Time-dependent configuration changes of the magnetotail and plasma sheet thinning

The configuration of the magnetotail magnetic field has been calculated for a situation where a disruption of a portion of the tail current system develops. The decrease of the current in a localized region of the magnetotail leads to a collapse of the magnetic field in that vicinity. The calculated configuration of the field resembles what is predicted by reconnection models with the field lines moving toward the neutral sheet and then connecting and either moving toward or away from the earth. Associated with this changing magnetic field there is an induced electric field which will then influence the motion of the plasma in the magnetotail via E × B drifts.When the current from X_sm = ?20 to ?40 R_E in the tail is decreasing with a tune-constant of 0.5 h the electric field produced, which is primarily westward, has a maximum value of 0.83 mV m^?1 and produces plasma sheet thinning velocities of 0.3 km s^?1. Higher velocities result for more rapid rates of current decrease, and they agree well with experimental observations. The plasma flows in the sunward direction are, however, much smaller than what has been observed. This is due in part to the inability of the magnetic field model to adequately represent the magnetic field in the immediate vicinity of the neutral sheet. Use of an improved model would give better agreement with the observations.The calculations show that the induced electric field of a time-dependent magnetic field is able to explain certain observed features of the plasma sheet motions. Also, this agreement suggests that the assumption that there is no charge separation contribution to the electric field may be reasonable during situations of large scale and rapid current disruptions in the magnetotail.     

Current sheet acceleration of ions in the geomagnetic tail and the properties of ion bursts observed at the lunar distance

Recent analyses of measurements obtained from the Rice University Apollo 14 SIDE on the lunar surface have revealed the frequent appearance of fast tailward-streaming ion “bursts” near the centre plane of the geomagnetic tail. In this paper the properties of these “bursts” are tested for compatibility with tail current sheet tangential stress balance conditions assuming that they are produced by current sheet acceleration of tail lobe plasma downstream and tailward of a magnetic neutral line. Calculations are performed taking the ions to be either protons or singly charged oxygen, the latter possibility being directly suggested by several recent observations. When “burst” bulk parameters are calculated by assuming that the ion distribution functions are convecting isotropic Maxwellians, the results are found to be difficult to reconcile with current sheet stress balance conditions for either protons or oxygen. Use of a different ion distribution based on theoretical expectations and observations in the near-Earth tail, however, results in number density estimates being increased by factors of around an order of magnitude. When the revised densities and ion distribution functions are taken into account, reasonable agreement between observed and expected ion bulk speeds is obtained. In some cases the agreement is better assuming oxygen ions rather than protons, but not by a large factor.     

Modeling of Proton Acceleration in a Magnetic Island Inside the Ripple of the Heliospheric Current Sheet

Crossings of the heliospheric current sheet (HCS) at the Earth’s orbit are often associated with observations of anisotropic beams of energetic protons accelerated to energies from hundreds of keV to several MeV and above. A connection between this phenomenon and the occurrence of small-scale magnetic islands (SMIs) near reconnecting current sheets has recently been found. This study shows how pre-accelerated protons can be energized additionally due to oscillations of multiple SMIs inside the ripple of the reconnecting HCS. A model of the electromagnetic field of an oscillating 3D SMI with a characteristic size of ~0.001 AU is developed. A SMI is supposed to be bombarded by protons accelerated by magnetic reconnection at the HCS to energies from ~1keV to tens of keV. Numerical simulations have demonstrated that the resulting longitudinal inductive electric fields can additionally reaccelerate protons injected into a SMI. It is shown that there is a local “acceleration” region within the island in which particles gain energy most effectively. As a result, their average escape energies range from hundreds of keV to 2 MeV and above. There is almost no particle acceleration outside the region. It is shown that energies gained by protons significantly depend on the initial phase and the place of their entry into a SMI but weakly depend on the initial energy. Therefore, low-energy particles can be accelerated more efficiently than high-energy particles, and all particles can reach the total energy limit upon their escape from a SMI. It is also found that the escape velocity possesses a strong directional anisotropy. The results are consistent with observations in the solar wind plasma.

     

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.     

Plasma-sheet dynamics and magnetospheric substorms

We present a conceptual model of the formation of the plasma sheet and of its dynamical behavior in association with magnetospheric substorms. We assume that plasma mantle particles $\text{E}\text{～}\text{×}\text{B}\text{～}$ drift toward the current sheet in the center of the tail where they are accelerated by magnetic-field annihilation to form the plasma sheet. Because of the velocity-dependent access of mantle particles to the current sheet, we argue that the convection electric field and the corresponding rate of field annihilation decrease with increasing radial distance. As a consequence, there exists no steady-state configuration for the plasma sheet, which must instead shrink continuously in thickness until the near-earth portion of the current sheet is disrupted by the formation of a magnetic neutral line. The current-sheet disruption launches a large-amplitude hydromagnetic wave which is largely reflected from the ionosphere. The reflected wave sets the neutral line in motion away from the earth; the neutral line comes to rest at a distance (which we estimate to be a few hundred earth radii) where the incoming mantle particles enter the current sheet at the local Alfvén velocity. At this “Alfvén point” reconnection ceases and the thinning of the plasma sheet begins again. Within this model, the magnetospheric substorm (which is associated with the current-sheet disruption) is a cyclical phenomenon whose frequency is proportional to the rate of convection in the magnetospheric tail.     

Three-dimensional particle anisotropies in and near the plasma sheet of Jupiter observed by the EPAC experiment onboard the Ulysses spacecraft

During its inbound journey into Jupiter's magnetosphere, Ulysses had several encounters with the Jovian plasma sheet near the magnetic equator, which were related with intensity maxima in the energetic particles. We show for the first time anisotropies in three dimensions of three ion species (protons, helium and oxygen) in the energy range 0.24 < E < 0.77 [MeV/nucleon]. The data, obtained with the Energetic Particle Composition Experiment (EPAC) onboard Ulysses have been analysed by using spherical harmonics in three dimensions. We show that the first-order anisotropies of ions in or near the plasma sheet are strongest in a plane parallel to the ecliptic plane and more or less azimuthal with respect to the rotation of Jupiter. We show that the first-order anisotropy amplitude is larger for helium and oxygen ions than for protons in nearly the same energy per nucleon range. We find flow velocities for helium ions which are not consistent with corotation, but are larger by a factor of 2 in and near the Jovian plasma sheet on the dayside magnetosphere. In contrast for protons we observe nearly corotation. Far from the plasma sheet, at high magnetic latitudes, the flow velocities are less than corotation for protons, as well as for helium and oxygen. The azimuthal particle anisotropies are explained by intensity gradients perpendicular to the centre of the plasma sheet, by E × B particle drifts, and by nonadiabatic orbits of the particles near the Jovian plasma sheet. All of the three phenomena act in the same azimuthal direction, perpendicular to the mainly radial magnetic field direction. Each of them can be estimated, but their individual effects cannot be distinguished from each other. In addition, we find a radial component of the anisotropy which apparently is stronger for protons than for heavier ions. This radial anisotropy component is interpreted as a result of the radial outward displacement of ions in an azimuthally swept back magnetic field.     

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.     

Dynamics of cosmic current layers with localized lower-hybrid-drift turbulence

A two-dimensional magnetohydrodynamic model of the dynamics of tail-like current layers caused by anomalous electrical resistivity in a plasma with lower-hybrid-drift (LHD) turbulence is considered. Additionally to the LHD-resistivity, a resistivity pulse in the magnetic neutral sheet is given initiating a magnetic reconnection process. Then the temporal and spatial evolution of the magnetic and electric fields, the plasma convection and the anomalous resistivity are obtained numerically. Taking into account more exact expressions for the LHD-resistivity in the current layer as done in former works, the LHD-turbulence is found to be excited farther from the neutral sheet, and thus, with the time, secondary current sheets are obtained in the plasma-magnetic field system. It is shown that the inductive electric field moving from the magnetic neutral sheet to the current layer periphery during the reconnection process may be considered as indicator of the plasma disturbances.     

The warm current sheet model, and its implications on the temporal behaviour of the geomagnetic tail

A simple model current sheet is studied numerically. Consistent fields and particle trajectories, and their dependence on electron and proton temperature, convection velocity and normal field, B_z, linking through the current sheet, are presented and discussed. It is shown that the protons, which are the major current carriers, largely retain the decoupling of the motion in the x-y plane from the normal oscillations as in the ‘cold’ current sheet. The positive potential of the current sheet is shown to be sufficient to trap some energetic electrons, the motion of which enables the predominance of energetic electrons towards the dawn side of the tail to be understood. Semi-empirical relationships for the thickness and the potential of the current sheet are obtained.

The consequences of such a current sheet on the behaviour of the geomagnetic tail are investigated. Using Faraday's law and the consistent cross tail electric field it is shown that the effect of a southward turning of the interplanetary field is to lead to a decrease in B_z,an increase of the current sheet conductivity, and a growth of stored field energy, i.e. the current sheet blocks merging. The decrease of the resistance of the current sheet is limited by the finite width of the tail. Finally, it is pointed out that if the conditions which bring about the growth of field energy persist, then the collapse of the field lines characteristic of substorms may occur.     

The absence of electric fields due to particle entry into the magnetosphere

The wide-spread belief that the neutral sheet current in Earth's magnetotail creates an accumulation of charge at the boundary with the magnetosheath is erroneous. Current continuity is maintained by the magnetization current on the upper and lower surfaces of the magnetotail. Hence no electric fields arise from charge separation supposedly brought about by the flow of particles between the neutral sheet and the magnetosheath. Claims to the contrary are based on the oversight of forgetting the current on the magnetopause.     

A 2-D model for the support of a polar-crown solar prominence

We present a 2-D potential-field model for the magnetic structure in the environment of a typical quiescent polar-crown prominence. The field is computed using the general method of Titov (1992) in which a curved current sheet, representing the prominence, is supported in equilibrium by upwardly directed Lorentz forces to balance the prominence weight. The mass density of the prominence sheet is computed in this solution using a simple force balance and observed values of the photospheric and prominence magnetic field. This calculation gives a mass density of the correct order of magnitude. The prominence sheet is surrounded by an inverse-polarity field configuration adjacent to a region of vertical, open polar field in agreement with observations.A perturbation analysis provides a method for studying the evolution of the current sheet as the parameters of the system are varied together with an examination of the splitting of an X-type neutral point into a current sheet.Program Systems Institute of the Russian Academy of Sciences, Pereslavl-Zalessky 152140, Russia.     

Consequences of an isotropic static plasma sheet in models of the geomagnetic tail

The equation of momentum balance and magnetic flux conservation are given for a static tail model with an isotropic plasma sheet. The possibility of magnetic field leakage into the solar wind and across the neutral sheet is allowed. Numerical integrations for a wide variety of adjustable model parameters are presented that give the dependence on distance from Earth of all tail parameters (field strength inside and outside of the plasma sheet, plasma pressure, plasma sheet area, tail radius, and normal field component to the neutral sheet). The model gives good agreement with the observed distance dependence of the tail field strength, and accounts for the scatter in the data in terms of a mixture of the fields inside and outside the plasma sheet in the data averages. However, compared with the present interpretations of the observations the model gives a too large plasma pressure at large distances and a too small normal component to the neutral sheet. The discrepancies imply that plasma flow and/or pressure anisotropy are required for an adequate model.     

Particle Acceleration in Reconnecting Current Sheets in Impulsive Electron-Rich Solar Flares

Electron and proton acceleration in reconnecting current sheets in electron-rich solar flares is considered. A significant three-dimensional magnetic field is assumed in the current sheet where the particles are accelerated by the DC electric field. The tearing instability of a pre-flare current sheet leads to the formation of multiple singular lines of magnetic field where the electric and magnetic fields are coaligned. Magnetized electrons are shown to be accelerated to a few tens of MeV before they leave the vicinity of a singular line. The acceleration time is estimated to be less than 10^–3 s. By contrast, much heavier protons are unmagnetized and their energy gain is more modest. The model explains a high electron-to-proton ratio and the unusually intense gamma-ray continuum above 1 MeV observed in the electron-rich flares.     

The reason for magnetospheric substorms and solar flares

It has been proposed that magnetospheric substorms and solar flares are a result of the same mechanism. In our view this mechanism is connected with the escape, or attempted escape, of energized plasma from a region of closed magnetic field lines bounded by a magnetic bottle. In the case of the Earth, it must be plasma that is able to maintain a discrete auroral arc, and we propose that the cross-tail current connected to the arc is filamentary in nature to provide the field-aligned current sheet above the arc. A localized meander of such an intense current filament could be caused by a tearing instability in the neutral sheet. Such a meander will cause an inductive electric field opposing the current change everywhere. In trying to reduce the component of the induction electric field parallel to the magnetic field lines, the plasma must enhance the transverse or cross-tail component; this action leads to eruptive behavior, in agreement with tearing theories. This enhanced induction electric field will cause a discharge along the magnetic neutral line at the apex of the magnetic arches, constituting an impulsive acceleration of all charged particles originally near the neutral line. The products of this phase then undergo betatron acceleration for a second phase. This discharge eventually reduces the electric field along the neutral line, and thereafter the enclosed magnetic flux through the neutral line remains nearly constant. The result is a plasmoid that has definite identity; its buoyancy leads to its escape. The auroral breakup (and solar flare) is the complex plasma response to the changing electromagnetic field.     

A short wavelength instability in the neutral sheet of the earth's geomagnetic tail

In an earlier paper, Bowers (1973), ion plasma oscillations were found to be unstable in the steady state developed by Cowley (1972) for the neutral sheet in the Earth's geomagnetic tail. In this paper a similar stability analysis is carried out but for a different steady state, suggested by Dungey, with the result that unstable waves with frequencies near the electron plasma frequency are found. In the Dungey steady state the current necessary for magnetic field reversal is carried by plasma originating from both the magnetosheath and the lobes of the tail. This modifies the steady state proposed by Alfvén and subsequently developed by Cowley in which all the current is carried by plasma from the lobes of the tail thereby fixing the cross-tail potential Φ. With magnetosheath plasma present the value of Φ is no longer fixed solely by parameters in the lobes of the tail but the cross-tail electric field is still assumed localised in the dusk region of the sheet as in the Cowley model due to the balance of charge required in the neutral sheet. The value of Φ can be expected to increase as magnetic flux is transported to the tail which inflates and causes flux annihilation because the magneto-sheath plasma in the neutral sheet has insufficient pressure to keep the two lobes of the tail apart. The Vlasov-Maxwell set of equations is perturbed and linearised enabling a critical condition for instability to be found for modes propagating across the tail. Typically, this condition requireseΦ≳KT _m whereT _m is the temperature of magnetosheath electrons. The instability occurs in the presence of cold plasma which hasE×B drifted into the neutral sheet from the lobes of the tail. This contrasts with the usual two stream instability which is stabilised by the cold plasma. Once precipitated the instability may be explosive provided current disruption occurs, for then a further increase in Φ will result which drives a greater range of wave numbers unstable thereby causing even more turbulence and an even larger cross-tail electric field. Because of this behaviour the instability may be a trigger for a substorm.     

Modulation of galactic cosmic ray anisotropy in heliomagnetosphere: Average sidereal daily variation

We formulate the modulation of galactic anisotropy of cosmic rays caused by their orbital deflection in the heliomagnetosphere. According to the formulation, the average sidereal i-th harmonic daily variation (i = 1,2,…) produced from the anisotropy from an arbitrary direction can be expressed by a linear combination of three basic vectors for uni-directional anisotropy and five basic vectors for bi-directional anisotropy. These vectors are obtained by calculating trajectories of cosmic rays (20?10⁴GV) in a model magnetosphere having Parker's Archimedian spiral structure with a flat or a wavy neutral sheet in either of two polarity states, one is called “Positive” state (away field in the northern space of the neutral sheet and toward field in the southern space) and the other is called “Negative” state (reversed state of the above). Among general characteristics of the sidereal daily variations, the most remarkable features are: (1) The observable variations in low rigidity (? 2000 GV) can be produced even from an uni-directional anisotropy in the direction of the Earth's rotation axis. These variations are strongly dependent on the polarity state, i.e., they are greater in the Positive state than in the Negative. (2) Those produced from the anisotropy in the Equatorial plane also show the polarity dependence but contrary to the previous case they are greater in the Negative state than in the Positive. Their magnitude in the former state is not so small even in the extremely low rigidity (～ 100 GV) as compared with that in high rigidity region. (3) These general characteristics are not altered by the introduction of the wavy neutral sheet or the magnetic irregularities, but the variations are affected more or less, depending on the heliolatitudinal extent of the wavy sheet or the degree of cosmic ray scattering with the irregularities, (4) Sidereal daily variation for the wavy sheet shows a toward-away field dependence similar to that of Swinson-type of solar origin, but the dependence is predominant in intermediate rigidity region (～ 500 GV), in marked contrast to that of solar origin. (5) Finally, whichever its direction may be, the uni-directional anisotropy produces the sidereal diurnal variation common to two conjugate stations in the Northern and Southern hemisphere. If there is any difference between the observed variations at the stations, it should be interpreted as being due to higher order anisotropy such as the bi-directional anisotropy.     

Ring Current Formed During the Bombardment of a Rotating Gas Torus by Neutral Beams

A new mechanism for the generation of the electric ring current is presented. During the radial bombardment of a rotating gas torus by a neutral beam, electrons and protons are dragged by rotating gas. Due to collisions electrons obtain the torus velocity faster than protons, therefore in some layer there is a difference in electron and proton beam toroidal velocities; the electric current is thus generated. This current is discussed as the seed magnetic field in early stages of evolving galaxies, which is then amplified by the dynamo process to present values of the magnetic field. This revised version was published online in July 2006 with corrections to the Cover Date.     

Model for the onset of a magnetospheric substorm

In view of observations which show that a substorm often begins in a small local time sector, a model is assumed in which the neutral sheet current is diverted around a small region we call a bubble. The simplest assumption is that of a linear variation of current with distance from the centre of the bubble in the x-direction in a SM coordinate system, with the diverted current being channelled within narrow paths of width δ_y on the dawn and dusk sides of the bubble. This assumption leads to vector potential integrals that can be evaluated analytically. The addition of this current loop into the magnetotail results in a magnetic field structure where new neutral lines of X- and 0-type can be observed; these are connected to each other as a continuous neutral ring in the xy equatorial plane. The magnetic and electric field components around the neutral regions are calculated, and the time dependent evolution of the neutral ring is studied. Comparison with some published satellite observations shows good agreement. Taking typical values for the various quantities on the basis of actual observations within the magnetotail, we show that the induced electric field is at least comparable to the average cross-tail electrostatic field, and it may well be one or two orders of magnitude greater. The response of the plasma to the induction field is discussed qualitatively. It is concluded that field aligned currents may be produced due to inertial forces of the expanding disturbance. Interpretation of the ground based precipitation patterns of energized particles during auroral breakup is given.     

Re-connexion of magnetic lines of force: Evolution in incompressible MHD fluids

Time-dependent incompressible MHD solutions in two dimensions are obtained numerically to study the evolutionary process involving a re-connexion of magnetic lines of force. Given an initial antiparallel magnetic field, or a current sheet, to which there is an injection of fluid in a transverse direction, we seek to see how the process of re-connexion builds up. In this numerical experiment, special considerations are given to the confirmation of reconnexion, the formation of X-type magnetic field, the speed of growth, conditions that control the evolution, acceleration of particles, the structure of the diffusion region and so forth. The findings are: magnetic lines of force can re-connect and grow to the X-type configuration in fluids of any finitely large hydromagnetic and hydrodynamic Reynolds numbers; the conditions local to the neutral point are less important than the boundary conditions that set up global flow patterns; acceleration of fluid in bulk only concerns whether the X-type configuration grows to the comparably large extent or not; the electric field at the neutral point due to the rapidly changing magnetic field is less efficient in accelerating charged particles.