Self-consistent electromagnetic field in a nearly co-rotating magnetosphere

An example of the self-consistent solution which belongs to the non-trivial solution, obtained in a previous paper (Kaburaki, 1985), is found in a nearly co-rotating inner magnetosphere. Though the stellar wind is neglected there compared with the co-rotatinal velocity, drift motion around the magnetic axis, which is a manifestation of inertial effects, is determined self-consistently with the electromagnetic field. In this process, explicit expressions for the energy integral in the rotating frame and for the density distribution are also obtained. These expressions contain a fundamental length, which is to be evaluated according to physical conditions of a magnetosphere and determines the asymptotic-kinetic energy of a plasma particle at infinity. The electric current associated with the drift motion is too small to alter the original magnetic field, but the electric field is modified by the inertial effects even in the inner magnetosphere. The integrated Ohm's law is used to describe a force balance in the rotating frame, in the limits of weak and strong magnetic field.     

Modulation of Jovian middle magnetosphere currents and auroral precipitation by solar wind-induced compressions and expansions of the magnetosphere: initial response and steady state

We present results from a theoretical model which has been used to investigate the modulation of the magnetosphere-ionosphere coupling currents in the Jovian middle magnetosphere by solar wind-induced compressions and expansions of the magnetosphere. We consider an initial system in which the current sheet field lines extend to 50R_J in the equatorial plane, and where the iogenic plasma in the current sheet undergoes steady outward radial diffusion under the influence of the ionospheric torque which tends to maintain corotation with the planet. We show using typical Jovian parameters that the upward-directed field-aligned currents flowing throughout the middle magnetosphere region in this system peak at values requiring the existence of significant field-aligned voltages to drive them, resulting in large precipitating energy fluxes of accelerated electrons and bright ‘main oval’ UV auroras. We then consider the changes in these parameters which take place due to sudden expansions or compressions of the magnetosphere, resulting from changes in the solar wind dynamic pressure. Two cases are considered and compared, these being first the initial response of the system to the change, determined approximately from conservation of angular momentum of the radially displaced plasma and frozen-in field lines, and second the subsequent steady state of steady outward radial diffusion applied to the compressed or expanded system. We show that moderate inward compressions of the outer boundary of the current sheet field lines, e.g. from 50 to 40R_J, are effective in significantly reducing the coupling currents and precipitation in the initial state, the latter then recovering, but only partly so, during the evolution to the steady state. Strong inward compressions, e.g. to 30R_J cause significant super-corotation of the plasma and a reversal in sense of the current system in the initial state, such that bright auroras may then be formed poleward of the usual ‘main auroral oval’ due to the ‘return’ currents. The sense of the currents subsequently reverts back to the usual direction as steady-state conditions are restored, but they are weak, and so is the consequent electron precipitation. For outward expansions of the current sheet, however, the field-aligned currents and electron precipitation are strongly enhanced, particularly at the poleward border mapping to the outer weak field region of the current sheet. In this case there is little evolution of the parameters between the initial expansion and the subsequent steady state. Overall, the results suggest that the Jovian middle magnetosphere coupling currents and resulting ‘main oval’ auroral acceleration and precipitation will be strongly modulated by the solar wind dynamic pressure in the sense of anti-correlation, through the resulting compressions and expansions in the size of the magnetosphere.     

Hydrogen from Jupiter's atmosphere in the Jovian magnetosphere

The passage of Ulysses through Jupiter's magnetosphere presents a new opportunity to investigate the contribution to the Jovian magnetosphere of ions of atmospheric origin. A determination of the magnetospheric H⁺/He²⁺ flux ratio allows an estimate of the relative abundance of ionospheric material in the Jovian magnetosphere. We find that the H⁺/He²⁺ flux ratio, measured in the energy/charge range between 0.65 and 60 keV/e, steadily increases from a solar wind level of 25 at the magnetopause to a value of 700 at the point of closest approach, and then steadily decreases whilst approaching the magnetopause on the outbound path. We conclude from this that: (1) there is a significant solar wind component throughout the outer and middle magnetosphere; and (2) a significant fraction of the protons in the middle magnetosphere are of nonsolar origin.     

Initial expansion phase of an artificially injected electron beam

We consider the expansion of an electron beam (E ～ 20 keV, I ～ 1 A) artificially injected into the magnetosphere at a high latitude (Λ ～ 60°). We show that, although the space charge effects play an important role during the initial phase of the expansion, it is the magnetic field at the place of the injection which governs the beam radius and the beam density. For an injection parallel to the magnetic field, the ratio between the beam kinetic energy density and the magnetic energy when the beam passes through the Equator, may reach important values (～ 2–5). However, taking into account possible beam instabilities could strongly modify this conclusion.     

Magnetar corona

Persistent high-energy emission of magnetars is produced by a plasma corona around the neutron star, with total energy output of ～10³⁶ erg/s. The corona forms as a result of sporadic starquakes that twist the external magnetic field of the star and induce electric currents in the closed magnetosphere. Once twisted, the magnetosphere cannot untwist immediately because of its self-induction. The self-induction electric field lifts particles from the stellar surface, accelerates them, and initiates avalanches of pair creation in the magnetosphere. The created plasma corona maintains the electric current demanded by curl B and regulates the self-induction e.m.f. by screening. This corona persists in dynamic equilibrium: it is continually lost to the stellar surface on the light-crossing time ～10^?4 s and replenished with new particles. In essence, the twisted magnetosphere acts as an accelerator that converts the toroidal field energy to particle kinetic energy. The voltage along the magnetic field lines is maintained near threshold for ignition of pair production, in the regime of self-organized criticality. The voltage is found to be about ～1 GeV which is in agreement with the observed dissipation rate ～10³⁶ erg/s. The coronal particles impact the solid crust, knock out protons, and regulate the column density of the hydrostatic atmosphere of the star. The transition layer between the atmosphere and the corona is the likely source of the observed 100 keV emission. The corona also emits curvature radiation up to 10¹⁴ Hz and can supply the observed IR-optical luminosity.     

Reconstruction of propagating Kelvin–Helmholtz vortices at Mercury's magnetopause

A series of quasi-periodic magnetopause crossings were recorded by the MESSENGER spacecraft during its third flyby of Mercury on 29 September 2009, likely caused by a train of propagating Kelvin–Helmholtz (KH) vortices. We here revisit the observations to study the internal structure of the waves. Exploiting MESSENGER's rapid traversal of the magnetopause, we show that the observations permit a reconstruction of the structure of a rolled-up KH vortex directly from the spacecraft's magnetic field measurements. The derived geometry is consistent with all large-scale fluctuations in the magnetic field data, establishes the non-linear nature of the waves, and shows their vortex-like structure. In several of the wave passages, a reduction in magnetic field strength is observed in the middle of the wave, which is characteristic of rolled-up vortices and is related to the increase in magnetic pressure required to balance the centrifugal force on the plasma in the outer regions of a vortex, previously reported in computer simulations. As the KH wave starts to roll up, the reconstructed geometry suggests that the vortices develop two gradual transition regions in the magnetic field, possibly related to the mixing of magnetosheath and magnetospheric plasma, situated at the leading edges from the perspectives of both the magnetosphere and the magnetosheath.     

Measurements of hot plasmas in the magnetosphere of Jupiter

This paper presents an overview of a number of the principal findings regarding the hot plasmas (E 50 keV) in Jupiter's magnetosphere by the HISCALE instrument during the encounter of the Ulysses spacecraft with the planet in February 1992. The hot plasma ion fluxes measured by HI-SCALE in the dayside magnetosphere are similar to those measured in the same energy range in this region by the Voyager spacecraft in 1979. Within the dayside plasma sheet, the hot-ion energy densities are comparable with, or larger than, the magnetic field energy densities; these hot ions are found to corotate at about one-half the planetary corotational speed. For ions of energies 500 keV/nucleon, the protons contributed from 50–60% to as much as 80% of the energy content of these plasmas. Strong, magnetic-field-aligned streaming was found for both the ions and electrons in the high-latitude duskside magnetosphere. The ion and electron pitch-angle distributions could be characterized by cos²⁵ α throughout many of the high anisotropy intervals of the outbound pass. There is some evidence in the ion pitch-angle distributions for a corotational component in the hot plasmas at high Jovian latitudes. While there are limitations owing to the finite geometries of the detector telescope systems on the determination of the angular spreads of the ion and electron beams, the measurements show that there are intervals when the particle distributions are not bidirectional. At such times, locally the hot plasmas could be carrying currents of 10⁻⁴μAm⁻². The temporal variations in the streaming electron fluxes are substantially larger than the variations measured for the fluxes that are more locally mirroring. The temporal variations contain periodicities that may correspond to hydromagnetic wave frequencies in the magnetosphere as well as to larger scale motions of magnetospheric plasmas. On nearly half of the days for about a 130 day interval around the time of the Ulysses encounter with the planet, particles of Jovian origin were measured in the interplanetary medium. An event discussed herein shows evidence of an energy dependence of the particle release process from the planetary magnetosphere into the interplanetary medium.     

Compressible turbulence in Hall Magnetohydrodynamics

By direct numerical simulations we investigate the nonlinear dynamics of a compressible Hall Magnetohydrodynamic (MHD) plasma. At small scales, where the Hall effect dominates, we found an increase of the compressibility of the system and the breakdown of the strong link between velocity and magnetic fields, typical of usual MHD. Moreover, we find that small-scale fluctuations are characterized by an anti-correlation between density and magnetic field intensity. These features characterize the excitation of a quasi-perpendicular magnetosonic turbulence that can be interpreted as the small-scale signature of the break-down of the MHD nonlinear energy cascade due to Hall effect. Fluctuations with the same properties, based on measurements by Cluster spacecraft in space plasma turbulence during different magnetopause crossings, have been recently observed.     

Quantitative Analysis of CME Deflections in the Corona

In this paper, ten CME events viewed by the STEREO twin spacecraft are analyzed to study the deflections of CMEs during their propagation in the corona. Based on the three-dimensional information of the CMEs derived by the graduated cylindrical shell (GCS) model (Thernisien, Howard, and Vourlidas in Astrophys. J. 652, 1305, 2006), it is found that the propagation directions of eight CMEs had changed. By applying the theoretical method proposed by Shen et?al. (Solar Phys. 269, 389, 2011) to all the CMEs, we found that the deflections are consistent, in strength and direction, with the gradient of the magnetic energy density. There is a positive correlation between the deflection rate and the strength of the magnetic energy density gradient and a weak anti-correlation between the deflection rate and the CME speed. Our results suggest that the deflections of CMEs are mainly controlled by the background magnetic field and can be quantitatively described by the magnetic energy density gradient (MEDG) model.     

MESSENGER observations of the plasma environment near Mercury

The MESSENGER Fast Imaging Plasma Spectrometer (FIPS) measured the bulk plasma characteristics of Mercury's magnetosphere and solar wind environment during the spacecraft's first two flybys of the planet on 14 January 2008 (M1) and 6 October 2008 (M2), producing the first measurements of thermal ions in Mercury's magnetosphere. In this work, we identify major features of the Mercury magnetosphere in the FIPS proton data and describe the data analysis process used for recovery of proton density (n_p) and temperature (T_p) with a forward modeling technique, required because of limitations in measurement geometry. We focus on three regions where the magnetospheric flow speed is likely to be low and meets our criteria for the recovery process: the M1 plasma sheet and the M1 and M2 dayside and nightside boundary-layer regions. Interplanetary magnetic field (IMF) conditions were substantially different between the two flybys, with intense reconnection signatures observed by the Magnetometer during M2 versus a relatively quiet magnetosphere during M1. The recovered ion density and temperature values for the M1 quiet-time plasma sheet yielded n_p∼1–10 cm⁻³, T_p∼2×10⁶ K, and plasma β∼2. The nightside boundary-layer proton densities during M1 and M2 were similar, at n_p∼4–5 cm⁻³, but the temperature during M1 (T_p∼4–8×10⁶ K) was 50% less than during M2 (T_p∼8×10⁶ K), presumably due to reconnection in the tail. The dayside boundary layer observed during M1 had a density of ∼16 cm⁻³ and temperature of 2×10⁶ K, whereas during M2 this region was less dense and hotter (n_p∼8 cm⁻³ and T_p∼10×10⁶ K), again, most likely due to magnetopause reconnection. Overall, the southward interplanetary magnetic field during M2 clearly produced higher T_p in the dayside and nightside magnetosphere, as well as higher plasma β in the nightside boundary, ∼20 during M2 compared with ∼2 during M1. The proton plasma pressure accounts for only a fraction (24% for M1 and 64% for M2) of the drop in magnetic pressure upon entry into the dayside boundary layer. This result suggests that heavy ions of planetary origin, not considered in this analysis, may provide the “missing” pressure. If these planetary ions were hot due to “pickup” in the magnetosheath, the required density for pressure balance would be an ion density of ∼1 cm⁻³ for an ion temperature of ∼10⁸ K.     

Some properties of geomagnetic field pulsations in the 0.1–1.0-Hz frequency range: A quantitative description and comparison with the satellite and ground-based observations

By using an image-dipole magnetic field model for a variety of plasma density profiles we have studied the latitude effect of the 0.1–1.0-Hz hydromagnetic wave propagation in the Earth's magnetosphere. On comparing the results of signal group delay time calculations for dipole and model magnetic fields with ground and satellite observations we obtain some propagation characteristics of Pc1s and localize the regions of their generation. Our results show that most high-latitude Pc1 events are generated in the outer magnetosphere in accordance with ground and satellite observations and theoretical considerations. The non-dipole geometry of the geomagnetic field in the outer magnetosphere (at geomagnetic latitudes φ₀ > 66°, L > 6) has a significant effect on the hydromagnetic wave propagation.     

Effect of hot injections on electromagnetic ion-cyclotron waves in inner magnetosphere of Saturn

Encounter of Voyager with Saturn’s environment revealed the presence of electromagnetic ion-cyclotron waves (EMIC) in Saturnian magnetosphere. Cassini provided the evidence of dynamic particle injections in inner magnetosphere of Saturn. Also inner magnetosphere of Saturn has highest rotational flow shear as compared to any other planet in our solar system. Hence during these injections, electrons and ions are transported to regions of stronger magnetic field, thus gaining energy. The dynamics of the inner magnetosphere of Saturn are governed by wave-particle interaction. In present paper we have investigated those EMIC waves pertaining in background plasma which propagates obliquely with respect to the magnetic field of Saturn. Applying kinetic approach, the expression for dispersion relation and growth rate has been derived. Magnetic field model has been used to incorporate magnetic field strength at different latitudes for radial distance of \(6.18~R_{{s}}\) (\(1~R_{{s}}= 60{,}268~\mbox{km}\)). Various parameters affecting the growth of EMIC waves in cold bi-Maxwellian background and after the hot injections has been studied. Parametric analysis inferred that after hot injections, growth rate of EMIC waves increases till \(10^{\circ}\) and decreases eventually with increase in latitude due to ion density distribution in near-equatorial region. Also, growth rate of EMIC waves increases with increasing value of temperature anisotropy and AC frequency, but the growth rate decreases as the angle of propagation with respect to \(B_{0}\) (Magnetic field at equator) increases. The injection events which assume the Loss-cone distribution of particles, affect the lower wave numbers of the spectra.     

Energy and momentum flow in electromagnetic fields and plasma

We consider macroscopic flow of energy and momentum between the solar wind and outer magnetosphere. We point out that using the integral form of magnetohydrodynamic equations is more natural than the differential form for consideration of energy and momentum flows and should yield more accurate results from magnetic field data. We use the notation of general relativity because it is straightforward and brief.     

Criticism of reconnection models of the magnetosphere

Reconnection involves singular lines called X-lines on the day and night sides of the magnetosphere, and the reconnection rate is proportional to the component of the electric field along the X-line. Although there is some indirect support for this model, nevertheless direct support is totally lacking. However, there are two distinct pieces of clearly contradictory observational evidence on the dayside. First is the failure to account for the implied energy dissipation by the magnetopause current, over 10¹¹ W, which should be easily observable as heating or enhanced flow of the plasma near the magnetopause. In marked contrast to this prediction, HEOS-2 satellite data reveal a plasma with decreased energy density and reduced flow. Second, the boundary of closed magnetic field lines is in the wrong location. In the reconnection process the plasma outflow would cut across open field lines toward higher latitudes; there should be a band of open field lines equatorward of the cleft. Observations of trapped energetic particles indicate closed field lines within the entry layer and cleft. Either one of these pieces of evidence is sufficient by itself to require drastic revision, even rejection, of the reconnection model. There is also contradictory evidence on the night side. The last closed field line capable of trapping energetic particles is poleward of auroral arcs. The implication is that the X-line is at the distant magnetopause, and not in the plasma sheet. Consequently, even if the reconnection process were operative at the nightside X-line, it would be isolated from steady state plasma sheet and auroral processes. On the other hand, substorm phenomena, in which stored magnetic energy is converted into particle kinetic energy, necessarily involve an induced electric field; that is excluded in theories of the reconnection process in which it is assumed that curl E = 0. Nevertheless, the observed easy access of energetic solar flare particles to the polar caps, and especially the preservation of interplanetary anisotropies as differences between the two polar caps, argues strongly for an open magnetosphere, with interconnection between geomagnetic and inter-planetary magnetic field lines. It is suggested that the resolution of this apparent paradox involves electric fields parallel to the magnetic field lines somewhere on the dawn and dusk sides of the magnetosphere, with an equipotential dayside magnetopause.     

Accretion disc–stellar magnetosphere interaction: field line inflation and the effect on the spin-down torque

We calculate the structure of a force-free magnetosphere which is assumed to corotate with a central star and which interacts with an embedded differentially rotating accretion disc. The magnetic and rotation axes are aligned, and the stellar field is assumed to be a dipole. We concentrate on the case when the amount of field line twisting through the disc–magnetosphere interaction is large , and consider different outer boundary conditions. In general the field line twisting produces field line inflation (e.g. Bardou & Heyvaerts), and in some cases with large twisting many field lines can become open. We calculate the spin-down torque acting between the star and the disc, and we find that it decreases significantly for cases with large field line twisting. This suggests that the oscillating torques observed for some accreting neutron stars could be caused by the magnetosphere varying between states with low and high field line inflation. Calculations of the spin evolution of T Tauri stars may also have to be revised in the light of the significant effect that field line twisting has on the magnetic torque resulting from star–disc interactions.     

The global structure of the pulsar magnetospheres

The model of the pulsar magnetosphere filled with massless charged particles (rest massm=0) is considered. The gas of charged massless particles can be found in two different phases: (1) dynamical phase (DP), when the particles move with nonvanishing energy along some base line, determined by the electromagnetic field only, (2) statical phase (SP), when the particles have vanishing energy =0. The pulsar magnetosphere occurs to be divided into regions of different types: (a) the accelerating regions (DP-regions) containing only DP, (b) the capture regions, containing only SP, (3) leaky capture regions, where DP moves through SP. The leaky capture regions are the active regions, which are responsible for the pulsar radioemission. In the case of oblique magnetic moment the equation for the capture surface has been obtained. The capture region is formed around this surface. Expressions for jumps of the electromagnetic field, the current density and the charge density on the capture region boundary have been obtained. The problem of the pulsar magnetosphere is stated mathematically in the case of oblique magnetic moment and ejection of only electrons.     

Theory of the plasma sheet in the jovian magnetosphere

The magnetic field in the middle magnetosphere of Jupiter was suggested to be the planetary dipole field plus a perturbation field due to a current sheet (Smith et al, 1974). Since no data of the low energy plasma are available the existence of a plasma sheet could not be confirmed directly. In this paper we show how the plasma pressure and density-can be derived from the magnetic field in the framework of a self-consistent theory. For the magnetic field model proposed by Goertz et al. (1976c) we compute the isobars and isodensity lines and confirm the existence of a thin plasma sheet.     

Magnetospheric plasma interactions

The Earth's magnetosphere (including the ionosphere) is our nearest cosmical plasma system and the only one accessible to mankind for extensive empirical study by in situ measurements. As virtually all matter in the universe is in the plasma state, the magnetosphere provides an invaluable sample of cosmical plasma from which we can learn to better understand the behaviour of matter in this state, which is so much more complex than that of unionized matter.It is therefore fortunate that the magnetosphere contains a wide range of different plasma populations, which vary in density over more than six powers of ten and even more in equivalent temperature. Still more important is the fact that its dual interaction with the solar wind above and the atmosphere below make the magnetosphere the site of a large number of plasma phenomena that are of fundamental interest in plasma physics as well as in astrophysics and cosmology.The interaction of the rapidly streaming solar wind plasma with the magnetosphere feeds energy and momentum, as well as matter, into the magnetosphere. Injection from the solar wind is a source of plasma populations in the outer magnetosphere, although much less dominating than previously thought. We now know that the Earth's own atmosphere is the ultimate source of much of the plasma in large regions of the magnetosphere. The input of energy and momentum drives large scale convection of magnetospheric plasma and establishes a magnetospheric electric field and large scale electric current systems that carry millions of ampère between the ionosphere and outer space. These electric fields and currents play a crucial role in generating one of the most spectacular among natural phenomena, the aurora, as well as magnetic storms that can disturb man-made systems on ground and in orbit. The remarkable capability of accelerating charged particles, which is so typical of cosmical plasmas, is well represented in the magnetosphere, where mechanisms of such acceleration can be studied in detail. In situ measurements in the magnetosphere have revealed an unexpected tendency of cosmical plasmas to form cellular structure, and shown that the magnetospheric plasma sustains previously unexpected, and still not fully explained, chemical separation mechanisms, which are likely to operate in other cosmical plasmas as well.Presented at the 2nd UN/ESA Workshop, held in Bogotá, Colombia, 9–13 November, 1992.     

Stochastic Acceleration of Energetic Particles in the Magnetosphere of Saturn

Voyager's plasma probe observations suggest that there are at least three fundamentally different plasma regimes in Saturn: the hot outer magnetosphere, the extended plasma sheet, and the inner plasma torus. At the outer regions of the inner torus some ions have been accelerated to reach energies of the order of 43 keV. We develop a model that calculates the acceleration of charged particles in the Saturn's magnetosphere. We propose that the stochastic electric field associated to the observed magnetic field fluctuations is responsible of such acceleration. A random electric field is derived from the fluctuating magnetic field – via a Monte Carlo simulation – which then is applied to the momentum equation of charged particles seeded in the magnetosphere. Taking different initial conditions, like the source of charged particles and the distribution function of their velocities, we find that particles injected with very low energies ranging from 0.129 eV to 5.659 keV can be strongly accelerated to reach much higher energies ranging from 22.220 eV to 9.711 keV as a result of 125,000 hitting events (the latter are used in the numerical code to produce the particle acceleration over a predetermined distance).     

Initial Venus Express magnetic field observations of the magnetic barrier at solar minimum

Although there is no intrinsic magnetic field at Venus, the convected interplanetary magnetic field piles up to form a magnetic barrier in the dayside inner magnetosheath. In analogy to the Earth's magnetosphere, the magnetic barrier acts as an induced magnetosphere on the dayside and hence as the obstacle to the solar wind. It consists of regions near the planet and its wake for which the magnetic pressure dominates all other pressure contributions. The initial survey performed with the Venus Express magnetic field data indicates a well-defined boundary at the top of the magnetic barrier region. It is clearly identified by a sudden drop in magnetosheath wave activity, and an abrupt and pronounced field draping. It marks the outer boundary of the induced magnetosphere at Venus, and we adopt the name “magnetopause” to address it. The magnitude of the draped field in the inner magnetosheath gradually increases and the magnetopause appears to show no signature in the field strength. This is consistent with PVO observations at solar maximum. A preliminary survey of the 2006 magnetic field data confirms the early PVO radio occultation observations that the ionopause stands at ∼250 km altitude across the entire dayside at solar minimum. The altitude of the magnetopause is much lower than at solar maximum, due to the reduced altitude of the ionopause at large solar zenith angles and the magnetization of the ionosphere. The position of the magnetopause at solar minimum is coincident with the ionopause in the subsolar region. This indicates a sinking of the magnetic barrier into the ionosphere. Nevertheless, it appears that the thickness of the magnetic barrier remains the same at both solar minimum and maximum. We have found that the ionosphere is magnetized ∼95% of the time at solar minimum, compared with 15% at solar maximum. For the 5% when the ionosphere is un-magnetized at solar minimum, the ionopause occurs at a higher location typically only seen during solar maximum conditions. These have all occurred during extreme solar conditions.