Vladimir A. Osherovich

A study of an expanding interplanetary magnetic cloud and its interaction with the Earth's magnetosphere: The interplanetary aspect

In a series of three interlinked papers we present a study of an interplanetary magnetic cloud and its interaction with the Earths magnetosphere on January 14/15, 1988. This first paper is divided into three parts describing the principal results concerning the magnetic cloud. First, by applying the cylindrically symmetric, magnetic flux rope model to the high time resolution magnetic field and plasma data obtained by the IMP-8 spacecraft, we show that the axis of the magnetic cloud in question is approximately in the ecliptic and orthogonal to the Earth-Sun line. We note the presence of pulsations of ∼5-hour period in the bulk flow speed which are superimposed on an otherwise monotonically falling bulk speed profile. Second, we apply ideal MHD to model the self-similar, radial expansion of a magnetic cloud of cylindrical geometry. As initial condition for the magnetic field we choose a constant-α, force-free magnetic configuration. We demonstrate that the theoretical velocity profile for the free expansion of a magnetic cloud is consistent with observations made during the January 14/15, 1988, magnetic cloud encounter. Comparing model with data, we infer that prior to the start of observations at 1 AU the magnetic cloud had been expanding for 65.4 hours; the radius of the magnetic cloud at the time it arrived at Earth was 0.18 AU; and its expansion speed at 1 AU was ∼114 km/s. Third, we discuss energetic (∼1 MeV) ion data, also from instrumentation on IMP-8. We highlight the appearance of a sharp enhancement in the intensity of ∼0.5-MeV ions while IMP-8 was inside the cloud. These ions travel as a collimated, field-aligned beam from the west of the Sun. This is an “impulsive” solar event in which particles accelerated at a magnetically well-connected solar flare arrive promptly at the spacecraft. The observation of solar flare particles inside the cloud suggests that field lines within the magnetic cloud remained connected to the Sun. The observation is, however, inconsistent with the supposition that the cloud is formed of closed magnetic field loops disconnected from the Sun.

Magnetic flux rope versus the Spheromak as models for interplanetary magnetic clouds

Magnetic clouds form a subset of interplanetary ejecta with well-defined magnetic and thermodynamic properties. Observationally, it is well established that magnetic clouds expand as they propagate antisunward. The aim of this paper is to compare and contrast two models which have been proposed for the global magnetic field line topology of magnetic clouds: a magnetic flux tube geometry, on the one hand, and a spheromak geometry (including possible higher multiples), on the other. Traditionally, the magnetic structure of magnetic clouds has been modeled by force-free configurations. In a first step, we therefore analyze the ability of static force-free models to account for the asymmetries observed in the magnetic field profiles of magnetic clouds. For a cylindrical flux tube the magnetic field remains symmetric about closest approach to the magnetic axis on all spacecraft orbits intersecting it, whereas in a spheromak geometry one can have asymmetries in the magnetic field signatures along some spacecraft trajectories. The duration of typical magnetic cloud encounters at 1 AU (1 to 2 days) is comparable to their travel time from the Sun to 1 AU and thus magnetic clouds should be treated as strongly nonstationary objects. In a second step, therefore, we abandon the static approach and model magnetic clouds as self-similarly evolving MHD configurations. In our theory, the interaction of the expanding magnetic cloud with the ambient plasma is taken into account by a drag force proportional to the density and the velocity of expansion. Solving rigorously the full set of MHD equations, we demonstrate that the asymmetry in the magnetic signature may arise solely as a result of expansion. Using asymptotic solutions of the MHD equations, we least squares fit both theoretical models to interplanetary data. We find that while the central part of the magnetic cloud is adequately described by both models, the “edges” of the cloud data are modeled better by the magnetic flux tube. Further comparisons of the two models necessarily involve thermodynamic properties, since real magnetic configurations are never exactly force-free and gas pressure plays an essential role. We consider a poly tropic gas. Our theoretical analysis shows that the self-similar expansion of a magnetic flux tube requires the poly tropic index γ to be less than unity. For the spheromak, however, self-similar, radially expanding solutions are known only for γ equal to 4/3. This difference, therefore, yields a good way of distinguishing between the two geometries. It has been shown recently (Osherovich et al., 1993a) that the polytropic relationship is applicable to magnetic clouds and that the corresponding polytropic index is ∼0.5. This observational result is consistent with the self-similar model of the magnetic flux rope but is in conflict with the self-similar spheromak model.

Dynamics of aging magnetic clouds

Abstract The dynamics of radially expanding magnetic clouds is rigorously analyzed within the framework of ideal MHD. The cloud is modelled as a cylindrically symmetric magnetic flux rope. In the force balance we include the gas pressure gradient and the Lorentz force. Interaction with the ambient solar wind due to expansion of the magnetic cloud is represented by a drag force proportional to the bulk velocity. We consider the self-similar expansion of a polytrope, and reduce the problem to an ordinary non-linear differential equation for the evolution function. Analyzing the asymptotic behaviour of the evolution function, we formulate theoretical expectations for the long-term behaviour of cloud parameters. We focus on the temporal evolution of (i) the magnetic field strength; (ii) the twist of the field lines; (iii) the asymmetry of the total field profile; and (iv) the bulk flow speed. We present data from two magnetic clouds observed at 1 AU and 2 AU, respectively, and find good agreement with theoretical expectations. For a peak magnetic field strength at 1 AU of 25 nT and a polytropic index of 0.5, we find that a magnetic cloud can be distinguished from the background interplanetary field up to a distance of ∼5 AU. Taking larger magnetic fields (up to 30 nT) and bigger polytropic indices (up to 0.6) this distance can double.

Kilohertz Quasi-periodic Oscillations in Neutron Star Binaries Modeled as Keplerian Oscillations in a Rotating Frame of Reference

Since the discovery of kHz quasi-periodic oscillations (QPOs) in neutron star binaries, the difference between peak frequencies of two modes in the upper part of the spectrum, i.e., Δω = ωh - ωK has been studied extensively. The idea that Δω is constant and (as a beat frequency) is related to the rotational frequency of the neutron star has been tested previously. The observed decrease of Δω when ωh and ωK increase has weakened the beat frequency interpretation. We put forward a different paradigm: a Keplerian oscillator under the influence of the Coriolis force. For such an oscillator, ωh and the assumed Keplerian frequency ωK hold an upper hybrid frequency relation: ωh2 - ωK2 = 4Ω2, where Ω is the rotational frequency of the stars magnetosphere near the equatorial plane. For three sources (Sco X-1, 4U 1608-52, and 4U 1702-429), we demonstrate that the solid-body rotation Ω = Ω0 = const. is a good first order approximation. Within the second-order approximation, the slow variation of Ω as a function of ωK reveals the structure of the magnetospheric differential rotation. For Sco X-1, the QPOs have frequencies ~45 and 90 Hz which we interpret as the first and second harmonics of the lower branch of the Keplerian oscillations for the rotator with Ω not aligned with the normal of the disk: ωL/2π = (Ω/π)(ωK/ωh) sin δ, where δ is the angle between Ω and the vector normal to the disk.

Polytropic relationship in interplanetary magnetic clouds

Interplanetary magnetic clouds are expanding MHD configurations characterized by strong magnetic fields, large rotations of the field vector, and low ion temperatures. In this paper we present high time resolution data from the ISEE 3 and IMP 8 spacecraft on the magnetic field and the proton and electron populations in a number of magnetic clouds. Our objective is to study aspects of the thermodynamics of magnetic clouds and the relation between their thermodynamic and magnetic structures. Our analysis suggests the following features of the thermodynamics of magnetic clouds: (1) The electron and ion populations are not in thermal equilibrium with each other, the electron temperature, Te, being in general up to an order of magnitude higher than the proton temperature, Tp. The temperature ratio Te/Tp in these magnetic clouds is larger than typical values of this quantity in the solar wind at comparable heliocentric distances. (2) For the proton component we find that a polytropic law with γp in the range 1.1 < γp < 1.3 is probably adequate to describe the relation between Tp and density. (3) For the electrons (E < 1.18 keV) the energetics are likewise governed by a polytropic law. Unlike the protons the polytrope that describes the electrons has an index that is less than unity, implying anticorrelation between Te and the number density. For the two clouds analyzed where electron data are available, γe ≈ 0.48 ± 0.2. (4) As a corollary of case 3, the variation of Te with density in magnetic clouds is the reverse of that generally found in the inner heliosphere. (5) Electron temperatures are well correlated with the magnetic field strength, the highest values being reached where the field strength maximizes. We interpret these experimental findings along the following lines. While the magnetic field of the cloud expands, the ions are cooled (though not so effectively as in the adiabatic case (γad = 5/3), indicating some exchange of energy with the ambient solar wind). In contrast, since γe < 1, when the density drops as a result of expansion, Te increases and, consequently, a temperature difference develops between the two species. The hot electrons are trapped by the magnetic field in the core of the magnetic cloud. If magnetic clouds originate in the region near the Sun where Tp < Te, the subsequent expansion accentuates this temperature disparity further. Such conditions are favorable for the generation of ion acoustic waves.

Nonlinear evolution of magnetic flux ropes. 2: Finite beta plasma

In this second paper on the evolution of magnetic flux ropes we study the effects of gas pressure. We assume that the energy transport is described by a poly tropic relationship and reduce the set of ideal MHD equations to a single, second-order, nonlinear, ordinary differential equation for the evolution function. For this conservative system we obtain a first integral of motion. To analyze the possible motions, we use a mechanical analogue—a one-dimensional, nonlinear oscillator. We find that the effective potential for such an oscillator depends on two parameters: the polytropic index γ and a dimensionless quantity κ the latter being a function of the plasma beta, the strength of the azimuthal magnetic field relative to the axial field of the flux rope, and γ. Through a study of this effective potential we classify all possible modes of evolution of the system. In the main body of the paper, we focus on magnetic flux ropes whose field and gas pressure increase steadily towards the symmetry axis. In this case, for γ>1 and all values of κ, only oscillations are possible. For γ 1. While in most cases the flux rope collapses, there are notable exceptions when, for certain ranges of κ and γ, collapse may be averted.

A comparative study of dynamically expanding force-free, constant-alpha magnetic configurations with applications to magnetic clouds

ABSTRACT We contrast two different solutions of the constant alpha, force-free MHD equation, both of which have been suggested as models for magnetic clouds: a solution in cylindrical coordinates and one in spherical polar coordinates. In line with the observation that magnetic clouds expand, we generalize these static models and construct their expanding counterparts. We find that expansion introduces in both cases a large asymmetry in the field strength signature which is in the same sense as that seen in the data, i.e. towards the leading edge of the cloud. We then do a least squares fit of the respective models to one-spacecraft data on a magnetic cloud. We find that the fitting routine converges in both cases. However, while purely formally we cannot distinguish between the two models using data from one spacecraft, the field components in the spherical’ model have features not compatible with data on magnetic clouds.

Multi‐tube model for interplanetary magnetic clouds

Measurements of the polytropic index γ inside a magnetic cloud showed that there are two non-equal tubes inside the cloud [Fainberg et al., 1996; Osherovich et al., 1997]. For both tubes, γ < 1, but each tube has its own polytrope. We test equilibrium solutions which are a superposition of solutions with cylindrical and helical symmetry [Krat and Osherovich, 1978] as a new paradigm for a multi-tube model. Comparison of magnetic and gas pressure profiles for these bounded MHD states with observations suggests that complex magnetic clouds can be viewed as multiple helices embedded in a cylindrically symmetric flux rope.

Classification of IMAGE/RPI‐stimulated plasma resonances for the accurate determination of magnetospheric electron density and magnetic field values

resonances, respectively, and also at other frequencies. While they are observed to have an inherent bandwidth of 300 Hz or less, the effective detection bandwidth for strong resonances is nearly 2 kHz. The Qn resonances are often observed with time durations exceeding the 178 ms limit of the RPI operating programs commonly used for resonance detection. The fuh resonance is also observed with a long time duration even when it is in the plasma domain where it is normally weaker, i.e., when fuh >2 fce. A strong resonance at fpe is often but not always observed. In earlier investigations, the Dn resonances had been related to natural magnetospheric plasma-wave emissions and to sounderstimulated plasma-wave emissions in Jupiter’s Io plasma torus. The present RPI observations represent the first evidence for the stimulation of these resonances by a sounder deep in the terrestrial magnetosphere. These observations suggest the possible widespread occurrence of Ne field-aligned irregularities (FAI) or the ease of sounderstimulated FAI based on one Dn generation mechanism involving eigen modes of cylindrical plasma oscillations which have been associated with FAI. The RPI observations provide additional support to earlier suggestions that the Qn and Dn resonances have components of natural origin. The capability of simultaneous reception on three mutually orthogonal dipole receiving antennas often aids in the identification of spectral features. The RPI capability to generate magnetospheric reflection traces, leading to well-defined wave cutoff frequencies at the satellite, provides independent Ne determinations and additional spectral-identification confidence. Combining these capabilities with new analysis techniques that produce three-antenna plasmagrams normalized by fce and amplitude plots based on averages over different range-bin intervals, Ne and jBj can often be accurately determined from the plasma-resonance spectra to within uncertainties of the order of 1% and 0.1%, respectively, when RPI sounds using frequency steps equal to the 300 Hz receiver bandwidth. Such accuracy in magnetospheric Ne determination, even when Ne � 1c m � 3 , is difficult to attain by other

Nonlinear evolution of magnetic flux ropes: 1. Low‐beta limit

An understanding of fully developed nonlinear MHD phenomena becomes increasingly essential for the interpretation of magnetospheric and interplanetary observations. In a series of four papers we shall study the nonlinear, self-similar evolution of a cylindrical magnetic flux tube with two components of the magnetic field, axial (Bz) and azimuthal (Bϕ). In this first paper we restrict ourselves to the case of a plasma of low beta. (Subsequent papers deal with finite beta effects, with dissipation, and with a data example.) Introducing a special class of configurations we call “separable fields,” we reduce the problem to an ordinary differential equation. Two cases are to be distinguished: (1) when the total field minimizes on the symmetry axis, the magnetic configuration inexorably collapses, and (2) when, on the other hand, the total field maximizes on the symmetry axis, the magnetic configuration behaves analogously to a nonlinear oscillator. Here we focus on the latter case. The effective potential of the motion contains two terms: a strong, repulsive term associated with the gradient of Bz²/8π and a weak, restoring term associated with the pinch. We solve the nonlinear differential equation of motion numerically and find that the period of oscillations grows exponentially with the energy of the oscillator. Our treatment emphasizes the role of the force-free configuration as the lowest potential energy state about which the system oscillates.