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.     

Temperature anisotropy instabilities in a plasma containing cold and hot species in the magnetosphere

The nature of convective instability has been investigated for an electromagnetic wave, either right circularly polarised or left circularly polarised, propagating along a magnetic line of force in a plasma whose distribution function exhibits a temperature anisotropy in the hot species, a loss cone structure and a beam of cold electrons or ions travelling along the line of force with velocity V₁. Detailed numerical calculations have been made using a computer for the growth and decay of the wave for different values of the anisotropy ratio T_⊥/T_∥ = δ of the perpendicular and parallel temperatures, the McIlwain parameter L, the loss cone index j, velocity V₁ of the streaming particle and the particle density ratio ε. The ranges of values of ε and δ for which the wave becomes unstable have been studied in detail. It is found that wave propagation shows no dependence on the loss cone index but shows very strong dependence on the temperature anisotropy δ.     

Electromagnetic instabilities in an anisotropic loss-cone plasma

A form of general dispersion relation for electromagnetic waves in a fully ionized anisotropic plasma with loss-cone that explicates the contribution of the loss-cone to the dispersion relation is developed. By initially ignoring effects due to anisotropy, it is shown by means of Nyquist diagram technique that an isotropic loss-cone distribution can be unstable to EM waves corresponding to the whistler mode (0<< _e ). The growth rate is then determined analytically for this distribution, assuming cyclotron resonance between the waves in the whistler mode and particles in the high energy tail of the velocity distribution. By including the effects of anisotropy, a general growth rate is obtained which is found to depend on the anisotropy, the size of the loss-cone, the softness of the energy spectrum, and the fraction of the particles which are resonant with the wave. For particular distributions the relative contributions of the anisotropy and of the loss-cone to the growth rate have been determined. It is seen that loss-cone effects, which depend on the size of the loss-cone as well as the softness of the energy spectrum, can be a significant factor in the determination of the growth rate. For the Lorentzian distribution, the half-width of unstable waves is considerably broadened and the growth rates are somewhat more severe as compared to a two-temperature Maxwellian. The threshold frequency is which confirms the presence of unstable EM waves in the magnetospheric plasma leading to turbulence.     

Parallel velocity shear instabilities in an inhomogeneous plasma

The stability of an inhomogeneous anisotropic plasma flowing along a straight magnetic field has been investigated. Both the flow velocity and the plasma density are spatially varying in a direction perpendicular to the magnetic field. The stability of an interface between an inhomogeneous anisotropic plasma flowing along the magnetic field and the non-conducting compressible gas of uniform density flowing parallel to the interface has also been discussed. The effect of gyroviscosity and inhomogeneity on the Kelvin-Helmholtz shear instability has been discussed in certain limiting situations.     

The study of instabilities in the solar wind and magnetosheath and their interaction with the Earth's magnetosphere

The thesis concentrates on an analysis of the experimental data as well as numerical simulation of propagation of fast forward (FF) shocks in the solar wind and their evolution through the magnetosheath to the inner magnetosphere. The thesis was defended at the Charles University, Prague, Faculty of Mathematics and Physics, Department of Plasma and Surface Science (V Holesovickach 2, 180 00 Prague 8, Czech Republic) on September 30, 2008 under supervision of Doc. Lubomír P?ech. The thesis is written in English and a resume can be found at http://physics.mff.cuni.cz/kfpp/phd/andreeova.pdf.     

The role of electrostatic instabilities in the critical ionization velocity mechanism

The role of electrostatic instabilities in the critical ionization velocity mechanism is investigated. The analysis is based on the theory developed by Sherman, which interprets Alfvén's critical velocity in terms of a circular process. This process involves the acceleration of electrons by a two-stream instability modified by the presence of a magnetic field. A general expression for the energy and momentum of ions and electrons associated with an electrostatic mode is derived in terms of the plasma dielectric constant. This is used in the case of the modified two-stream instability to determine the distribution of energy between ions and electrons. An extrapolation from the linear phase then gives an estimate of the energy delivered to the electrons which is compared to that required to ionize the neutral gas.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978.     

Magnetoactive lines in the medium with the velocity gradient

The magnetic splitting peculiarities of the absorption lines in the sunspot spectrum are considered. The most common and typical of them is breaking of all Stokes parameter symmetry in regard to the line center. The possible reason of this effect is the macroscopic gas motion with inhomogeneous velocity. Computed contours are given for the line Fe i λ5250 Å with various combinations of magnetic and velocity fields. Magneto-optical effects within the line which are connected with the magnetic and velocity field inhomogeneity are discussed. The observation results are discussed for longitudinal magnetic field zero lines. These observations were carried out for the sunspot and photosphere in two spectral lines Fe i λλ 5250 and 5233 Å. In the sunspot the regular displacement of one zero line with respect to the other zero line takes place whereas in the photosphere the displacements are random. The possible reason of the regular displacement is the change of the magnetic field direction in the different optical layers wherein corresponding spectral lines are formed effectively. The connection between the zero line displacement of a longitudinal magnetic field and the crossover effect is discussed. The computation results are given which agree with observations and illustrate the above-mentioned relationship. The influence of the Stokes parameter asymmetry on the measured magnetic field signals is considered.     

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.’     

An experiment to observe the vertical gradient in line-of-sight velocity oscillations

Using intermediate degree p-mode frequency datasets for solar cycle 22, we find that the frequency shifts and magnetic indices show a `hysteresis' phenomenon. It is observed that the magnetic indices follow different paths for the ascending and descending phases of the solar cycle, as the descending path always seems to follow a higher track than the ascending one. However, for the radiative indices, the paths cross each other indicating phase reversal.     

Sodium in the Jovian magnetosphere

Observations of sodium D-line emission from Io and the magnetosphere of Jupiter are reported. A disk-shaped cloud of sodium is found to exist in the Jovian magnetosphere with an inner edge at about 4R and an outer edge at about 10R . The gravitational scale height above the equatorial plane is a few Jovian radii. The data are interpreted in terms of a sputtering model, in which the sodium required to maintain the cloud is sputtered off the surface of Io by trapped energetic radiation-belt protons. Conditions on the atmospheric density are obtained. The Keplerian orbits attainable by such escaping sputtered atoms can provide the observed spatial distribution. The required 500-keV proton flux required to provide the 1–10 keV protons which will sputter the sodium at the surface of Io is consistent with the limiting trapped flux determined by ion-cyclotron turbulence.Publication No. 1410, Institute of Geophysics and Planetary Physics, University of California, Los Angeles 90024, Cal., U.S.A.     

VLF waves in the magnetosphere

The study of VLF waves at ground based stations is an important source of information on particles trapped in the magnetosphere. By various techniques it is also possible to measure plasma densities, electric fields and monitor energetic particle injection. By studying the propagation of waves beneath the ionosphere it is possible to study particle precipitation from the magnetosphere. In this paper we summarise some of the techniques and results obtained from the study of VLF waves at the South African research station in Antarctica.     

Inductive electric fields in the magnetosphere

A quantitative estimate of the electric fields induced by the time dependent ring current is made incorporating the drifts and induced electric fields in a self-consistent manner. It has been shown that in the ring current region, the results of the self-consistent calculations deviate substantially from the first order estimates hitherto obtained. Since for a rapidly varying ring current, the induced electric field can be of the same order as the convection electric field in the magnetosphere, these deviations have to be taken into account in substorm studies.     

Birkeland currents in the Earth's magnetosphere

As a result of his polar expeditions at the beginning of this century, Kristian Birkeland determined that intense ionospheric currents were associated with the aurora. Birkeland suggested that these currents originated far from the Earth and that they flowed ointo and away from the polar atmosphere along the geomagnetic field lines. The existence of such field-aligned or Birkeland currents was disputed because it was not possible to unambiguously identify current systems that are field-aligned (as suggested by Alfvén, 1939, 1940) and those which are completely contained in the ionosphere (as developed by Vestine and Chapman, 1938) with surface magnetic field observations. The presence of Birkeland currents has been absolutely confirmed with satellite-borne particle and magnetic field experiments conducted over the past two decades. These satellite observations have determined the large-scale patterns, flow directions, and intensities of Birkeland currents in the auroral and polar regions, and their relationship to the orientation and magnitude of the interplanetary magnetic field. The Birkeland currents are directly associated with visible and UV auroral forms observed with satellites. The results obtained from a variety of recently launched satellites are discussed here. These include Sweden's first satellite, VIKING, which has provided evidence for resonant Alfvén waves on the same geomagnetic field lines that guide stationary Birkeland currents. These observations demonstrate the important role that these currents play in the coupling of energy between the interplanetary medium and the lower ionosphere and atmosphere.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

VLF two-wave-electron interactions in the magnetosphere

The mutual influence between two whistler mode waves, through cyclotron resonant interaction of each wave with the same set of energetic electrons, is analysed both theoretically and by computer simulations ; this two-wave interaction mechanism seems to be an important process in understanding recently observed phenomena in Siple Station VLF multi-wave injection experiments. A criterion is established to estimate the threshold for the critical frequency spacing (for given wave amplitudes) for a significant mutual interaction between two monochromatic waves to occur. This criterion is based on the overlap of coherence bandwidths associated with the trapping domains of each wave and it takes into account the geomagnetospheric medium inhomogeneity. The effects of a perturbing second wave on electrons trapped by a first wave is discussed, considering the general situation of varying-frequency waves, and a simulation model is used to track the motion of test-electrons in the two-waves field. Conditions leading to detrapping and subsequent trapping by the second wave of previously first-wave trapped electrons are analysed and suggest the possibility of this phenomenon to play an important role in frequency entrainment and energy exchange between two waves.     

Pi2 pulsations in the magnetosphere

Several substorms were observed at Explorer 45 in November and December 1971, and January and February 1972, while the satellite was in the evening quadrant near L = 5. These same substorms were identified in ground level magnetograms from auroral zone and low latitude stations. The satellite vector magnetic field records and rapid run ground magnetograms were examined for evidence of simultaneous occurrence of Pi2 magnetic pulsations. Pulsations which began abruptly were observed at the satellite during 7 of the 13 substorms studied and the pulsations occurred near the estimated time of substorm onset. These 7 pulsation events were also observed on the ground and 6 were identified in station comments as Pi2. All of the events observed were principally compressional waves, that is, pulsations in field magnitude. There were also transverse components elliptically polarized counter-clockwise looking along the field line. Periods observed ranged from 40 to 200 sec with 80 sec often the dominant period.     

Charged dust in the Earth's magnetosphere

We have considered the electrodynamic effects on small Al₂O₃ spherules dumped into the Earth's magnetosphere in large quantities during solid rocket propellant burns. The charges acquired by these grains in all regions of the terrestrial environment (plasmasphere, magnetosphere, and solar wind) are modest. Consequently electrodynamic effects are significant only at the lower end of the dust size spectrum (R _g0.1 m). In that case, the electrodynamic forces conspire with solar radiation pressure to eliminate the grains from the magnetosphere in a comparatively short time. Although not studied here in detail, we anticipate a similar fate for fine micrometeoroids entering the Earth's magnetosphere, with the electro-dynamic effects playing an even more important role.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Tearing instability in the pulsar magnetosphere

Equations governing the coupling of the scalar and vector potentials for a resistive electron-positron plasma in a strong magnetic field are derived. It is shown that in the presence of magnetic shear, a tearing instability may occur. The latter can lead to magnetic field line reconnection and the formation of magnetic islands which could affect the dynamics of the pulsar magnetosphere.     

Standing hydromagnetic oscillations in the magnetosphere

Many types of ULF pulsations observed at geosynchronous orbit exhibit properties of standing shear Alfvén waves. Observation of the harmonic mode, polarization state and azimuthal wave number is crucial for determining the source of energy responsible for excitation of these waves. In recent years it has become possible to identify the harmonic mode of standing waves from dynamic spectral analysis, as well as simultaneous observations of electric and magnetic fields of the waves or a comparison between plasma mass density estimated from the frequency of the waves and that observed by direct measurement. It is then more reasonable to classify pulsations according to their physical properties, including the harmonic mode, polarization state, azimuthal wave number, and localization in occurrence, than according to the conventional scheme based on the wave form and period range. From analysis of magnetic pulsations observed at geosynchronous orbit, at least two distinctively different types of waves have been identified. One is azimuthally polarized waves simultaneously excited at the fundamental and several harmonics of a standing Alfvén wave which are observed throughout the day side. They have relatively small azimuthal numbers (less than 10) and propagate tailward. They are likely to be excited by the interaction of the solar wind with the magnetopause or bow shock. Another type is radially polarized waves most strongly excited at the second harmonic. They are observed mainly on the afternoon side. Bounce resonance of a few keV ions has been suggested as the mechanism for excitation of the radially polarized waves.