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.     

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.     

Computations on the interaction of an interplanetary shock with the Earth's magnetosphere

We present the results of a one-dimensional computer simulation of the interaction between interplanetary shocks and the Earth's magnetosphere. The position of the bowshock as a function of solar wind velocity and interplanetary field direction is studied.     

An analytic model for the epoch of halo creation

In this paper we describe the Bayesian link between the cosmological mass function and the distribution of times at which isolated haloes of a given mass exist. By assuming that clumps of dark matter undergo monotonic growth on the time-scales of interest, this distribution of times is also the distribution of 'creation' times of the haloes. This monotonic growth is an inevitable aspect of gravitational instability. The spherical top-hat collapse model is used to estimate the rate at which clumps of dark matter collapse. This gives the prior for the creation time given no information about halo mass. Applying Bayes' theorem then allows any mass function to be converted into a distribution of times at which haloes of a given mass are created. This general result covers both Gaussian and non-Gaussian models. We also demonstrate how the mass function and the creation time distribution can be combined to give a joint density function, and discuss the relation between the time distribution of major merger events and the formula calculated. Finally, we determine the creation time of haloes within three N -body simulations, and compare the link between the mass function and creation rate with the analytic theory.     

An analytic version of Jacchia's 1977 model atmosphere

Celestial Mechanics and Dynamical Astronomy - Closed-form expressions are derived for the density of the atmosphere as a function of altitude and exospheric temperature. The numerical model used as...     

A three-ring circuit model of the magnetosphere

We have modeled the magnetosphere by superimposing a dipole field, a uniform field and a perturbation field due to a simple current system. This current system consists of a ring current in the neutral line of the dipole plus uniform fields, together with vertical currents representing field-aligned currents to the neutral line. The current circuit is closed by two additional ring currents above and below the equatorial plane representing distributed adiabatic perpendicular currents. This system produces many magnetospheric features including a magnetopause, bending of magnetic field lines in the anti-solar direction, a magnetotail, and cusps on the day-side of the Earth. Our aim is to demonstrate that it is not necessary to think of the magnetic field topology as being caused by the flowing plasma carrying field lines. The fundamental physical problem is to derive the current system from the self-consistent interaction of the solar-wind and magnetospheric plasmas and fields.     

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.     

An analytical approach to the Choe-Beard magnetosphere

An analytical simplified model of the Choe-Beard magnetosphere is obtained through a perturbation method. As only the most important terms are selected, the field line topology up to the synchronous region is described in a compact form. One application of this allows the diurnal motion of conjugate points to be derived analytically.     

Analytical two-dimensional model of a quadrupole magnetosphere

A model of a quadrupole magnetosphere is developed with the aid of conformal mappings. Such a type of magnetosphere might have occurred at the Earth during times of polarity reversals of the dipole field, when the residual field essentially may have had a quadrupole structure. The magnetospheric field-line configuration is calculated for an axial quadrupole directed perpendicular to the solar-wind flow. The model is two-dimensional and leads to analytical formulae.     

Molecular distribution in the comae of H2O-comets: An analytic model

Density distribution in cometary comae resulting from photodissociation, ionization and ion-molecule reaction of H₂O is investigated in an analytic manner. It is assumed that particles expand isotropically around the nucleus, and that each species has its own constant radial velocity. Formulae for the density distribution of photochemical products are presented throught the coma, and approximate formulae are given for the distribution of ion-molecule reaction products in the inner coma. Characterictics of the density profile are discussed on the basis of these analytic formulae.     

A magnetohydrodynamic model of whistler duct structure in the magnetosphere

In this study, the physical structure for the propagation of whistler waves within a duct in the Earth's magnetosphere is investigated by means of magnetohydrodynamic (MHD) theory. Expressions for the current density and induced magnetic field are determined analytically and evaluated in terms of two models for the duct plasma density distribution. It is found that once the duct is formed, forces associated with the current structure will maintain it. MHD instabilities are examined briefly and found to be unlikely to threaten duct maintenance in regions where whistlers are typically observed. Examination of some effects of field-aligned currents suggest that this may be a viable mechanism for duct formation.     

Analytical two-dimensional model for a pole-on magnetosphere

Magnetospheres, which result from a solar wind flow parallel to the magnetic dipole, are expected for Uranus at its solstitial points and perhaps for the Palaeo-Earth during the times of field reversal. We present a two-dimensional analytical model for a pole-on magnetopause and the magnetospheric magnetic field line configuration, employing a conformal mapping method.     

On the self-consistent model of an axisymmetric radio pulsar magnetosphere

We consider a model of axisymmetric neutron star magnetospheres. In our approach, the current density in the region of open field lines is constant and the returning current flows in a narrow layer along the separatrix. In this case, the stream equation describing the magnetic field structure is linear both in the open and closed regions; the main problem is matching the solutions along the separatrix. We demonstrate that it is the stability condition on the separatrix that allows us to obtain a unique solution of the problem. In particular, the zero point of magnetic field is shown to be located near the light cylinder. Moreover, the hypothesis of the existence of the non-linear Ohm's Law, connecting the potential drop in the pair creation region and the longitudinal electric current flowing in the magnetosphere, is confirmed.     

An analytic model for non-spherical lenses in covariant MOdified Newtonian Dynamics

Strong gravitational lensing by galaxies in MOdified Newtonian Dynamics (MOND) has until now been restricted to spherically symmetric models. These models were able to account for the size of the Einstein ring of observed lenses, but were unable to account for double-imaged systems with collinear images, as well as four-image lenses. Non-spherical models are generally cumbersome to compute numerically in MOND, but we present here a class of analytic non-spherical models that can be applied to fit double-imaged and quadruple-imaged systems. We use them to obtain a reasonable MOND fit to 10 double-imaged systems, as well as to the quadruple-imaged system Q2237+030 which is an isolated bulge-disc lens producing an Einstein cross. However, we also find five double-imaged systems and three quadruple-imaged systems for which no reasonable MOND fit can be obtained with our models. We argue that this is mostly due to the intrinsic limitation of the analytic models, even though the presence of small amounts of additional dark mass on galaxy scales in MOND is also plausible.     

An analytic model for disc disruption by strong stellar magnetic fields

An analytic model is presented for the inner structure of an accretion disc in the presence of a strong stellar magnetic field. The model is valid inside the radius at which the electron scattering opacity starts to exceed the Kramers opacity. It illustrates how the increasing stellar poloidal field leads to an elevated disc temperature, ultimately causing a breakdown in the vertical equilibrium owing to rapidly increasing radiation pressure which cannot be balanced by the vertical stellar gravity. Viscous instability also occurs. The solution gives an accurate representation of numerical results, and enables useful expressions to be derived for the radius at which the disc is marginally thin and the radius at which viscous instability occurs. The disruption mechanism appears to have general validity for accretion discs around strongly magnetic stars.     

A theoretical model of the bow shock and the magnetosphere of Jupiter

Using the data obtained from the Pioneer 10 and 11 observations, a theoretical model is proposed for the bow shock and the magentosphere of Jupiter. This indicates that the distance of the magnetopause from Jupiter on the sunlit side is (50–55) × r_J (r_J: Jupiter radius, = 7 × 10⁹ cm) and that the ratio of the stand-off distance to this distance is about equal to or slightly larger than unity. Hence the Mach number of the solar wind seems to be less than 1.5 at Jupiter's orbit. This result necessarily leads to a blunt body model of the Jovian magnetosphere, the tail region of which is not as extended as observed in the Earth's case.     

A self-consistent model of the magnetosphere with centrifugal wind,I

Under the purely centrifugal approximation (gravity and pressure force are neglected), stellar magnetospheres are classified into three main types of different physical properties in the two-dimensional parameter space. They are characterized essentially by the strength of the magnetic field and the plasma density, at the base of the magnetosphere. Among the three types, the type II magnetosphere has moderate surface densities for a given field strength, and is expected to possess a centrifugal wind blowing across the magnetic field lines without affecting them appreciably. Such a situation may be realized through a modification of the electric field from that under the ideal-MHD condition, owing to the inertia of a plasma. In order to illustrate this mechanism, the type II magnetosphere is taken up for a numerical simulation. The effect of artificial viscosity is avoided by integrating the characteristic equations for both components of the plasma, instead of solving the fluid equations directly. Our model reproduces a disk-like outflow of the centrifugal wind across the magnetic field lines which are closed through the equatorial plane.