Magnetic energy buildup in a quadrupole field by photospheric shear motion

Using a two-dimensional, dissipative magnetohydrodynamic model, this paper presents a numerical simulation of the magnetic energy buildup in a quadrupolar field by photospheric shear motion. When electric current density is larger than a certain critical value, an anomalous resistivity is introduced in order to account for the dissipation caused by instabilities in high current regions. It is shown that like a bipolar field, a quadrupolar field can efficiently store magnetic free energy through photospheric shear motion. Electric current formed by shear concentrates on the separatrix and magnetic loops rooted in areas where the shear velocity gradient is large. The atmosphere is heated by anomalous resistive dissipation during the shear. Both magnetic and thermal energy increases nonlinearly with shearing displacement. When the anomalous resistivity increases or the critical current density decreases, the growth rate reduces for magnetic energy but goes up for thermal energy.     

An analytical model of the Comet's collision with Jupiter

An important feature observed in the wake of the Jupiter-comet clash was the appearance of the ring structure axisymmetrically positioned around the center of the impact. The persistent expansion of the dark rings and its speed indicated an outward propagating gravity wave (Benka, 1995). We employ an analytical model of constant density, uniform finite depth and inviscid fluid layer to investigate the wave motion produced by the impact of Comet Shoemaker-Levy 9 on the Jovian atmosphere. The relevant thermal effects are neglected and an explosion resulting from the collision is then described by an initial impulsive pressure at the surface of the Jovian atmosphere. Under the assumption that all the kinetic energy of a comet fragment is completely converted into the energy of wave motions in the Jovian atmosphere, an analytical formula describing the relationship between the resulting wave motion in the atmosphere and the parameters of a comet fragment (the radius, density and speed) is derived. Results from the present simple analytical model give a qualitative agreement with observations regarding the distance and speed of the waves.     

Asymmetry of the Venus nightside ionosphere: Magnus force effects

A study of the dawn-dusk asymmetry of the Venus nightside ionosphere is conducted by examining the configuration of the ionospheric trans-terminator flow around Venus and also the dawn-ward displacement of the region where most of the ionospheric holes and the electron density plateau profiles are observed (dawn meaning the west in the retrograde rotation of Venus and that corresponds to the trailing side in its orbital motion). The study describes the position of the holes and the density plateau profiles which occur at neighboring locations in a region that is scanned as the trajectory of the Pioneer Venus Orbiter (PVO) sweeps through the nightside hemisphere with increasing orbit number. The holes are interpreted as crossings through plasma channels that extend downstream from the magnetic polar regions of the Venus ionosphere and the plateau profiles represent cases in which the electron density maintains nearly constant values in the upper ionosphere along the PVO trajectory. From a collection of PVO passes in which these profiles were observed it is found that they appear at neighboring positions of the ionospheric holes in a local solar time (LST) map including cases where only a density plateau profile or an ionospheric hole was detected. It is argued that the ionospheric holes and the density plateau profiles have a common origin at the magnetic polar regions where plasma channels are formed and that the density plateau profiles represent crossings through a friction layer that is adjacent to the plasma channels. It is further suggested that the dawn-dusk asymmetry in the position of both features in the nightside ionosphere results from a fluid dynamic force (Magnus force) that is produced by the combined effects of the trans-terminator flow and the rotational motion of the ionosphere that have been inferred from the PVO measurements.     

External and internal solutions for the twisted,flux-tube,prominence model

In this paper the twisted flux-tube model for the support of a prominence sheet with constant axial current density, given by Ridgway, Priest, and Amari (1991), is considered.The model is extended in Section 2 to incorporate a current sheet of finite height. The sheet is supported in a constant current density force-free field in the configuration of a twisted flux tube. The mass of the prominence sheet, using a typical height and field strength, is computed. Outside the flux tube the background magnetic field is assumed to be potential but the matching of the flux tube onto this background field is not considered here.Instead our attention is focussed, in Section 3, on the interior of the prominence. An expanded scale is used to stretch the prominence sheet to a finite width. We analytically select solutions for the internal magnetic field in this region which match smoothly onto the external force-free solutions at the prominence edge.The force balance equation applied inside the prominence then yields expressions for the pressure and density and a corresponding temperature may be computed.     

Dynamics of emission clouds in quasar nuclei

The motion of emission clouds in quasar nuclei under the action of central-source radiative pressure, deceleration force of the intercloud medium, and the central-body gravitation is considered. It is shown that the properties of the intercloud medium have an essential bearing on the cloud dynamics. The cloud velocity increases with the distance from the source and tends to a constant value which depends from the central-source luminosity and the intercloud medium density.     

Dynamical friction for accelerated motion in a gaseous medium

Dynamical friction arises from the interaction of a perturber and the gravitational wake it excites in the ambient medium. This interaction is usually derived assuming that the perturber has a constant velocity. In realistic situations, motion is accelerated as for instance by dynamical friction itself. Here, we study the effect of acceleration on the dynamical friction force. We characterize the density enhancement associated with a constantly accelerating perturber with rectilinear motion in an infinite homogeneous gaseous medium and show that dynamical friction is not a local force and that its amplitude may depend on the perturber's initial velocity. The force on an accelerating perturber is maximal between Mach 1 and Mach 2, where it is smaller than the corresponding uniform motion friction. In the limit where the perturber's size is much smaller than the distance needed to change the Mach number by unity through acceleration, a subsonic perturber feels a force similar to uniform motion friction only if its past history does not include supersonic episodes. Once an accelerating perturber reaches large supersonic speeds, accelerated motion friction is marginally stronger than uniform motion friction. The force on a decelerating supersonic perturber is weaker than uniform motion friction as the velocity decreases to a few times the sound speed. Dynamical friction on a decelerating subsonic perturber with an initial Mach number larger than 2 is much larger than uniform motion friction and tends to a finite value as the velocity vanishes in contrast to uniform motion friction.     

The Lagrange and Two-Center Problems in the Lobachevsky Space

The generalization of the two-center problem and the Lagrange problem (a mass point motion under the action of attracting center field and the analog of a constant homogeneous field) to the case of a constant curvature space, in the three-dimensional space of Lobachevsky (³), is investigated in this paper. The integrability of these problems is proved. The bifurcation set in the plane of integrals of motion is constructed and the classification of the domains of possible motion is carried out. An analog of a constant homogeneous field is obtained in the Lobachevsky space.     

Effective potential energy in Størmer’s problem for an inclined rotating magnetic dipole

We discuss the dynamics of a charged nonrelativistic particle in electromagnetic field of a rotating magnetized celestial body. The equations of motion of the particle are obtained and some particular solutions are found. Effective potential energy is defined on the base of the first constant of motion. Regions accessible and inaccessible for a charged particle motion are studied and depicted for different values of a constant of motion.     

Oscillating pulsar polar gaps

An analytical model for oscillating pair creation above the pulsar polar cap is presented in which the parallel electric field is treated as a large amplitude, superluminal, electrostatic wave. An exact formalism for such wave is derived in one dimension and applied to both the low-density regime in which the pair plasma density is much lower than the corotating charge density and the high-density regime in which the pair plasma density is much higher than the corotating charge density. In the low-density regime, which is relevant during the phase leading to a pair cascade, a parallel electric field develops resulting in a rapid acceleration of particles. The rapid acceleration leads to bursts of pair production and the system switches to the oscillatory phase, corresponding to the high-density regime, in which pairs oscillate with net drift motion in the direction of wave propagation. Oscillating pairs lead to a current that oscillates with large amplitude about the Goldreich–Julian current. The drift motion can be highly relativistic if the phase speed of large amplitude waves is moderately higher than the speed of light. Thus, the model predicts a relativistic outflow of pairs, a feature that is required for avoiding overheating of the pulsar polar cap and is also needed for the pulsar wind.     

One more explanation of superluminal motion

The occurrence of superluminal motion in extragalactic radio sources is believed to be quite common. Among others, the geometrical scattering of radio radiation can also cause superluminal expansion and or motion and halo formation, In this paper, the effectiveness of the stimulated Raman scattering in producing these features is investigated. The scattering medium is a plasma whose position, density and temperature decide the rate and angle of scattering. When the radiation from a stationary and constant source gets scattered from a stationary plasma, a halo is formed around the source. However, the scattering of a rotating radiation beam does produce superluminal motion of the virtual source. It is found that the plasma should have the characteristics of the emission-line regions and the intercloud medium in order to Raman scatter the radiation. Since the scattering is polarization dependent, it is possible to estimate the rotation of the electric vector along the direction of the apparent motion of a radio source.     

Density models for the upper atmosphere

Modeling the effects of atmospheric drag is one of the more important problems associated with the determination of the orbit of a near-earth satellite. Errors in the drag model can lead to significant errors in the determination and prediction of the satellite motion. The uncertainty in the drag acceleration can be attributed to three separate effects: (a) errors in the atmospheric density model, (b) errors in the ballistic coefficient, and (c) errors in the satellite relative velocity. In a number of contemporary satellite missions, the requirements for performing the orbit determination and predictions in near real-time has placed an emphasis on density model computation time as well as the model accuracy. In this investigation, a comparison is made of three contemporary atmospheric density models which are candidates for meeting the current orbit computation requirements. The models considered are the analytic Jacchia-Roberts model, the modified Harris-Priester model, and the USSR Cosmos satellite derived density model. The computational characteristics of each of the models are compared and a modification to the modified Harris-Priester model is proposed which improves its ability to represent the diurnal variation in the atmospheric density.This investigation was supported by the NASA Goddard Spaceflight Center under contract NAS5-20946 and Contract NSG 5154.     

Contraction of satellite orbits using KS uniformly regular canonical elements in an oblate diurnally varying atmosphere

A new non-singular analytical theory for the motion of near Earth satellite orbits with the air drag effect is developed in terms of the Kustaanheimo and Stiefel (KS) uniformly regular canonical elements, by assuming the atmosphere to be oblate diurnally varying with constant density scale height. The series expansions include up to third-order terms in eccentricity and c (a small parameter dependent on the flattening of the atmosphere). Only two of the nine equations are solved analytically to compute the state vector and change in energy at the end of each revolution, due to symmetry in the equations of motion. Numerical comparisons of the important orbital parameters semimajor axis and eccentricity up to 1000 revolutions, obtained with the present solution, with the third-order analytical theories of Swinerd and Boulton and in terms of the KS elements, with respect to the numerically integrated values, show the superiority of the present solution over the other two theories over a wide range of eccentricity, perigee height and inclination.     

MHD effects triggered by beams of fast particles in magnetic tubes and their possible relation to plasma heating and dynamics during solar flares

We study the magnetohydrodynamic response of a plasma in the low solar atmosphere to a changing current system of a flaring magnetictube, which contains a beam of fast non-thermal electrons. The local disturbances of a current system of a magnetic tube when the beam is injected into it are estimated using the classical idea of a return current. According to this idea, after injection of abeam, the total current density in a magnetic tube, which includes as well the current density of the beam j_b, should not change compared to the current density in the tube before the injection. In order to keep constant the total current density j=j'+ j_b, the current density of the magnetic tube j'in fact changes. This change is due to a return current j_r.c.= –j_b, which compensates the current density of the injected beam of fast electrons. At the same time, any changes of the current density in the magnetic tube change the Joule heating and disturb the thermodynamic equilibrium of the system. Changing of the plasma temperature destroys also the force balance and starts the process of complex dynamics of the whole plasma-magnetic structure. The impulsive character of a beam injection causes two stages in the dynamic behavior of the tube. During the first stage, characterized by the presence of a beam, the preliminary equilibrium state of a magnetic tube is disturbed and complex dynamics of the plasma start in the region of the beam propagation. During the second stage, when the injection of the beam is already over, the plasma and magnetic field continue to evolve from the disturbed state and gradually relax to an equilibrium state. Various types of magnetic tube response onto injection of a beam of energetic electrons are studied using the dynamic models of the magnetic tube (Khodachenko, 1996a; 1996b) built on the basis of known self-similar solutions of plasma MHD. The model results are applied to the interpretation of observed flaring and burst phenomena.     

Cassini Langmuir probe measurements in the inner magnetosphere of Saturn

In the inner magnetosphere of Saturn, the plasma density and drift velocity are high enough, and the photoelectron current low enough, for a Langmuir probe to produce useful data on ion parameters. Plasma density and velocity are found by analyzing the current due to collected ions and emitted photoelectrons for a negative probe potential. In order to correctly analyze the data, the current caused by photoelectrons emitted from the probe must be known. For a spherical probe at negative bias this should be a constant current, but for Cassini's probe it varies with attitude. A likely cause of this is a leakage current from the stub to the probe. The plasma drift velocities derived from Langmuir probe measurements did not agree with those found by the Cassini plasma spectrometer in the inner magnetosphere, but did so elsewhere. A possible solution to this is a two-component plasma where the components have different drift velocities.     

The onset of chaotic motion in the restricted problem of three bodies

A full characterization of a nonintegrable dynamical system requires an investigation into the chaotic properties of that system. One such system, the restricted problem of three bodies, has been studied for over two centuries, yet few studies have examined the chaotic nature of some ot its trajectories. This paper examines and classifies the onset of chaotic motion in the restricted three-body problem through the use of Poincaré surfaces of section, Liapunov characteristic numbers, power spectral density analysis and a newly developed technique called numerical irreversibility. The chaotic motion is found to be intermittent and becomes first evident when the Jacobian constant is slightly higher thanC ₂.     

The role of plasma interchange motion for the formation of a plasmapause

Mcllwain's electric and magnetic field distributions (E3H and M2) have been used to calculate the drift path of plasma density irregularities taking into account plasma interchange motion driven by the gravitational and inertial forces acting on the whole mass of the plasma elements.It has been shown that there is a region in the magnetosphere which is unstable with respect to the interchange motion of the cold plasma element. Any plasma hole in the background density drifts ultimately toward an asymptotic trajectory. Along this trajectory the inward gravitational force is balanced by the outward inertial force averaged over one revolution around the Earth. This asymptotic trajectory, along which all plasma holes ultimately accumulate, is identified with the equatorial plasmapause. The maximum velocity for the interchange motion is proportional to the excess (or defect) of density in the plasma element, and inversely proportional to the integrated Pedersen conductivity. Plasma detachment is shown to occur preferentially in the post-midnight sector.     

Rayleigh-Taylor instability of a plasma with finite ion Larmor radius effects

The stability of an infinitely conducting plasma of variable density has been investigated taking into account the finiteness of the ion Larmor radius. The perturbations propagating along the ambient magnetic field are considered. It is established that, in general,n ² is necessarily real, wheren is the growth rate of disturbance, thus ruling out the possibility of overstability or damped oscillations. The solution is shown to be characterized by a variational principle, which provides the basis for obtaining an approximate solution of the problem. Two density distributions are considered: (i) a continuously stratified plasma layer and (ii) two semi-infinitely extending plasmas of constant densities separated by a horizontal interface. In both cases it has been shown that for the said disturbances the stability criterion remains unaffected by the inclusion of finite Larmor radius effects, though the amplified motion is strongly inhibited due to their inclusion.     

Note on Kepler's problem with variable angular momentum

Based on the equations of planar motion with drag used in point dynamics, a simple derivation is presented that shows how a constant Keplerian (elliptical) orbit can be obtained with a non-central force field and variable angular momentum.     

Analytical orbit predictions with air drag using KS uniformly regular canonical elements

A new nonsingular analytical theory for the motion of near Earth satellite orbits with the air drag effect is developed for long term motion in terms of the KS uniformly regular canonical elements by a series expansion method, by assuming the atmosphere to be symmetrically spherical with constant density scale height. The series expansions include up to third order terms in eccentricity. Only two of the nine equations are solved analytically to compute the state vector and change in energy at the end of each revolution, due to symmetry in the equations of motion. Numerical comparisons of the important orbital parameters semi major axis and eccentricity up to 1000 revolutions, obtained with the present solution, with KS elements analytical solution and Cook, King-Hele and Walker's theory with respect to the numerically integrated values, show the superiority of the present solution over the other two theories over a wide range of eccentricity, perigee height and inclination.