Quasi-periodical small-scale magnetic disturbances in the low-altitude cusp

Satellite data from measurements of thermal plasma and electric and magnetic fields are considered for the low-altitude cusp. Small-scale magnetic disturbances (SSMDs) are studied in relation to other plasma parameters. The SSMDs sometimes have a quasi-periodical structure and probably a compressional component. The analysis of their polarization structure provides grounds to conclude in some cases at least that the SSMDs represent compressional surface MHD waves.     

Torsional Alfvén modes in dipole and toroidal magnetospheres

Propagation of torsional Alfvén waves in the magnetosphere is examined for two models of the Earth's magnetic field, one where the field is toroidal, the other being a dipole field. Both models yield magnetically guided torsional wave modes which are strongly localized in all directions transverse to the steady magnetic field. The transverse structure is determined by a self-consistent solution of the ideal MHD equations. It is shown that the torsional wave is guided even when b is finite, where b is the component of the wave magnetic field in a direction parallel to the steady magnetic field.     

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.     

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.     

Auroral N2(c′4Σu → aΠg emission

Inspection of recent spectra presented by Sivjee (1983) show evidence of the 0–4 and 0–5 bands of the N₂(c′₄¹Σ_u⁺ → a¹Π_g) Gaydon-Herman system. In conjunction with earlier spectra, it is now possible that this band system is a significant auroral component, with an intensity approx. 7% that of the N2 2P system. The absence in aurorae of the potentially far stronger N₂(c′₄¹Σ_u⁺ → X¹Π_g) system is discussed. It is that the O₂(A³Σ_u⁺ → X³Σ_g⁻) band system is indiscernible in Sivjee's auroral spectra, under conditio the foreground nightglow is expected to be clearly visible. On the other hand, at least one relatively strong O₂(A′³Δ_u → a¹Δ_g) band appears to be present in these spectra.     

Wave-particle interactions in the ulf range: GEOS-1 and -2 results

Electromagnetic waves in the frequency range 0.2–11 Hz have been detected onboard the GEOS-1 and -2 satellites. The purpose of this paper is to report on these observations. The three orthogonal magnetic sensors allow us to determine the polarization of the waves. Two kinds of waves are commonly observed, which can easily be distinguished by their polarization.

(1) Waves with a magnetic field aligned with the DC magnetic field. These events often present a typical harmonic structure. The fundamental—which is not always observed—is often in the neighbourhood of the proton gyrofrequency F_H+. These waves are generally observed above F_H+. We will show that these emissions can be interpreted as magnetosonic waves destabilized by energetic protons (E 15 keV) with a ringlike distribution function.

(2) Waves with a magnetic field in a plane perpendicular to the DC magnetic field. These emissions are identified as Ion Cyclotron Waves (ICW's). These waves can, under certain conditions, propagate along the line of force of the magnetic field and reach the ground. They can be identified with the well-known Pcl oscillations, which generally have a clear periodic structure. In contrast these periodic structures are seldom observed onboard the satellites. At the geostationary orbit, these emissions exist in limited frequency domains, which are well organized by the helium gyrofrequency F_He+.     

Spatial structure and stability of coupled Alfvén and drift compressional modes in non-uniform magnetosphere: Gyrokinetic treatment

The spatial structure and stability properties of the coupled Alfvén and drift compressional modes in a space plasma are studied in a gyrokinetic framework in a model taking into account field-line curvature and plasma and magnetic field inhomogeneity across the magnetic shells. The perturbation is found to be localized in two transparent regions, the Alfvén and drift compressional transparent regions, where the wave vector radial component squared is positive. Both regions are bounded by the resonance and cut-off surfaces, where the wave vector radial component turns into infinity and zero, respectively. An existence of the drift compressional resonance is one of the most important results of this work. It is argued that on the surface of this resonance the longitudinal and azimuthal components of the wave's magnetic field have a pole and logarithmic singularities, respectively. The instability conditions and expressions for the growth rate of the coupled modes have been obtained. In the Alfvénic transparent region, an instability occurs in the presence of the negative plasma temperature gradient. This instability does not lead to a non-stationary wave behavior: all the energy gained from the resonance particles was finally absorbed owing to any dissipation process. In a drift compressional transparent region, a necessary condition for the instability is the growth of the temperature with the radial coordinate. The growth rate is almost independent of the radial coordinate, which means that the wave energy gained from the particles cannot disappear. It will lead to an ever increasing wave amplitude, and no stationary picture for the unstable drift compressional mode is possible.     

Structures in a class of magnetized scale-free discs

We construct analytically stationary global configurations for both aligned and logarithmic spiral coplanar magnetohydrodynamics (MHD) perturbations in an axisymmetric background MHD disc with a power-law surface mass density  Σ₀∝ r ^−α  , a coplanar azimuthal magnetic field   B ₀∝ r ^−γ  , a consistent self-gravity and a power-law rotation curve   v ₀∝ r ^−β  , where v ₀ is the linear azimuthal gas rotation speed. The barotropic equation of state  Π∝Σ ⁿ   is adopted for both MHD background equilibrium and coplanar MHD perturbations where Π is the vertically integrated pressure and n is the barotropic index. For a scale-free background MHD equilibrium, a relation exists among  α, β, γ  and n such that only one parameter (e.g. β) is independent. For a linear axisymmetric stability analysis, we provide global criteria in various parameter regimes. For non-axisymmetric aligned and logarithmic spiral cases, two branches of perturbation modes (i.e. fast and slow MHD density waves) can be derived once β is specified. To complement the magnetized singular isothermal disc analysis of Lou, we extend the analysis to a wider range of  −1/4 < β < 1/2  . As an illustrative example, we discuss specifically the  β= 1/4  case when the background magnetic field is force-free. Angular momentum conservation for coplanar MHD perturbations and other relevant aspects of our approach are discussed.     

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

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

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

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

The relation between low-latitude neutral density variations near 400 km and magnetic activity indices

Neutral density data were obtained near 400km (1600 LT) from a microphone density gauge on OGO-6 from 0°G to 40°N magnetic latitude for 25 September–3 October 1969. Several geomagnetic storms occurred during this period (a_p varied from 0 to 207). Least-squares fits were made to data points on density-a_p and density-D_st scatter diagrams, where the density values selected were delayed in time behind a_p and D_st. An equation representing the least-squares fit was computed for each delay time. The equation of best fit (and the corresponding time delay between the density and the magnetic index which resulted in this best fit) was found by choosing the equation that gave the minimum standard error. For example, the best fit at 10°N geomagnetic latitude occurred for a_p at t — 3 hr, where t is the time of the density values. The implications of the time differences associated with the best fits at various latitudes and longitudes are discussed with regard to the time delays involved in geomagnetic heating of the neutral upper atmosphere.

A low-latitude density bulge has been found between 0°N and 40°N whose magnitude varies with a_p. DeVries (1972b) has independently discovered this daytime phenomenon. If the bulge is a semi-permanent feature near the equinoxes because of the enhanced geomagnetic activity, this may help explain the semi-annual effect in density, which was uncovered first in the drag data from low inclination satellites.     

Magnetospheric Cusps under Extreme Conditions: Cluster Observations and MHD Simulations Compared

MHD simulations are here applied to aid in the interpretation of three apparent cusp encounters by the Cluster 4 spacecraft in unusual places when the magnetosphere was under extreme solar wind and interplanetary magnetic field (IMF) conditions associated with the passage of magnetic clouds imbedded within fast ICMEs. At the time of each cusp encounter the IMF was very strong, generally northward in one case, generally equatorial in a second case, and generally southward in the third case. In the southward IMF case, the MHD models locate the origin of the cusp-like plasma by showing that the position of the spacecraft at the time of encounter was engulfed in a tongue of high-pressure plasma extending from the magnetopause into the magnetosphere. This tongue points to the northern-hemisphere cusp as the source of the feature. In the equatorial IMF case an elevated-pressure feature that apparently marked a cusp encounter in the computations coincided, however, with a passage in the solar wind of a dynamic pressure pulse, thus giving an alternative interpretation of the feature. However, Cluster data unambiguously identified the event as an encounter with magnetosheath-like plasma. Given that the Cluster observations classify the event as a true encounter with a cusp-like plasma feature (and not a compression event), the model simulations can be interpreted as identifying the origin of the feature to have been the northern-hemisphere cusp even though?—?and this is the interesting point?—?the observation point was in the southern hemisphere. In the northward IMF case, neither cusp (defined as a magnetic funnel linking the magnetopause to the Earth) was directly connected to the observation point. Instead, this encounter of magnetosheath-like plasma appears to be an instance of boundary-layer formation by means of the Song?–?Russell mechanism in which two-point magnetic reconnection entrains magnetosheath plasma on closed field lines when the IMF is northward.     

Modification of the mean field theory of super-dense matter

We further discussed the Modified Mean Field Theory proposed in [1,2]. We found that this model has a new solution ml = 2; adding -meson, we calculated the symmetric energy of nuclear matter a₄; with the new parameters we calculated the equations of state with and without the addition of -meson; we compared the two; we also compared with the results for ml = 4.3; we made a preliminary theoretical investigation of the form of the vector meson mean field using the two-body correlation function; lastly, using the structural equation of neutron star we calculated the maximum mass for the various equations of state. The results are:

MMFT-2 (ml = 2): M_max = 2.22M (without -meson) M_max = 2.27M (with -meson)

MMFT-1 (ml = 4.3): M_max = 1.69M (without -meson) M_max = 1.89M (with -meson)

     

The γ-ray burst phenomenon treated as the collapse of a QED magnetized vacuum bubble: analogy with sonoluminescence

We treat the phenomenon of a γ -ray burst as the non-linear collapse of a magnetic cavity surrounding a neutron star with extremely large magnetic field B ∼10¹⁵–10¹⁶ G due to the process of bubble shape instability in the resonant MHD field of an accreting plasma or on a neutron star surface. The QED effect of vacuum polarizability by a strong magnetic field is taken into a consideration. We develop an analogy with the phenomenon of sonoluminescence in which the gas bubble is located in a surrounding liquid with a driven sound intensity.     

On the resonant modes of a cavity and the dynamical properties of micropulsations

Certain classes of micropulsations are customarily explained in terms of guided (toroidal) and isotropic (poloidal) hydromagnetic waves m the magnetosphere. The physical properties of these waves are not well understood and their utility in explaining observed polarization patterns is questionable. In an effort to understand and explain the physics underlying these modes, a study is made of a cylindrical cavity (the hydromagnetic wedge), filled with a plasma having a large but finite conductivity and magnetized by an azimuthal magnetic field. Coupling between the toroidal and poloidal modes is effected by the inclusion of the Hall current in the generalized Ohm's law. Physically meaningful solutions to the wave equation are obtained and the toroidal eigenfunctions are demonstrated to be non-degenerate and well-behaved throughout the configuration, and exhibit for each mode a unique spatial resonance whose location, given by a line of force, is specified by the corresponding eigenvalue. The non-degenerate, discrete and spatially independent eigenvalues for the modes are shown to obey a selection rule that limits the spectrum. For a given mode, the states of polarization of the transverse field are determined and it is shown (as has been observed) that, depending on the line of force singled out, the magnetic polarization may be linear, elliptical or circular, right or left-handed, and whatever the state, it is immutable along the line of force. More complicated polarization patterns are derived and explained by superposing different modes vectorially. Classical concepts such as guided and isotropic modes and vibrating field lines are reinterpreted and evaluated in terms of the model. To examine the dependence of modal amplitude on source, the amplitude is expressed in terms of a sinusoidal driving pressure for a simple steady-state case. Symmetries of the model and the magnetosphere are specified and the detailed numerical results are ‘scaled’ for plasmaspheric application. The resonant spectrum, encompassing pc 2–4, is described and the variation of period spectrum with magnetic latitude and activity is presented. The agreement between the semi-quantitative analysis and the observational results is sufficiently close to indicate that the basic physics of the model encompasses the fundamental dynamics of pc activity.     

Influence of a uniform coronal magnetic field on solar p modes: coupling to slow resonant MHD waves

The influence of a constant coronal magnetic field on solar global oscillations is investigated for a simple planar equilibrium model. The model consists of an atmosphere with a constant horizontal magnetic field and a constant sound speed, on top of an adiabatic interior having a linear temperature profile. The focus is on the possible resonant coupling of global solar oscillation modes to local slow continuum modes of the atmosphere and the consequent damping of the global oscillations. In order to avoid Alfvén resonances, the analysis is restricted to propagation parallel to the coronal magnetic field. Parallel propagating oscillation modes in this equilibrium model have already been studied by Evans and Roberts (1990). However, they avoided the resonant coupling to slow continuum modes by a special choice of the temperature profile. The physical process of resonant absorption of the acoustic modes with frequency in the cusp continuum is mathematically completely described by the ideal MHD differential equations which for this particular equilibrium model reduce to the hypergeometric differential equation. The resonant layer is correctly dealt with in ideal MHD by a proper treatment of the logarithmical branch cut of the hypergeometric function. The result of the resonant coupling with cusp waves is twofold. The eigenfrequencies become complex and the real part of the frequency is shifted. The shift of the real part of the frequency is not negligible and within the limit of observational accuracy. This indicates that resonant interactions should definitely be taken into account when calculating the frequencies of the global solar oscillations.     

The effective acceleration of plasma outflow in the paraboloidal magnetic field

The problem of the efficiency of particle acceleration for a paraboloidal poloidal magnetic field is considered within the approach of steady axisymmetric magnetohydrodynamic (MHD) flow. For the large Michel magnetization parameter σ it is possible to linearize the stream equation near the force-free solution and to solve the problem self-consistently as was done by Beskin, Kuznetsova & Rafikov for a monopole magnetic field. It is shown that, on the fast magnetosonic surface (FMS), the particle Lorentz factor γ does not exceed the standard value  σ^1/3  . On the other hand, in the supersonic region, the Lorentz factor grows with the distance z from the equatorial plane as  γ≈ ( z / R _L)^1/2  up to the distance   z ≈σ² R _L  , where   R _L= c /Ω_F  is the radius of the light cylinder. Thus, the maximal Lorentz factor is  γ_max≈σ  , which corresponds to almost the full conversion of the Poynting energy flux into the particle kinetic one.     

Magnetohydrodynamic Waves in an Asymmetric Magnetic Slab

Analytical models of solar atmospheric magnetic structures have been crucial for our understanding of magnetohydrodynamic (MHD) wave behaviour and in the development of the field of solar magneto-seismology. Here, an analytical approach is used to derive the dispersion relation for MHD waves in a magnetic slab of homogeneous plasma enclosed on its two sides by non-magnetic, semi-infinite plasma with different densities and temperatures. This generalises the classic magnetic slab model, which is symmetric about the slab. The dispersion relation, unlike that governing a symmetric slab, cannot be decoupled into the well-known sausage and kink modes, i.e. the modes have mixed properties. The eigenmodes of an asymmetric magnetic slab are better labelled as quasi-sausage and quasi-kink modes. Given that the solar atmosphere is highly inhomogeneous, this has implications for MHD mode identification in a range of solar structures. A parametric analysis of how the mode properties (in particular the phase speed, eigenfrequencies, and amplitudes) vary in terms of the introduced asymmetry is conducted. In particular, avoided crossings occur between quasi-sausage and quasi-kink surface modes, allowing modes to adopt different properties for different parameters in the external region.     

Resistive relaxation of a magnetically confined mountain on an accreting neutron star

Three-dimensional numerical magnetohydrodynamic (MHD) simulations are performed to investigate how a magnetically confined mountain on an accreting neutron star relaxes resistively. No evidence is found for non-ideal MHD instabilities on a short time-scale, such as the resistive ballooning mode or the tearing mode. Instead, the mountain relaxes gradually as matter is transported across magnetic surfaces on the diffusion time-scale, which evaluates to  τ_I∼ 10⁵–10⁸ yr  (depending on the conductivity of the neutron star crust) for an accreted mass of   M _a= 1.2 × 10⁻⁴ M_⊙  . The magnetic dipole moment simultaneously re-emerges as the screening currents dissipate over  τ_I  . For non-axisymmetric mountains, ohmic dissipation tends to restore axisymmetry by magnetic reconnection at a filamentary neutral sheet in the equatorial plane. Ideal-MHD oscillations on the Alfvén time-scale, which can be excited by external influences, such as variations in the accretion torque, compress the magnetic field and hence decrease  τ_I  by one order of magnitude relative to its standard value (as computed for the static configuration). The implications of long-lived mountains for gravitational wave emission from low-mass X-ray binaries are briefly explored.     

Space–time foam and cosmic-ray interactions

It has been proposed that propagation of cosmic-rays at extreme-energy may be sensitive to Lorentz-violating metric fluctuations (“foam”). We investigate the changes in interaction thresholds for cosmic-rays and gamma-rays interacting on the CMB and IR backgrounds, for a class of stochastic models of space–time foam. The strength of the foam is characterized by the factor (E/M_P)^a, where a is a phenomenological suppression parameter. We find that there exists a critical value of a (dependent on the particular reaction: a_crit3 for cosmic-rays, 1 for gamma-rays), below which the threshold energy can only be lowered, and above which the threshold energy may be raised, but at most by a factor of two. Thus, it does not appear possible in this class of models to extend cosmic-ray spectra significantly beyond their classical absorption energies. However, the lower thresholds resulting from foam may have signatures in the cosmic-ray spectrum. In the context of this foam model, we find that cosmic-ray energies cannot exceed the fundamental Planck scale, and so set a lower bound of 10⁸ TeV for the scale of gravity. We also find that suppression of p→pπ⁰ and γ→e⁻e⁺ “decays” favors values aa_crit. Finally, we comment on the apparent non-conservation of particle energy–momentum, and speculate on its re-emergence as dark energy in the foamy vacuum.