Full-wave VLF modes in a cylindrically symmetric enhancement of plasma density

VLF waves in the magnetosphere may be guided by ducts, i.e. enhancements of plasma density aligned with the geomagnetic field. It is required to account for the good transmission properties of these ducts as some leakage of energy is expected, with consequent attenuation. We consider a cylindrical duct, whose axis is parallel to a uniform magnetic field. The electron density of a cold plasma is a function only of radial distance r from the axis, taking constant values in inner and outer regions r < a and r > b, and varying smoothly in the duct wall a < r < b. We compute full-wave ‘trapped’ VLF modes. Results are presented for a range of values of the parameters of the model. In general we find that attenuation of leading modes is very low, agreeing with observation. Specific features are that leakage (arising from mode conversion in the duct wall) increases as the wall is made thinner, that leakage for the leading modes is less for weaker ducts, that many modes may propagate, and that, because of interference effects, some higher order modes also suffer little attenuation.     

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.     

Basics of Rotating Magnetospheres: Equilibrium and Stability

We present the basic characteristics of a rotating magnetosphere. More specifically, we describe its overall equilibrium state, explain the ‘subcorotation’ phenomenon resulting from plasma production or from outward transport, discuss the conditions under which a magnetospheric system is driven unstable, and comment on the nature of the unstable motions, with emphasis on the interchange motions believed to be responsible for the outward plasma transport. This revised version was published online in July 2006 with corrections to the Cover Date.     

Magnetic portraits of Tethys and Rhea

The Cassini spacecraft made a single flyby each of Saturn's icy moons Tethys and Rhea in late 2005. The magnetic field observations from these flybys provide unique portraits of the magnetic properties of these moons. These are the first observations of interactions of these inert moons with the sub-magnetosonic plasma of Saturn's magnetosphere. Because the upstream field and plasma conditions are extremely stable, we are able to observe the interaction in great detail. One of the major findings of this study is that the region of plasma depletion is greatly elongated along the field direction in a sub-magnetosonic interaction. Based on the consideration of field aligned velocities of thermal ions, we show that overlapping particle shadow wings form downstream of an inert moon such that in each of the particle shadow wings, particles of specific field aligned velocities are depleted. Other major findings of this study are: (1) Tethys and Rhea are devoid of any internal magnetic field; (2) No induction generated field was observed, as expected because of the extremely weak primary inducing (time varying) field; (3) There is no appreciable mass-loading of Saturn's magnetosphere from Tethys and Rhea; (4) We predict that wave particles interactions would be generated that smooth out the phase space holes created by the moon/plasma interaction. These waves serve to isotropize the plasma distribution function.     

Generation mechanism of Pc3 magnetic pulsations at very low latitudes

Polarization properties of Pc3 magnetic pulsations at very low latitudes cannot be explained by existing theories which are based on the field line resonance model, because magnetic field lines at ¦Φ¦ < 22° are almost entirely in the ionosphere. In order to interpret Pc3 polarization characteristics observed at very low latitudes (¦Φ¦ < 20°), I would like to propose a possible, new qualitative model in which two superimposed ionospheric eddy currents, oscillating with slight differences in frequency in the Pc3 range and in azimuthal wave number, move azimuthally at very low latitudes. The equatorial ionospheric Pedersen eddy currents are believed to be predominantly caused by inductive electric fields of compressional Pc3 source waves which may possibly arrive in the equatorial ionosphere from the outer magnetosphere.     

Numerical simulations of aligned neutron star magnetospheres

We present detailed numerical simulations of the magnetosphere of an isolated neutron star in which the spin and magnetic dipole axes of the star are aligned. We demonstrate that stable charge distributions are always found, rather than particle outflows. A stable magnetosphere consists of a dome above the polar cap containing plasma of one charge and an equatorial belt containing plasma of the other sign: E · B =0 inside both of these. These are separated by a vacuum gap in which E · B ≠0 ( ρ =0 instead). We show that the charge distribution used in the 'standard' Goldreich–Julian pulsar model is inherently unstable: it collapses to a stable configuration that is very similar to the others illustrated here. An instructive video of this collapse is available at http://spacsun.rice.edu/~ian/. For typical pulsars, the stable solution has no particles near to the light cylinder, and if there were any there then their loss from the system would not lead to a replacement from the star (in contradiction to the explicit assumption used in the Goldreich–Julian model). We discuss the generic effects of pair creation, in particular as an additional source of ionization in the vacuum gap. The overall effect is simply to reduce the value of E · B in the vacuum gap so that the pair-production rate drops towards zero. A dome, disc and gap geometry is still the resulting solution. In conclusion, we confirm previous studies that the aligned rotator cannot make an active pulsar.     

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.     

On the variation of pulsar periods in close binary systems

X-ray pulsars, which form together with a main sequence star or a giant a close binary system, show strong variations in their pulse period. Epochs of spin-up and spin-down interchange on timescales of some tens up to some thousand days.

We study this phenomenon in the framework of the disk-fed model by Ghosh and Lamb, which we generalize by allowing for an inclination angle χ between the magnetic dipole moment μ and the rotation axis. Moreover, we take into account the relatively small magnetic field induced by currents in the magnetosphere flowing along the dipole field lines. This component, which we calculate numerically, leads to a torque perpendicular to the rotation axis and induces a precession of it. Due to this additional degree of freedom, the calculated pulse period history is much smoother than in the classical Ghosh and Lamb model. Within this extended model we compute, as an example, the pulse period history of Cen X-3 using the observed X-ray flux as a measure for the mass accretion rate. Qualitative accordance with the measured pulse period data (see e.g. Nelson et al., 1997 [ApJ, 488, L117]) is found to be good.     

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).     

On the Kelvin-Helmholtz instability of structured plasma layers in the magnetosphere

The hydromagnetic Kelvin-Helmholtz (K-H) instability problem is studied for a three-layered system analytically by arriving at the marginal instability condition. As the magnetic field directions are taken to vary in the three regions, both the angle and finite thickness effects are seen on the instability criterion. When the relative flow speed of the plasmas on the two sides of the interfaces separating the inner and the surrounding layers is U < U_c, where U_c is the critical speed, the system is stable both for symmetric and asymmetric perturbations. However, unlike the case of the interface bounded by two semiinfinite media, U_c is no longer the minimum critical speed above which the system will be unstable for all wavenumbers; another critical speed U^* > U_c is introduced due to the finiteness of the system. When U_c < U < U^*, the instability can set in either through the symmetric or asymmetric mode, depending on the ratio of the plasma parameters and angle between the magnetic field directions across the boundaries. The instability arises for a finite range of wavenumbers, thus giving rise to the upper and lower cut-off frequencies for the spectra of hydromagnetic surface waves generated by the K-H instability mechanism. When U > U^*, both the modes are unstable for short wavelengths. The results are finally used to explain some observational features of the dependence of hydromagnetic energy spectra in the magnetosphere on the interplanetary parameters.     

Thermal emission areas of heated neutron star polar caps

Observed hot spots on neutron stars are often associated with polar caps heated by the backflow of energetic electrons or positrons from accelerators on bundles of open magnetic field lines. Three effects are discussed that may be relevant to formation of hot spots and their areas. (1) The area of a polar cap is proportional to the ratio of the star’s surface dipole field to the local field at the polar cap. Because the field is coupled to the evolving spin of the superfluid core of the star, this ratio can depend on the stellar spin and its history. (2) The hot emission area may appear smaller to a distant observer when emitted X-rays propagate through electron-positron plasma created in the magnetosphere. The X-rays then change their energy spectrum because of cyclotron resonant scattering by pairs. (3) Hot spots may form on the star’s surface as a result of crust motions that are driven by the pull of core flux tubes pinned to the crust. Such motions twist the footprints of closed magnetic loops of the magnetosphere and induce an electric current in the loop, which will heat those footprints.     

Reflection and refraction of hydromagnetk waves at the magnetopause

Reflection and transmission coefficients of MHD waves are obtained at a stable, plane interface which separates two compressible, perfectly conducting media in relative motion to each other. The coefficients are evaluated for representative conditions of the quiettime, near-Earth magnetopause. The transmission coefficient averaged over a hemispherical distribution of incident waves is found to be 1–2 per cent. Yet the magnitude of the energy flux deposited into the magnetosphere in a day averaged over a hemispherical distribution of waves having amplitudes of say 2–3 gamma, is estimated to be of the order 10²² erg. Therefore the energy input of MHD waves must contribute significantly to the energy budget of the magnetosphere. The assumption that the boundary surface is a tangential discontinuity with no curvature limits the present theory to hydromagnetic frequencies higher than about 10⁻¹ Hz. The ion gyrofrequencies for the models assumed here lie above 2 × 10⁻¹ Hz. Therefore the present treatment applies to MHD waves near 10⁻¹ Hz.     

Vorticity in the magnetosphere

It is shown that Birkeland current and vorticity in the magnetosphere are intimately related, suggesting the importance of taking explicit account of vorticity, particularly velocity shear, when considering magnetospheric motions. An equation of motion for the magnetosphere coupled to the ionosphere is derived. It is suggested that experience with MHD fluids generally might fruitfully be brought to bear on certain problems in the magnetosphere to answer the question, not ‘why a sheet of Birkeland current,’ but rather ‘why a localised velocity shear.’     

The mechanism of magnetospheric substorm and the MHD waves of the solar wind

A mechanism of the Earth's magnetospheric substorm is proposed. It is suggested that the MHD waves may propagate across the magnetopause from the magnetosheath into the magnetotail and will be dissipated in the plasma sheet, heating the plasma and accelerating the particles. When the solar wind parameters change, the Poynting flux of the waves transferred from the magnetosheath into the tail, may be greater than 10¹⁸ erg s^?1. The heated plasma and accelerated particles in the plasma sheet will be injected into the inner magnetosphere, and this may explain the process of the ring current formation and auroral substorm.The Alfvén wave can only propagate along the magnetic force line into the magnetosphere in the open magnetosphere, but the magnetosonic wave can propagate in both the open and closed magnetosphere. When the IMF turns southward, the configuration of the magnetosphere will change from a nearly closed model into some kind of open one. The energy flux of Alfvén waves is generally larger than that of the magnetosonic wave. This implies that it is easy to produce substorms when the interplanetary magnetic field (IMF) has a large southward component, but the substorm can also be produced even if the IMF is directed northward.     

Solar wind induction in Mercury: Constraints on the formation of a magnetosphere

The discovery of Mercury's magnetosphere by Mariner 10 was surprising since the conventional view of regenerative planetary dynamos had been that the spin requirement would likely have been in excess of the observed spin rate of Mercury. Also internal fluid motions were not expected to be sufficiently large. This paper explores the alternative model of the formation of Mercury's magnetosphere via electromagnetic induction forced by the solar wind. It is shown, however, that the constraints are so severe as to limit severely the applicability of such a model. Although induction is easily observed on the Moon, the modification of the magnetic boundary condition associated with a plasma magnetosphere on Mercury rules out its formation via induction except for interplanetary driving fields which are decreasing in amplitude. That model is explored but retains the difficulty that induced magnetospheres tend to be of small radial and temporal extent compared to that inferred by Ness et al. for Mercury.     

Two simple methods for the determination of the resonance frequencies of magnetic field lines

It has previously been shown that application of the “gradient method” to simultaneous recordings of geomagnetic pulsation fields at two stations on a meridian can determine the resonant frequency of a magnetic field line, and that the distribution of resonant frequencies along the meridian can be calculated from three stations. It is shown here that if the D-component spectrum of the pulsations is taken to be a representation of the driving wave, the same information can be derived from one and two station measurements, respectively, albeit with some slight loss of accuracy. It is also suggested that the empirical method of inferring the intensity of the interplanetary magnetic field from the measurement of the period of ground magnetic pulsations would be more accurate if D-component observations only were used.     

Plasma boundaries at 6.6 RE as observed by GEOS-2: Large plasmapause discontinuity and injection event. Discussion of diamagnetic effects

An impulsive event observed from the nightside geostationary orbit by the GEOS-2 European satellite is analysed in detail in the case of a very quiet magnetosphere. It is characterized by a very sharp and steep plasma density gradient observed near 2230 L.T. A quite detailed picture of the situation can be sketched as a result of the GEOS-2 set of experiments. The observations roughly organize themselves as follows along the geostationary orbit: an intense and well localized d.c. electric field appeared between the outbound crossing of the plasmapause and local midnight; at the same time a sudden ULF activity arose probably indicating the presence of field-aligned currents; GEOS-2 then entered a quieter plasmasheet where clear diamagnetic effects are evidenced. These observations are consistent with a stabilization of a possible interchange instability, which would maintain the density gradient at the plasmapause. The validity of the plasma density measurements which are made through an active wave method is discussed in connection with the 2 keV mean energy of the plasmasheet particles. The macroscopic evolution equation of the plasma bulk velocity is considered. It appears that the gradients of the macroscopic drift velocity of the plasma may have a non-negligible effect rendering invalid the unsophisticated scheme of a balance between kinetic and magnetic pressures.     

The example of effective plasma acceleration in a magnetosphere

The problem of effective transform of Poynting flux energy into the kinetic energy of relativistic plasma outflow in a magnetosphere is considered. In this article we present an example of such acceleration. In order to perform it, we use the approach of ideal axisymmetric magnetohydrodynamics (MHD). For highly magnetized plasma outflow we show that a linear growth of Lorentz factor with a cylindrical distance from the rotational axis is a general result for any field configuration in the sub-magnetosonic flow. In the far region the full magnetohydrodynamics problem for one-dimensional flow is considered. It turns out that the effective plasma outflow acceleration is possible in the paraboloidal magnetic field. It is shown that such an acceleration is due to the drift of charged particles in the crossed electric and magnetic field. The clear explanation of the absence of acceleration in the monopole magnetic field if given.      

The dawn polar cap boundary at high altitude

Comparison of hot plasma data from ATS-6 and GEOS-1 when the satellites were near dawn L.T. conjunction reveals the presence of strong gradients separating plasmas differing by more than two orders of magnitude in keV particle fluxes. These gradients are observed at off-equatorial geomagnetic latitudes of 25–30° on field lines outside the synchronous orbit. They are associated with magnetic storms and are distinct from magnetopause crossings. Interpretation of these events in terms of a boundary between magnetospheric and polar-cap plasma leads to the following conclusions: (1) the polar cap/lobe region is essentially devoid of keV plasma at these times; (2) the field lines defining this boundary are significantly distorted from a dipolar to a more stretched form consistent with the presence of a storm-ring current, (3) smaller substorm-scale motions are superposed on the gross motion of the boundary with some evidence present for structure in the plasma spatial profile, and (4) magnetosheath-like plasma finds access to the inner magnetosphere at dawn L.T., much as it does near noon, along polar-cap boundary-layer field lines which close through the low latitude magnetospheric boundary layer.     

Electromagnetic wave propagation and instabilities in the magnetosphere

Growth rates for both the RH- and LH-modes of an EM wave propagating along a magnetic field through an isotropic loss-cone plasma have been obtained. It is found that growing modes can exist, and are found to depend critically on the mirror ratioR, and the specific details of the distribution function of the energetic component. To study the energetic-particle distribution observed at low energies by satellites within the magnetosphere, an isotropic double-humped loss-cone velocity distribution is then studied with a view to determining whether the secondary hump can introduce an instability not present for monotonic distribution. It is found that such a distribution can be unstable in a mirror geometry if the energetic component is sufficiently monoenergetic. Within the magnetosphere, nearly monoenergetic fluxes are observed, peaking in the energy range 1–10 keV, depending on the McIlwain parameterL. It is possible that the initial injection of monoenergetic particles may have been much more sharply peaked than the one presently observed, and, as a result of wave-particle interactions, subsequently relaxed to the presently observed distribution. It is seen here that the EM waves within the magnetosphere can contribute to the relaxation of such an initial injection.