Numerical investigation of non-resonant and resonant scattering of charged particles with a spatially varying magnetic field

By integrating many charged particle trajectories in a magnetic field model consisting of a series of equally spaced field discontinuities with equal angular displacements, constant ¦B¦ and successive displacements oppositely directed, a parallel diffusion coefficient K _∥ is obtained. The particle gyroradius was kept sufficiently small for the interaction to be non-resonant. The diffusion coefficient is found to be in good agreement with that predicted by the known reflection properties for charged particles of individual discontinuities. However an attempt to reproduce the diffusion coefficient using the results of a recent study by Klimas and Sandri of a non-local diffusion equation applying to the non-resonant case lead to too low a value of K _∥. The computational approach was also applied to the case where the particle motion was in resonance with the wavelength of the train of discontinuities and a lower limit to K _∥ obtained. This lower limit exceeded the quasi-linear approximation value for K _∥ under resonant scattering conditions.     

On high-latitude convection field inhomogeneities,parallel electric fields and inverted-V precipitation events

Assuming a certain horizontal distribution of the convection field at a certain altitude above the ionosphere, the associated electric field and current distributions in a vertical plane are calculated using a model with finite current-dependent conductivity along the magnetic field lines. It is seen that given the kind of horizontal distribution of E₆ commonly observed by polar-orbiting satellites at inverted-V electron precipitation events, the calculated distribution of E_∥ is able to reproduce the basic spatial structure of the precipitation. It is also seen that the combined effect of a locally increased ionization within auroral forms and a large potential difference (ΔV)_∥ along the magnetic field lines at higher altitudes is a strong reduction of E₆ within the auroral forms. From the basic features of the electric field, it is concluded that an interpretation of auroral precipitation in terms of a static E_∥ may require a mechanism that can support a large (ΔV)_∥ even at relatively weak current densities and at the same time allow local enhancements of the parallel conductivity within the region of non-zero E_∥. It is suggested that the magnetic mirroring combined with gyro-resonant wave-particle interactions may be a suitable mechanism.     

The influence of a turbulent region on the flux of auroral electrons

The influence of low-frequency electrostatic turbulence on the flux of precipitating magnetospheric electrons is analyzed in the framework of the quasilinear kinetic equation. It is shown that an electron population in a turbulent region, with an electric field parallel to the ambient magnetic field, can be separated into two parts by introducing a pitch angle dependent runaway velocity v_r(θ). Lower energy electrons with parallel velocity v_∥ < v_r are effectively scattered by plasma waves, so that they remain in the main population and are subjected to an anomalous transport equation. A distribution function f ∞ v^?4 (or the particle flux vs energy J ∞ E^?1) is established in this velocity range. Faster electrons with v_∥ ? v_r are freely accelerated by a parallel electric field, so that they contribute directly to hot electron fluxes which are observed at ionospheric altitudes. New expressions are derived for the magnetic-field aligned current and the electron energy flux implied by this model. These expressions agree well with empirical relations observed in auroral inverted-V structures.     

Flapping motions of the tail plasma sheet induced by the interplanetary magnetic field variations

Flapping motions of the magnetotail with an amplitude of several earth radii are studied by analysing the observations made in the near (x = ?25 ~ ?30 R_E and the distant (x? ?60 R_E) tail regions. It is found that the flapping motions result from fluctuations in the interplanetary magnetic field, especially Alfvénic fluctuations, when the magnitude of the interplanetary magnetic field is larger than ~10 γ and they propagate behind the Earth with the solar wind flow. Flappings tend to be observed in early phases of the magnetospheric substorm, and they have two fundamental modes with periods of ~200 and ~500 sec. In some limited cases a good correspondence with the long period micropulsations (Pc5) in the polar cap region is observed. These observational results are explained by the model in which the Alfvénic fluctuations in the solar wind penetrate into the magnetosphere along the connected interplanetary-magnetospheric field lines. The characteristics of the flapping reveal that the geomagnetic tail is a good resonator for the hydromagnetic disturbances in the solar wind.     

Heavy ion reflection and heating by collisionless shocks in polar solar corona

We propose a new model for explaining the observations of preferential heating of heavy ions in the polar solar corona. We consider that a large number of small scale shock waves can be present in the solar corona, as suggested by recent observations of polar coronal jets by the Hinode and STEREO spacecraft. The heavy ion energization mechanism is, essentially, the ion reflection off supercritical quasi-perpendicular collisionless shocks in the corona and the subsequent acceleration by the motional electric field E=−(1/c)V ×B. The acceleration due to E is perpendicular to the magnetic field, giving rise to large temperature anisotropy with T_⊥?T_∥, which can excite ion cyclotron waves. Also, heating is more than mass proportional with respect to protons, because the heavy ion orbit is mostly upstream of the quasi-perpendicular shock foot. The observed temperature ratios between O⁵⁺ ions and protons in the polar corona, and between α particles and protons in the solar wind are easily recovered. We also discuss the mechanism of heavy ion reflection, which is based on ion gyration in the magnetic overshoot of the shock.     

On the distribution of By in the geomagnetic tail

The distribution of B_y in the geomagnetic tail associated with a net cross-tail magnetic flux, recently experimentally discovered, is here investigated within the framework of two-dimensional but non-planar field adiabatic time-independent equilbria. It is found that the flux distribution is controlled by the pressure anisotropy of the plasma, B_y being enhanced at the current sheet centre relative to that in the lobes for P_∥>P_⊥ and vice-versa for P_⊥>P_∥. For P_⊥>P_∥ a broad region of depressed field strength is found across the centre plane of the current sheet, terminated at its outer boundaries by spikes in the perpendicular current, across which B_y and B_x are “switched on” and rapidly increase towards their values in the low-β lobes. For P_∥>P_⊥ a thin high-current density layer forms at the sheet centre if the marginal firehose condition is approached, across which the B_x field reverses by rotation at nearly constant magnitude about the z-axis. The field magnitude in this thin layer depends upon the pressure anisotropy, such that the plasma remains just firehose stable within it, and may approach an appreciable fraction of the lobe field strength even for moderate anisotropies. Such structures have been observed in the geomagnetic tail, but do not appear to be a common feature of the quiet-time plasmasheet, where the field strength at the centre plane can reach small values with little obvious enhancement of B_y. In terms of the present model these observations require that either P_⊥>P_∥ in the quiet-time tail or that the plasma is within one or two per cent of isotropy if P_∥>P_⊥. These results then indicate that the production of plasma pressure anisotropy during adiabatic inward transport towards the Earth, which is generally expected to lead to P_∥>P_⊥ and its destruction by either macroscopic or microscopic processes, requires further study.     

Possible variability of the magnetic field of T Tau

Using the Main Stellar Spectrograph of the 6-m Special Astrophysical Observatory telescope equipped with a polametric analyzer, we measured the longitudinal magnetic field component B_∥ for the T Tauri stars T Tau and AS 507 on January 16 and 18 and February 15, 2003. For both stars, we determined only the upper limits on B_∥ from photospheric lines: +15±30 G for T Tau and ?70±90 G for AS 507. The magnetic field of AS 507 was not measured previously, while B_∥ for T Tau is lower than its values that we obtained in 1996 and 2002 (B_∥?150±50G), suggesting that the longitudinal magnetic field component in the photosphere of T Tau is variable. We also measured the longitudinal magnetic field component for T Tau in the formation region of the He I 5876 Å emission line. We found B_∥ in this region to be ?+650, ?+350, and ?+1100 G on January 16, 18, and February 15, 2003, respectively. Our observations on January 18 and February 15 correspond to virtually the same phase of the star's rotation period, but the profiles of the He I 5876 Å line differ markedly on these two nights. Therefore, we believe that the threefold difference between the B_∥ values on these nights does not result from observational errors. We discuss the possible causes of the B_∥ variability in the photosphere and the magnetosphere of T Tau.     

Latitudinal structures of discrete arcs resulting from viscous interaction between sheared plasma flows

Latitudinal structures of discrete arcs are modelled as a consequence of the quasi-steady magnetosphere-ionosphere coupling involving viscous interaction between sunward and anti-sunward plasma flows in the magnetosphere. The quasi-steady state in the magnetosphere and ionosphere coupling is described by the magnetospheric and ionospheric current conservation and the field-aligned currentpotential relation assuming adiabatic electron motion along field lines. The upward and downward fieldaligned currents are assumed to be stably maintained by vorticity-induced space charges in the region of plasma flow reversal, where divergence of the magnetospheric electric field E_⊥ is negative and positive, respectively. By introducing the effective conductance Σ_dc arising from the anomalous viscosity, a specific relation between the dc field-aligned current density J_∥ and the magnetospheric electric field E_⊥ is derived as $\text{J}{}_{\mathrm{\parallel }}\text{=−Σ}{}_{\mathrm{dc}}\text{div}\text{E}{}_{\mathrm{\perp }}$. Sufficiently large potential drops to accelerate auroral electrons are shown to exist along the auroral field lines originating from the flow reversal region with div $\text{E}{}_{\mathrm{\perp }}\text{< 0}$. It is shown that the latitudinal structure of a discrete arc is primarily determined by the magnetospheric potential structure and the characteristic width is on the order of 10 km at the ionospheric altitude.     

Diffusion tensor for Galactic cosmic rays in the interplanetary medium with a magnetic field

The Boltzmann kinetic equation is analyzed in the MHD approximation. This analysis requires an explicit expression for the collision integral F _c. In the classical theory, F _c=?vf _μ ⁽¹⁾ Ω_μ, where f _μ ⁽¹⁾ is the first spherical harmonic in the Galactic-cosmic-ray (GCR) distribution, Ω_μ are the components of a unit particle velocity vector, and the frequency ν of collisions between GCRs and interplanetary magnetic-field nonuniformities is assumed to be a scalar. The assumption that ν_ij is a tensor (which is the result of anisotropy in the interplanetary medium) distinguishes this study from others. Since the anisotropic GCR effects in the heliomagnetosphere are marginal, the nondiagonal elements of tensor ν_ij were set equal to zero. Our analysis has yielded the diffusion-tensor components D _∥, and D _A, which are expressed in terms of interplanetary parameters. The energy dependencies of D _∥, and D _A are in good agreement with the experimental data and calculations by other authors.     

Electron runaway in turbulent astrophysical plasmas

An astrophysical electron acceleration process is described which involves turbulent plasma effects: the acceleration mechanism will operate in ‘collision free’ magnetoactive astrophysical plasmas when ion-acoustic turbulence is generated by an electric field which acts parallel to the ambient magnetic lines of force. The role of ‘anomalous’ (ion-sound) resistivity is crucial in maintaining the parallel electric field. It is shown that, in spite of the turbulence, a small fraction of the electron population can accelerate freely, i.e. runaway, in the high parallel electric potential. The number density n^(B) of the runaway electron component is of order $\text{n}{}^{\mathrm{(B)}}\text{?}\text{n}\text{2}\text{(}\text{c}{}_{\mathrm{s}}\text{U}{}_{\mathrm{\parallel }}{}^{\mathrm{?}}\text{)}{}^2$, where n = background electron number density, c_s = ion-sound speed and U_∥^? = relative drift velocity between the electron and ion populations. The runaway mechanism and the number density n^(B) do not depend critically on the details of the non-linear saturation of the ion-sound instability.     

Energy partition into translational and rotational motion of fragments in catastrophic disruption by impact: An experiment and asteroid cases

Translational kinetic energy E_t and rotational kinetic energy E_r of the fragments produced in the laboratory catastrophic disruption of a basalt sphere by the impact of a high-speed projectile were determined. It was found that the maximum value of E_t/E_t is of the orders of 10⁻², which is not so different in the order of magnitude from the value estimated for family asteroids in spite of the great difference of the scale. However, the laboratory value is significantly higher than the value for the family.     

Evidence of energy dependent mechanisms for the precipitation of auroral electrons

This paper discusses the experimental results on electron precipitation in a diffuse aurora obtained by a sounding rocket launched from ANDENES (L ～ 6·2) on 3 November 1968. A considerable increase in the intensity of low energy electrons, E_e ? 5 keV, followed a large precipitation of more energetic electrons E_e ? 5 keV. From the observation of angular distributions and an estimate of the diffusion coefficient (D_α ? 10^?3 (sec)^?2), it is suggested that this higher energy precipitation is induced by gyroresonant interactions of magnetospheric electrons with radiation in the whistler mode. The lower energy precipitation separated in time and/or space, shows quasi-periodic modulations in the 5–15 sec range with periods close to the bounce period. It is suggested that this precipitation is the result of bounce-resonance interactions with electrostatic waves in the equatorial plane. Finally, from a comparison between the experimental energy spectra and plasma sheet spectra it can be concluded that these electrons are injected from the plasma sheet during a substorm and are then diffused and precipitated by energy dependent mechanisms.     

Theoretical ion densities in the lower ionosphere

We have solved the coupled momentum and continuity equations for NO⁺, O₂⁺, and O⁺ions in the E- and F-regions of the ionosphere. This theoretical model has enabled us to examine the relative importance of various processes that affect molecular ion densities. We find that transport processes are not important during the day; the molecular ions are in chemical equilibrium at all altitudes. At night, however, both diffusion and vertical drifts induced by winds or electric fields are important in determining molecular ion densities below about 200 km. Molecular ion densities are insensitive to the O⁺ density distribution and so are little affected by decay of the nocturnal F-region or by processes, such as a protonospheric flux, that retard this decay. The O⁺ density profile, on the other hand, is insensitive to molecular ion densities, although the O⁺ diffusion equation is formally coupled to molecular ion densities by the polarization electrostatic field. Nitric oxide plays an important role in determining the NO⁺ to O₂⁺ ratio in the E-region, particularly at night. Nocturnal sources of ionization are required to maintain the E-region through the night. Vertical velocities induced by expansion and contraction of the neutral atmosphere are too small to affect ion densities at any altitude.     

Electrodynamic heating and movement of the thermosphere

The theory of dissipation of ionospheric electric currents is extended to include viscosity. In a steady state (i.e. usually above about 140 km altitude) the joule plus viscous heating may be calculated by μ∇²v. E × B/B². At lower altitudes where viscosity may, in some circumstances, be relatively unimportant the joule dissipation is calculated by the usual formula j. (E + v × B). In a prevalent model of the auroral electrojets it is found that the joule heating can be much more intense outside auroral forms than within them. Heating due to auroral electrojets cause a semi-annual variation in the thermosphere. Movement caused by auroral electric fields make a contribution to the super-rotation of the midlatitude upper atmosphere. Random electric fields lead to an eddy ‘viscosity’ or ‘exchange coefficientrs in the upper thermosphere of magnitude ρE_R²/B³t_R²|∇E|. where t_R is the correlation time of the random component of electric fields E_R and ρ is air density. Theoretical conditions for significant heating by field-aligned currents are derived.     

Enhanced X-ray emission above 3.5 keV in active regions in the absence of flares

We demonstrate that even in the absence of flares there are very often volumes of hot plasma in the corona above active regions with temperatures in excess of 10 million degrees. Characteristics of this hot plasma and its time variations seem to be different in active regions of different phase of development. These hot plasma regions are sources of very weak, but clearly recognizable, X-ray emission above 3.5 keV. Long-lived X-ray brightenings, 10⁴ times weaker than a flare, but lasting up to 10 hr occur predominantly along the H _∥ = 0 line, apparently low in the corona. After major flares, long-lived X-ray emission is also radiated from tops of arches extending high into the corona. Some other long-lived sources, far from the H_∥ = 0 line, may be associated with newly emerging flux. Short-lived X-ray sources, with fluxes ranging from subflare levels to 10^?3 times the flare flux, last for 2 to more than 30 min and are probably microflares. They seem to be most frequent in growing young active regions and appear often in areas with newly emerging flux.     

Effect of noise on sunspot magnetic field parameters

Using a perturbated (noised) dipole model of a sunspot magnetic field structure we simulated the influence of background noise or apparent noise (unresolved small-scale magnetic field structure) on sunspot magnetic field parameters. We evaluated mean values of the vertical and horizontal electric current densities |j|_∥ and |j|_⊥, respectively, of the force-free parameter α and of the Lorentz force |F|. For comparison we estimated |j_⊥| and |F| of a standard sunspot magnetic field model (return-flux model, OSHEROVICH 1982). Furthermore, we compared our results with those from observations resulting in estimated values of |j|_∥ for quiet sunspots. Our investigation led to the following results: the estimated values of 〈|F|〉 show clearly that due to the noise the axisymmetric magnetic dipole model is clustered into several subsystems of fluxbundles. The latter are connected with a system of electric current densities of the order of |j|_∥ ∼ 10⁻³ Am⁻² and |j|_⊥ = 10⁻¹ Am⁻², i.e., this system is a noise-generated nonaxisymmetric magnetohydrostatic model.     

Investigations of Pi2 micropulsations—I. Frequency spectra and polarisation

Pi2 micropulsations are recorded at four sites with approximately the same geo-magnetic longitude but spanning 36° in latitude. Frequency analyses on these signals show that they normally contain more than one spectral component and that these components, all of which commence simultaneously, are not normally harmonically related. In addition, the spectral content is found not to vary significantly with latitude.No significant correlations are found between K_p and the maximum period, the minimum period, or the number of frequency components, in a Pi2. However the ‘average’ Pi2 frequency is found to vary linearly with both K_p and the magnitude of the accompanying auroral bay. In addition, the signals measured at the ‘low’ and at the ‘high’ latitude sites are found to exhibit an overwhelming preference for the left-hand sense of polarisation, while those at the ‘middle’ latitude sites show no preference for either sense.     

On the MOND external field effect in the solar system

In the framework of the MOdified Newtonian Dynamics (MOND), the internal dynamics of a gravitating system s embedded in a larger one S is affected by the external background field E of S even if it is constant and uniform, thus implying a violation of the Strong Equivalence Principle: it is the so-called External Field Effect (EFE). In the case of the solar system, E would be A _cen≈10^?10 m?s^?2 because of its motion through the Milky Way: it is orders of magnitude smaller than the main Newtonian monopole terms for the planets. We address here the following questions in a purely phenomenological manner: are the Sun’s planets affected by an EFE as large as 10^?10 m?s^?2? Can it be assumed that its effect is negligible for them because of its relatively small size? Does E induce vanishing net orbital effects because of its constancy over typical solar system’s planetary orbital periods? It turns out that a constant and uniform acceleration, treated perturbatively, does induce non-vanishing long-period orbital effects on the longitude of the pericenter ? of a test particle. In the case of the inner planets of the solar system and with E≈10^?10 m?s^?2, they are 4–6 orders of magnitude larger than the present-day upper bounds on the non-standard perihelion precessions \(\Delta\dot{\varpi}\) recently obtained with by E.V. Pitjeva with the EPM ephemerides in the Solar System Barycentric frame. The upper limits on the components of E are E _x ≤1×10^?15 m?s^?2, E _y ≤2×10^?16 m?s^?2, E _z ≤3×10^?14 m?s^?2. This result is in agreement with the violation of the Strong Equivalence Principle by MOND. Our analysis also holds for any other exotic modification of the current laws of gravity yielding a constant and uniform extra-acceleration. If and when other corrections \(\Delta\dot{\varpi}\) to the usual perihelion precessions will be independently estimated with different ephemerides it will be possible to repeat such a test.     

Oscillations of coronal loops and second pulsations of solar radio emission

The dispersion properties of the sausage eigenmodes of oscillations in a thin magnetic flux tube are numerically analyzed in terms of ideal magnetohydrodynamics (MHD). The period of the modes accompanied by the emission of MHD waves into the surrounding medium, which leads to acoustic damping of oscillations, is determined by the radius of the tube, not by its length. The dissipation of the sausage oscillations in comparatively high (?0.7R _⊙) and tenuous (?6 × 10⁸ cm^?3) coronal loops is considered. Their Q factor has bound found to be determined by the acoustic damping mechanism. The ratio of the plasma densities outside and inside the loop and the characteristic height of the emission source have been estimated by assuming the quasi-periodic pulsations of meter-wavelength radio emission to be related to the sausage oscillations.     

Spectra of radiation from a strongly magnetized plasma

Radiation from an optically thick, tenuous, isothermal and magnetized plasma is considered under conditions typical for X-ray pulsars, in the approximation of coupled diffusion of normal modes. The spectra are calculated of the fluxes and specific intensities of outgoing radiation, their dependences on the plasma densityN, temperatureT and magnetic fieldB are analysed with due regard to the vacuum polarization by a strong magnetic field. Simple analytical expressions are obtained in the limiting cases for the fluxes and intensities. It is shown that atE _B »E _a (E _B =11.6B ₁₂ keV,E _a ?0.1N ₂₂ ^1/2 T ₁ ^?3/4 keV,B ₁₂=B/10¹² G,N ₂₂=N/10²² cm^?3,T ₁=T/10 keV) the magnetic field strongly intensifies the flux and changes its spectrum in the regionE _a ?E ?E _B . AtE ?T the spectrum of the energy flux is almost flat in the region \(\sqrt {E_a E_B } \lesssim E \lesssim E_B \) . For homogeneous plasma without Comptonization the cyclotron line atE?=E _B appears in emission, though in many other cases it may appear in absorption. The vacuum polarization may produce the ‘vacuum feature’ atE?E _W ?13N ₂₂ ^1/2 B ₁₂ ^?1 keV, which, as a rule, appears in absorption. The intensity spectra vary noticeably with the direction of radiation, in particular, at some directions nearB, the spectra become harder than in other directions. Quantization of the magnetic field (E _B >T) strongly increases the plasma luminosity (∝E _B /T for homogeneous plasma). The results obtained explain a number of basic features in the observed X-ray pulsar spectra.