnetic field fluctuations. The dependence of the K_p index on plasma parameters (concentration of protons n, bulk velocity v and temperature T) is weak for both stages.     

The causes of recurrent geomagnetic storms

We studied the causes of recurrent geomagnetic activity by analyzing interplanetary magnetic field and plasma data from Earth-orbiting spacecraft in the interval from November 1973 to February 1974. This interval includes the start of two long sequences of geomagnetic activity and two corresponding corotating interplanetary streams. In general, the geomagnetic activity was related to an electric field which was primarily due to two factors: (1) the ordered, mesoscale pattern of the stream itself and (2) random, smaller-scale fluctuations in the southward component of the interplanetary magnetic field B_z. The geomagnetic activity in each recurrent sequence consisted of two successive stages. The first stage was usually the most intense and it occurred during the passage of the interaction region at the front of a stream. It was related to a V × B electric field which was large primarily because the amplitude of the fluctuations in B_z was large in the interaction region. It is suggested that these large amplitudes of B_z were primarily produced in the interplanetary medium by compression of ambient fluctuations as the stream steepened in transit to 1 A.U. The second stage of geomagnetic activity immediately following the first was associated with the highest speeds in the stream. It was, among other things, related to a V × B electric field which was large mainly because of the high speeds.     

The features of auroral bulge expansion

The development of the auroral bulge during substorms is studied using all-sky data from the dense net of stations and also riometer data. A few features seem to be essential for the interpretation of the expansive phase mechanism. The first is the existence of low energy electron precipitation (auroral arcs with the lower border height near 140 km) polewards of the expanding bulge, suggesting that the bulge often arises and develops on closed field lines. Secondly only the localized bulges (with dimensions 2° and 40°Λ) are generated by the continuous deformation of the auroral arc. The greater expansions develop mainly at the expense of the new bright arc formations at the front of the expanding auroral bulge. During each new arc formation impulsive acceleration and precipitation of energetic electrons takes place and brief changes of plasma sheet geometry are sometimes observed at 18 R_E in the magnetotail. This apparently shows a re-distribution of plasma sheet current during the substorm expansive phase.     

Detectability of lunar X-rays

We have examined several theories that imply the generation of X-rays by the Moon. The X-ray fluxes to be expected at the top of the Earth's atmosphere are estimated and compared. For example, we find that an X-ray flux is to be expected when the Moon is full and K_p high, as a consequence of the configuration of the auroral electrons in space deduced from the long tail model of the magnetosphere. The X-ray photons are caused by energetic electrons in the tail that bombard the lunar surface. Alternatively, Gold has suggested that lunar X-rays are produced by the bombardment by solar-wind electrons; this results in a lunar phase dependence that is different from the long tail model. The background is discussed and we conclude that the lunar X-ray flux may be detectable. Experiments of this kind may provide useful tools for investigating the models.     

The effect of an electric field induced by a time-dependent ring current on the particle drift motion

The effect of an electric field induced by a rapidly decaying ring current on the motion of charged particles in the magnetosphere has been investigated using Euler potentials. For a model consisting of the earth dipole and the symmetric ring current, the electric field satisfies the condition E . B = 0.

Under this circumstance, the E × B drift of the particle can be identified as the motion of the magnetic field lines and vice versa. The time dependent electric field induced can be evaluated in a Spherical polar coordinate system by the formula

where and β are Euler potentials.

A model calculation on the particle drift velocity v_D = E × B/B² shows that the radial component of the drift velocity is in good agreement with those deduced from whistler duct studies.     

Solar wind access to the plasma sheet along the flanks of the magnetotail

Low-energy particle trajectories in an idealized magnetotail magnetic field are investigated to determine the accessibility of magnetosheath protons and electrons to the plasma sheet along the flanks of the tail magnetopause. The drift motion of the positively (negatively) charged particles incident on the dawn (dusk) magnetotail flank causes such particles to penetrate deeper into the magnetotail. For certain combinations of particle energy, incident velocity vector and initial penetration point on the tail magnetopause, the incident particles can become trapped in the plasma sheet, after which their net drift motion then provides a current capable of supporting the entire observed magnetotail field. The results further indicate that the bulk of the solar wind plasma just outside the distant tail boundary, which streams preferentially in a direction along the magnetopause away from the Earth at velocities around 400 km s^?1, can be caught up in the tail if the initial penetration point is within about 2R_E, of the quasi-neutral sheet. It is suggested that a large fraction of the magnetotail plasma is composed of former solar wind particles which have penetrated the magnetospheric boundary at the tail flanks.     

Energetic particle losses and trapping boundaries as deduced from calculations with a realistic magnetic field model

An interpretation of the stable trapping boundaries of energetic electrons and protons during quiet periods is given basing on a realistic magnetospheric magnetic field model. Particle losses are explained in terms of an ionospheric and drift loss cone filling due to a non-adiabatic pitch-angle scattering in the nightside magnetotail current sheet. The proposed mechanism is shown to provide a good agreement of the observed and calculated positions of the energetic particle trapping boundaries, as well as their energy dependence. The obtained results can be applied as a tool for investigating the magnetospheric magnetic field structure using the particle data of low-altitude satellites.     

Multiperiodic irradiance changes caused by r-modes and g-modes

The acceleration of the influential 100 keV electrons in flares observed in hard X-rays and several radio emissions is unknown. Shock-waves and MHD turbulence, successfully applied to interprete interplanetary energetic particles, have recently been called in question concerning energetic flare electrons and ions. Other possible mechanisms are considered which are closely related to the primary flare energy release. In particular, runaway acceleration by the electric field of the reconnection current sheet, bulk heating by microturbulence, and cross-field ion currents due to bulk motion as a primary result of reconnection are reviewed. All three are likely to occur in some way. Their relative importance cannot be definitively assessed due to the lack of information on non-thermal, low energy protons.Proceedings of the Second CESRA Workshop on Particle Acceleration and Trapping in Solar Flares, held at Aubigny-sur-Nère (France), 23–26 June, 1986.     

A theoretical prediction of ion plasma oscillations in a neutral sheet

Starting from the Vlasov equation the steady state and stability properties of the electron sheet in the Cowley neutral sheet model of the geomagnetic tail are considered. Electrostatic ion plasma oscillations propagating from dusk to dawn are found to be unstable provided the thermal spread normal to the current is sufficiently large. Assuming the population of the neutral sheet to be supplied by the polar wind it is shown how a localisation of the cross tail electric field could lead to the instability first appearing around midnight. It is conjectured that the localisation of the cross tail electric field could continually feed the instability, so leading to enough turbulence to give enhanced reconnection of the magnetic field.List of symbols f distribution function - B magnetic field strength far from the neutral sheet - a sheet half thickness - total potential drop across the tail which is localised to the dusk end of the tail in Cowley's model - potential for the steady state electric field normal to the electron current sheet. This potential exists in that region of the tail that excludes the localised region of cross tail electric field - average velocity across the tail of electrons in the current sheet - v average velocity of the electrons normal to the current sheet - p canonical momentum of a particle - energy of a particle - KT electron energy normal to the sheet (1/2m ^e v ² ) - KT ⁱ ion energy (1/2m ⁱ V ² ) - electron gyrofrequency far from the neutral sheet - ⁱ ion gyrofrequency far from the neutral sheet - Ay steady state vector potential for the magnetic field - A –Ay/aB ₀ (normalised vector potential) When perturbing the steady state, dashes have been used to denote the time dependent first order quantities. Where no confusion could arise the dashes are dropped, e.g.Ey=Ey since there is no zero orderEy in the region considered in the stability analysis.     

The eastward electrojet in the dawn sector

Many previous researchers have shown that convection in the magnetosphere is reflected in the ionosphere by an eastward electrojet in the evening sector and a westward electrojet in the post-midnight sector. In this paper we shall demonstrate the existence of eastward electrojet flow in the dawn sector in the latitude regime normally occupied by the westward convection electrojet. It will be shown that the convection westward electrojet near dawn may co-exist with the eastward electrojet while lying poleward of it. It is suggested that this eastward electrojet consists of Pedersen current flow driven by an eastward electric field and it is shown that the field lines which penetrate the eastward electrojet are populated by energetic electrons normally associated with the plasma sheet as well as high energy electrons normally associated with the trapped particle population. The high conductivity channel is generated by processes associated with the precipitation of high energy (E > 20 keV) electrons drifting eastwards from midnight in the trapping region. It is further shown that antiparallel current sheets may flow on the magnetic lines of force penetrating the electrojet, and that this flow is closed in the ionosphere by Hall currents flowing equatorward in the high conductivity channel.     

Nature of solar-cycle and heliomagnetic-polarity dependence of cosmic rays, inferred from their correlation with heliomagnetic spherical surface harmonics in the period 1976–1985

Correlation of cosmic-ray intensity (I) with the solar magnetic field expanded into the spherical surface harmonics, B_ns(n 9), by Hoeksema and Scherrer has been studied using the following regression equation:

, where are subgroups of B_ns classified in ascending order of n, and τ_i is the time lag of I behind correlation coefficient between the observed and simulated intensities (I_obs, I_sml) in the period 1976–1985 is 0.87 and considerably better than that derived from any single index of solar activity. The lag time τ₃ is greater than others, indicating that the higher order magnetic disturbances effective to the cosmic-ray modulation have a longer lifetime in space than the lower order disturbances. The rigidity spectrum of the cosmic-ray intensity variation responsible for A_I due to the dipole moment is harder than those for others (A₂,A₃), indicating that the lowest order (i.e. largest scale) magnetic disturbances can modulate cosmic rays more effectively than the higher order disturbances. As another result of the present analysis, it has been found that the intensity depends also on the polarity of the polar magnetic field of the Sun; the residual (I_obs−I_sml) of the simulation changes its sign from positive to negative with a time lag (0–5 Carrington rotation periods) behind the directional change of the solar magnetic dipole moment from northward to southward, and has a softer rigidity spectrum than A_iS. The dependence is consistent with the result having been obtained in the previous period, 1936–1976, by one (K.N.) of the present authors. The polarity dependence can be found also in the 22-year variation of the time lags obtained every solar cycle in the period 1936–1985. The theoretical interpretation of these polarity dependences is discussed on the basis of the diffusion-convection-drift model.     

The polar substorm and electron ‘islands’ in the Earth's magnetic tail

The behaviour of energetic electrons in the distant magnetosphere near the midnight meridian during polar substorms has been studied for the period March 5th–April 4th, 1965, using data from two end window Geiger counters flown on the IMP 2 satellite (apogee 15.8 Earth radii) and magnetic records from a chain of auroral zone stations around the world at magnetic latitudes equivalent to L = 7.4 ± 2.0.

When the satellite was in the distant radiation zone or in the plasma sheet which extends down the Earth's magnetic tail, sudden decreases in the horizontal magnetic field component at ground stations near the midnight meridian (negative magnetic bays) were followed by sudden increases in 40 keV electron fluxes (electron islands) at the satellite. When the satellite was at high latitudes in the magnetic tail ‘bays’ often were not followed by ‘islands.’ When the satellite was near the centre of the plasma sheet, energetic electron fluxes were observed even during magnetically quiet periods. The time delay between the sharp onset of magnetic bays in the auroral zone and the corresponding rapid increase in energetic electron intensity at the satellite, typically some tens of minutes, was least when the satellite was close to the Earth and increased with its increasing radial distance from the Earth. The delay was also a function of distance of the satellite from the centre of the plasma sheet, and of the magnitude of the intensity increase (smaller delays for larger intensity increases). We deduce that the disturbance producing the magnetic bays and associated particle acceleration originates fairly deep in the magnetosphere and propagates outward to higher L values, and down the plasma sheet in the Earth's magnetic tail on the dark side of the Earth. It is unlikely that the accelerated electrons are themselves drifting away from the Earth, because the apparent velocity with which the islands move away from the Earth decreases with increasing distance from the Earth.

It is suggested that the polar substorm and the associated particle acceleration are part of an impulsive ejection mechanism of magnetospheric energy into the ionosphere, rather than an impulsive injection mechanism of solar wind energy into the magnetosphere.     

Energy spectra of particles accelerated in a reconnecting current sheet with the guiding magnetic field

Electron and proton acceleration by a super-Dreicer electric field is investigated in the non-neutral reconnecting current sheet (RCS) with a non-zero longitudinal component of the magnetic field ('guiding field'). The guiding field is assumed parallel to the direction of electric field and constant within an RCS. The other two magnetic field components, transverse and tangential, are considered to vary with distances from the X null point of an RCS. The proton and electron energy spectra are calculated numerically from a motion equation using the test particle approach for model RCSs with constant and variable densities. In the presence of a strong or moderate guiding field, protons were found fully or partially separated from electrons at ejection from an RCS into the opposite, 'electron' and 'proton', semiplanes. In the case of a weak guiding field, both protons and electrons are ejected symmetrically in equal proportions as neutral beams. The particles ejected from an RCS with a very weak or very strong guiding field have power-law energy spectra with spectral indices of about 1.5 for protons and 2.0 for electrons. For a moderate guiding field, the energy spectra of electrons ejected into the opposite semiplanes are mixed, i.e. in the 'electron-dominated' semiplane power-law energy spectra for electrons and thermal-like for protons, while in the 'proton' semiplane they are symmetrically mirrored.     

Particle acceleration during the explosive phase of a solar flare

Starting with the quasi-linear equation of the distribution function of particles in a regular electric field, a combined diffusion coefficient in the momentum space conbining the effects of the regular field and a turbulent field is obtained and a combined mechanism of acceleration by the regular and turbulent fields in the neutral sheet of solar proton flares is proposed. It is shown by calculation that conditions in solar proton flares are such that the charged particles can be effectively accelerated to tens of MeV, even ~1 GeV. It is shown that the combined acceleration by a regular electric field and ion-acoustic turbulence pumps the protons and other heavy ions into ranges of energy where they can be accelerated by Langmuir turbulence. By considering the combined acceleration by Langmuir turbulence and the regular electric field, the observed spectrum of energetic protons and the power-law spectrum of energetic electrons can be reproduced.     

Pitch-angle scattering of energetic particles in the current sheet of the magnetospheric tail and stationary distribution functions

An investigation of pitch-angle scattering of energetic particles in magnetic field configurations with a current sheet similar to that observed in the geomagnetotail has been performed. The magnetic field model is specified by two parameters which are the current sheet thickness in units of particle gyroradius and the angle between the magnetic field lines and the sheet plane. Computations of a considerable number of trajectories (about 20,000 for each model case) has provided the possibility of obtaining the matrix of pitch-angle scattering and the corresponding kernel function of the integral equation for the stationary particle distribution function. Solution of this equation shows that isotropic distributions are formed only in the case of a sufficiently thick current sheet. Particle scattering in a thin field reversal region leads to the formation of an anisotropic stationary distribution. The results can be used for interpretation of the data on the spatial distribution of energetic particle fluxes in the near part of the magnetospheric tail and in the vicinity of the outer boundary of the radiation belt.     

Field-aligned beams and reconnection in the jovian magnetotail

The release of plasma in the jovian magnetotail is observed in the form of plasmoids, travelling compression regions, field-aligned particle beams and flux-rope like events. We demonstrate that electrons propagate along the magnetic field lines in the plasma sheet boundary layer (PSBL), while close to the current sheet center the electron distribution is isotropic. The evidences of the counterstreaming electron beams in the PSBLs are also presented. Most of the field-aligned energetic ion beams are associated with the field-aligned electron beams and about half of them have the bipolar fluctuation of the meridional magnetic field component. Moreover they often show a normal velocity dispersion for the different species which fits well in the scenario of particle propagation from a single source. All features above are observed during jovian reconfiguration events which are typically bonded with plasma flow reversals. From all these characteristics, which are based on energetic particle and magnetic field measurements, we believe that the reconfiguration processes in the jovian magnetotail are associated with reconnection.