Reflection Driven MHD Turbulence in the Solar Atmosphere and Wind

Alfvénic turbulence is usually invoked and used in many solar wind models (Isenberg and Hollweg, 1982, J. Geophys. Res. 87:5023; Tu et al. 1984, J. Geophys. Res. 89:9695; Hu et  al. 2000, J. Geophys. Res. 105:5093; Li 2003, Astron. Astrphys. 406:345; Isenberg 2004, J. Geophys. Res. 109:3101) as a process responsible for the transfer of energy, released at large scale in the photosphere, towards small scale in the corona, where it is dissipated. Usually an initial spectrum is prescribed since the closest constraint to the spectrum is given by Helios measurements at 0.3 AU. With this work we intend to study the efficiency of the reflection as a driver for the nonlinear interactions of Alfvén waves, the development of a turbulent spectrum and its evolution in the highly stratified solar atmosphere inside coronal holes. Our main finding is that the perpendicular spectral slope changes substantially at the transition region because of the steep density gradient. As a result a strong turbulent heating occurs, just above the transition region, as requested by current solar wind models.     

Currents over the auroral arc

The three-dimensional current system over an enhanced conductivity strip identified with an auroral arc is calculated for the case of the magnetospheric plasma convection across this strip. The strip produces a stationary Alfvén wave which propagates along magnetic field lines and is carried simultaneously by the convecting plasma. The Alfvén wave generation corresponds to an appearance of field-aligned currents over the arc. The three-dimensional current system generated over the arc is studied, taking into account reflection of the waves from the ionosphere of the opposite hemisphere. The correspondence of the theory with the experimental results is found.     

Suppression of resonant field line oscillations by a turbulent background

Stochastic fluctuations of the magnetospheric plasma and background magnetic field, especially intense during geomagnetically active periods, can provide an additional mechanism of damping of Alfvén field line oscillations. To quantify this hypothesis, we consider a driven Alfvén field line resonator with stochastic fluctuations of the Alfvén resonant frequency. This problem is first considered analytically for a low level of fluctuations, then a more general numerical approach is introduced. The results of analytical calculations and numerical modeling both indicate the deterioration of resonant properties of the resonator owing to stochastic background fluctuations.     

Reflection of Alfvén waves by non-uniform ionospheres

Magnetospheric Alfvén waves are reflected by the ionosphere. We investigate the effect of horizontally varying ionospheric conductivity on the process of Alfvén wave reflection. Four idealised ionospheric models are considered in detail. We find that the reflection process is strongly dependent on the orientation of the wave electric field vector with respect to the boundary between high and low conductivities, and under certain conditions subsidiary Alfvén waves are generated. The field-aligned currents in the subsidiary Alfvén waves serve to close divergent horizontal currents resulting from the non-uniform ionospheric conductivity. The implications for ground-based pulsation studies are discussed.     

Two-dimensional Non-linear Alfvén Wings Generated by the Electrodynamic Interaction between Callisto and the Jovian Magnetosphere

When a highly conducting magnetized plasma passes an object with lower conductivity, or a body with inhomogeneous conductivity, 2-D structures are formed, the so-called `Alfvén wings'. These structures may arise, for example, at a Jovian moon without an intrinsic magnetic field (Callisto). In this case, Alfvén wings could be generated in the magnetized Jovian magnetospheric plasma flow owing to the in homogeneity of the moon's ionosphere/atmosphere conductivity. Such Alfvén wings may be considered as a satellite magnetosphere; the satellite magnetospheric magnetic field is a disturbed field of the Jovian magnetospheric plasma flow. An analytical solution is obtained in a simple proposed model. This revised version was published online in July 2006 with corrections to the Cover Date.     

Predictions on the application of the Hanle effect to map the surface magnetic field of Jupiter

In this paper we evaluate the possibility of detecting, for the first time, the surface magnetic field of Jupiter (∼1 bar level) by observing the change of linear polarization induced by the Hanle effect on the H Lyman-alpha (Lyα) emission line of the planet. We find that, indeed, the Hanle effect, which results from the interaction between a local magnetic field and the atomic polarization induced by absorption of anisotropic radiation, is sensitive to relatively weak values of the strength of the magnetic fields expected on planets. First, we show that for the Lyα emission backscattered by atomic H in the presence of a magnetic field, the Hanle effect is polarizing. This new result is in total contrast to the depolarizing effect predicted and observed for emission lines scattered at right angles in solar prominences. Additionally, to estimate the polarization rate for the case of Jupiter, we have considered three magnetic field models: a dipole field for reference, an O₄ based model [Connerney, J.E.P., 1981. The magnetic field of Jupiter—A generalized inverse approach. J. Geophys. Res. 86, 7679-7693], and finally, an O₆ based model [Khurana, K.K., 1997. Euler potential models of Jupiter's magnetospheric field. J. Geophys. Res. 102, 11295-11306]. In all models, we show that for the jovian backscattered Lyα line, the Hanle effect does enhance the Lyα linear polarization; the polarization rate may exceed 2% at specific regions of the jovian disc, making detection possible either remotely or from an orbiter around Jupiter. In general, depending on the instrumental sensitivity and the observing strategy used, we show that accurate mapping of the linear polarization rate at the planetary surface (thermosphere) or off-disc (corona) may provide a rather accurate estimate of the jovian total magnetic field strength on large area scales.     

Three-Dimensional MHD Wave Propagation and Conversion to Alfvén Waves near the Solar Surface. I. Direct Numerical Solution

The efficacy of fast?–?slow MHD mode conversion in the surface layers of sunspots has been demonstrated over recent years using a number of modelling techniques, including ray theory, perturbation theory, differential eigensystem analysis, and direct numerical simulation. These show that significant energy may be transferred between the fast and slow modes in the neighbourhood of the equipartition layer where the Alfvén and sound speeds coincide. However, most of the models so far have been two dimensional. In three dimensions the Alfvén wave may couple to the magnetoacoustic waves with important implications for energy loss from helioseismic modes and for oscillations in the atmosphere above the spot. In this paper, we carry out a numerical “scattering experiment,” placing an acoustic driver 4 Mm below the solar surface and monitoring the acoustic and Alfvénic wave energy flux high in an isothermal atmosphere placed above it. These calculations indeed show that energy conversion to upward travelling Alfvén waves can be substantial, in many cases exceeding loss to slow (acoustic) waves. Typically, at penumbral magnetic field strengths, the strongest Alfvén fluxes are produced when the field is inclined 30°?–?40° from the vertical, with the vertical plane of wave propagation offset from the vertical plane containing field lines by some 60°?–?80°.     

Deep Solar Activity Minimum 2007 – 2009: Solar Wind Properties and Major Effects on the Terrestrial Magnetosphere

We discuss the temporal variations and frequency distributions of solar wind and interplanetary magnetic field parameters during the solar minimum of 2007?–?2009 from measurements returned by the IMPACT and PLASTIC instruments on STEREO-A. We find that the density and total field strength were significantly weaker than in the previous minimum. The Alfvén Mach number was higher than typical. This reflects the weakness of magnetohydrodynamic (MHD) forces, and has a direct effect on the solar wind–magnetosphere interactions. We then discuss two major aspects that this weak solar activity had on the magnetosphere, using data from Wind and ground-based observations: i) the dayside contribution to the cross-polar cap potential (CPCP), and ii) the shapes of the magnetopause and bow shock. For i) we find a low interplanetary electric field of 1.3±0.9 mV?m^?1 and a CPCP of 37.3±20.2 kV. The auroral activity is closely correlated to the prevalent stream–stream interactions. We suggest that the Alfvén wave trains in the fast streams and Kelvin–Helmholtz instability were the predominant agents mediating the transfer of solar wind momentum and energy to the magnetosphere during this three-year period. For ii) we determine 328 magnetopause and 271 bow shock crossings made by Geotail, Cluster 1, and the THEMIS B and C spacecraft during a three-month interval when the daily averages of the magnetic and kinetic energy densities attained their lowest value during the three years under survey. We use the same numerical approach as in Fairfield’s (J. Geophys. Res. 76, 7600, 1971) empirical model and compare our findings with three magnetopause models. The stand-off distance of the subsolar magnetopause and bow shock were 11.8 R _E and 14.35 R _E, respectively. When comparing with Fairfield’s (1971) classic result, we find that the subsolar magnetosheath is thinner by ～1 R _E. This is mainly due to the low dynamic pressure which results in a sunward shift of the magnetopause. The magnetopause is more flared than in Fairfield’s model. By contrast the bow shock is less flared, and the latter is the result of weaker MHD forces.

     

Alfvén drag for satellites orbiting in Jupiter's plasmasphere

According to a mechanism discovered by S. D. Drell, H. M. Foley, and M. A. Ruderman ((1965). J. Geophys. Res.70, 3131–3145), a satellite orbiting around a planet having a strong magnetic field and a dense ionospheric plasma dissipates orbital energy via radiation of Alfvén waves. The dissipation process is effective for objects larger than a minimum size and made of material exceeding a minimum electrical conductivity. It is shown that the corresponding drag effect could have influenced in a significant way the orbital evolution of the small natural moons orbiting inside or in proximity of Jupiter's ring. In particular this mechanism could explain the absence in the ring of objects in the size range from ～0.1 to ～10 km.     

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.     

Coupled guided modes in the magnetotails: spatial structure and ballooning instability

The problem of the spatial structure of coupled azimuthally small-scale Alfvén and slow magnetosonic (SMS) waves is solved in an axisymmetric magnetotail model with a current sheet. It is shown that the linear transformation of these waves occurs in the current sheet on magnetic field lines stretched into the magnetotail. From the ionosphere to the current sheet these modes are linearly independent. Due to the high ionospheric conductivity the structure of coupled modes along magnetic field lines represents standing waves with very different typical scales in different parts of the field line. In most of the field line their structure is determined by the large-scale Alfvén wave structure. Near the ionosphere and in the current sheet, small-scale SMS wave field starts to dominate. In these regions coupled modes becomes small-scale. Such modes are neutrally stable on the field lines that do not cross the current sheet, but switch to the ballooning instability regime on field lines crossing the current sheet. An external source is required to generate these modes and this paper considers external currents in the ionosphere as a possible driver. In the direction across magnetic shells the coupled modes are waves running away from the magnetic shell on which they were generated.     

Multiple field line resonances: Optical,magnetic and absorption signatures

We present multi-instrument observations of ultra low frequency (ULF) wave activity from the dawn flank magnetosphere during the period 12:00–13:30 UT on the 16 December 2003. Optical, magnetic and riometer measurements from the Churchill line meridian in the Canadian sector are presented which demonstrate the presence of multiple discrete auroral arc structures accompanied by periodic magnetic and riometer absorption perturbations in the Pc5 (150–600 s) ULF band. Clear polewards propagation is demonstrated in all the instrument data sets, the magnetic signals showing most clearly the amplitude and phase characteristics consistent with discrete frequency field line resonances (FLRs) on closed field lines. Two discrete frequency field line resonant signals are apparent, at 1.8 and 3.0 mHz which resonate at approximately the same latitude. We explain this via the calculation of the Alfvén continuum, and show that both frequencies may be resonant in the same latitudinal region within instrumental resolution. The meridian scanning photometer (MSP) observations from polewards of the magnetometer determined resonant latitudes show evidence of low intensity (∼200 R) poleward moving discrete arcs related to the ULF waves. Interestingly the MSP observations demonstrate poleward phase propagation with variable rates across the field of view; faster apparent polewards phase propagation being seen at higher latitudes. We demonstrate that the complicated “braided” phase of the arcs can be explained via the precipitation resulting from the superposition of two discrete FLRs. Furthermore, we characterise the ≳25 keV energetic electron precipitation in the region of the FLRs and the arc structures via periodic D-region absorption. In this way, we link the magnetic and both soft and energetic particle precipitation signatures of FLRs together for the first time. Our results demonstrate that riometer absorption can be used to characterise FLRs, however, this is only generally possible at lower L-shells where energetic electrons in the ring current overlap with the FLR fields in the equatorial plane.     

An investigation of the field-aligned currents associated with a large-scale ULF wave in the morning sector

Previous work by Scoffield, H.C., Yeoman, T.K., Wright, D.M., Milan, S.E., Wright, A.N., Strangeway, R.J. [2005. An investigation of the field aligned currents associated with a large scale ULF wave using data from CUTLASS and FAST. Ann. Geophys. 23, 487–498) investigated a large-scale ULF wave, occurring in the dusk sector (∼1900 MLT). The wave had a period of ∼800 s (corresponding to 1.2 mHz frequency), an azimuthal wave number of ∼7 and a full-width at half-maximum (FWHM) across the resonance of 350 km. IMAGE ground magnetometer and SuperDARN radar observations of the wave's spatial and temporal characteristics were used to parameterise a simple, two-dimensional field line resonance (FLR) model. The model-calculated field-aligned current (FAC) was compared with FACs derived from the FAST energetic particle spectra and magnetic field measurement. Here the authors use the same method to investigate the FAC structure of a second large-scale ULF wave, with a period of ∼450 s, occurring the dawn sector (∼0500 MLT) with an opposite sense background region 1–region 2 current system. This wave has a much larger longitudinal scale (m∼4.5) and a smaller latitude scale (FWHM=150 km). Unlike the dusk sector wave, which was dominated by upward FAC, FAST observations of the dawn sector wave show an interval of large-scale downward FAC of ∼1.5 μA m⁻². Downgoing magnetospheric electrons with energies of a few keV were observed, which are associated with upward FACs of ∼1 μA m⁻². For both wave studies, downward currents appear to be carried partially by upgoing electrons below the FAST energy detection threshold (5 eV), but also consist of a mixture of hotter downgoing magnetospheric electrons and upgoing ionospheric electrons of energies 30 eV–1 keV. Strong intervals of upward current show that small-scale structuring of scale ∼50 km has been imposed on the current carriers. In general, this study confirms the findings of Scoffield, H.C., Yeoman, T.K., Wright, D.M., Milan, S.E., Wright, A.N., Strangeway, R.J. [2005. An investigation of the FACs associated with a large-scale ULF wave using data from CUTLASS and FAST. Ann. Geophys. 23, 487–498).     

Quiet auroral arcs: Ionosphere effect of magnetospheric convection stratification

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

The Alfvén wave parallel electric field in non-uniform space plasmas

We suggest a two-step mechanism for the generation of the parallel electric field at the Alfvén wave. At the first step, the coupling with the compressional mode due to the magnetic field non-uniformity and finite plasma pressure provides the parallel magnetic field of Alfvén wave. At the second step, the compressional mode acquires the parallel electric field due to coupling with the electrostatic mode as required by the quasi-neutrality condition in kinetics. The parallel electric field acquired by the Alfvén mode is considerably larger than that due to the single-step coupling between the Alfvén and electrostatic modes in kinetics.     

Pi-2 pulsations as a result of evolution of an Alfvén impulse originating in the ionosphere during a brightening of aurora

It is assumed that the original impulse producing Pi-2 pulsations is generated in the ionosphere at the moment of a brightening of aurora. The electric field is known to decrease in the auroral arc almost by an order of magnitude. The electric impulse that appears will be transferred along magnetic field lines and reflected from the ionosphere of the opposite hemisphere, forming the standing Alfvén wave. The electric field impulse of 100 $\text{mV}\text{m}$ is capable of causing magnetic field oscillations of order of 100 γ. Reflection of the Alfvén impulse from the ionosphere with horizontal inhomogeneities corresponding to different forms of auroras is studied. The following is found: (a) the resonance is possible only for harmonics with the rotating vector of polarization; (b) the resonance periods appear to depend essentially on the ionospheric conductivity; this may bring a significant error into determination of the magnetospheric plasma density from the pulsation periods; (c) the auroral zone exerts a screening influence on the pulsations excited at latitudes higher than the zone itself.     

3D MHD Coronal Oscillations about a Magnetic Null Point: Application of WKB Theory

This paper is a demonstration of how the WKB approximation can be used to help solve the linearised 3D MHD equations. Using Charpit’s method and a Runge?–?Kutta numerical scheme, we have demonstrated this technique for a potential 3D magnetic null point, B=[x,ε y,?(ε+1)z]. Under our cold-plasma assumption, we have considered two types of wave propagation: fast magnetoacoustic and Alfvén waves. We find that the fast magnetoacoustic wave experiences refraction towards the magnetic null point and that the effect of this refraction depends upon the Alfvén speed profile. The wave and thus the wave energy accumulate at the null point. We have found that current buildup is exponential and the exponent is dependent upon ε. Thus, for the fast wave there is preferential heating at the null point. For the Alfvén wave, we find that the wave propagates along the field lines. For an Alfvén wave generated along the fan plane, the wave accumulates along the spine. For an Alfvén wave generated across the spine, the value of ε determines where the wave accumulation will occur: fan plane (ε=1), along the x-axis (0<ε<1) or along the y-axis (ε>1). We have shown analytically that currents build up exponentially, leading to preferential heating in these areas. The work described here highlights the importance of understanding the magnetic topology of the coronal magnetic field for the location of wave heating.     

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.     

Roles of Fast-Cyclotron and Alfvén-Cyclotron Waves for the Multi-Ion Solar Wind

Using linear Vlasov theory of plasma waves and quasi-linear theory of resonant wave–particle interaction, the dispersion relations and the electromagnetic field fluctuations of fast and Alfvén waves are studied for a low-beta multi-ion plasma in the inner corona. Their probable roles in heating and accelerating the solar wind via Landau and cyclotron resonances are quantified. In this paper, we assume that i) low-frequency Alfvén and fast waves, emanating from the solar surface, have the same spectral shape and the same amplitude of power spectral density (PSD); ii) these waves eventually reach ion cyclotron frequencies due to a turbulence cascade; iii) kinetic wave–particle interaction powers the solar wind. The existence of alpha particles in a dominant proton/electron plasma can trigger linear mode conversion between oblique fast-whistler and hybrid alpha–proton cyclotron waves. The fast-cyclotron waves undergo both alpha and proton cyclotron resonances. The alpha cyclotron resonance in fast-cyclotron waves is much stronger than that in Alfvén-cyclotron waves. For alpha cyclotron resonance, an oblique fast-cyclotron wave has a larger left-handed electric field fluctuation, a smaller wave number, a larger local wave amplitude, and a greater energization capability than a corresponding Alfvén-cyclotron wave at the same wave propagation angle θ, particularly at 80^°<θ<90^°. When Alfvén-cyclotron or fast-cyclotron waves are present, alpha particles are the chief energy recipient. The transition of preferential energization from alpha particles to protons may be self-modulated by a differential speed and a temperature anisotropy of alpha particles via the self-consistently evolving wave–particle interaction. Therefore, fast-cyclotron waves, as a result of linear mode coupling, constitute a potentially important mechanism for preferential energization of minor ions in the main acceleration region of the solar wind.     

Joule heating of Io's ionosphere by unipolar induction currents

The unexpectedly large scale height of Io's ionosphere (Kliore, A., et al., 1975, Icarus24, 407–410) together with the relatively large molecular weight of the likely principal constituent, SO₂ (Pearl, J., et al., 1979, Nature280, 755–758), suggest a high ionospheric temperature. Electrical induction in Io's ionosphere due to the corotating plasma bound to the Jovian magnetosphere is one possible source for attainment of such high temperatures. Accordingly, unipolar induction models were constructed to calculate ionospheric joule heating numerically. Heating rates produced by highly simplified models lie in the range 10^?9 to 10^?8 W/m³. These heating rates are lower than those determined from uv photodissociative heating models (Kumar, S., 1980, Geophys. Res. Lett.7, 9–12) at low levels in the ionosphere but are comparable in the upper ionosphere. The low electrical heating rate throughout most of the ionosphere is due to the power limitation imposed by the Alfvén wings which complete the electrical circuit (Neubauer, F.M., 1980, J. Geophys. Res.85, 1171–1178). Contrary to the pre-Voyager calculations of Cloutier, P. A., et al. (1978, Astrophys. Space Sci.55, 93–112), our numerical results show that the J × B force density due to unipolar induction currents in the ionosphere is much less than the gravitational force density when the combined mass of the neutral species is included. The binding and coupling of the ionosphere is principally due to the relatively dense (possibly localized) neutral SO₂ atmosphere. In regions where the ions and neutrals are collisionally coupled the ionosphere will not be stripped off by the J × B forces. However at a level above that (to which the ions move by diffusion only) the charged species would be removed. Thus there appears to be no need to postulate the existence of an intrinsic Ionian magnetic field as suggested by Kivelson, M. G., et al. (79, Science 205, 491–493) and Southwood, S. J., et al. (1980, J. Geophys. Res., in press) in order to retain the observed ionosphere.