Interchange Motions Research Articles

Radial interchange motions of plasma filaments

Radial convection of isolated filamentary structures due to interchange motions in magnetized plasmas is investigated. Following a basic discussion of vorticity generation, ballooning, and the role of sheaths, a two-field interchange model is studied by means of numerical simulations on a biperiodic domain perpendicular to the magnetic field. It is demonstrated that a blob-like plasma structure develops dipolar vorticity and electrostatic potential fields, resulting in rapid radial acceleration and formation of a steep front and a trailing wake. While the dynamical evolution strongly depends on the amount of collisional diffusion and viscosity, the structure travels a radial distance many times its initial size in all parameter regimes in the absence of sheath dissipation. In the ideal limit, there is an inertial scaling for the maximum radial velocity of isolated filaments. This velocity scales as the acoustic speed times the square root of the structure size relative to the length scale of the magnetic field. The plasma filament eventually decelerates due to mixing and collisional dissipation. Finally, the role of sheath dissipation is investigated. When included in the simulations, it significantly reduces the radial velocity of isolated filaments. The results are discussed in the context of convective transport in scrape-off layer plasmas, comprising both blob-like structures in low confinement modes and edge localized mode filaments in unstable high confinement regimes.

Proposed model for Saturn's auroral response to the solar wind: Centrifugal instability model

We present a model of Saturn's global auroral response to the solar wind as observed by simultaneous Hubble Space Telescope (HST) auroral images and Cassini upstream measurements of the solar wind taken during the month of January 2004. These observations show a direct correlation between solar wind dynamic pressure and (1) auroral brightening toward dawn local time, (2) an increase of rotational movement of auroral features to as much as 75% of the corotation speed, (3) the movement of the auroral oval to higher latitudes, and (4) an increase in the intensity of Saturn Kilometric Radiation (SKR). Our model, referred to as the centrifugal instability model, provides an alternative to the reconnection model of Cowley et al. (2004a, 2004b, 2005); we suggest the above observations result from Saturn's magnetosphere being a fast rotator. Since the torques on Saturn's outer magnetosphere are relatively low, its outer magnetosphere will tend to conserve angular momentum. When compressed on the dayside, the outer magnetosphere spins up to higher angular velocities, and when it expands, the outer magnetosphere spins down to lower angular velocities. This response occurs since Saturn's ionosphere is unable to enforce corotation. The outer boundary of the plasma sheet at L ∼ 15 is identified as the primary source location for the auroral precipitating particles. Enhanced wave activity, which can precipitate the auroral producing particles, may be present at this boundary. If radial transport is dominated by centrifugally driven flux tube interchange motions, when the magnetosphere spins up, outward transport will increase, and the precipitating particles will move radially outward (since the radial gradient in electron energy flux is negative). This mechanism will cause the auroral oval to move to higher latitudes as observed. The Kelvin‐Helmholtz instability may contribute to the enhanced emission along the dawn meridian, as observed by HST, via enhanced wave activity and corresponding charged particle precipitation.

Two-dimensional convection and interchange motions in fluids and magnetized plasmas

In this contribution some recent investigations of two-dimensional thermal convection relevant to ordinary fluids as well as magnetized plasmas are reviewed. An introductory discussion is given of the physical mechanism for baroclinic vorticity generation and convective motions in stratified fluids, emphasizing its relation to interchange motions of non-uniformly magnetized plasmas. This is followed by a review of the theories for the onset of convection and quasi-linear saturation in driven-dissipative systems. Non-linear numerical simulations which result in stationary convective states reveal the process of laminar scalar gradient expulsion, leading to the formation of temperature plumes and vorticity sheets. These dissipative structures are demonstrated to result in temperature profile consistency and power law transport scaling far from the threshold. The last part of this paper deals with the generation of differential rotation by fluctuating motions through tilting of the convective structures. The role of kinetic energy transfer and shearing due to differential advection is pointed out. Numerical simulations for strongly driven systems reveal turbulent states with a bursty behaviour of the fluctuation level which is associated with relaxation oscillations in the kinetic energy of the azimuthally mean flows. This leads to a state of large-scale intermittency manifested by exponential tails in the single-point probability distribution function of the dependent variables. The global bursting is interpreted in terms of a predator–prey regulation from the point of view of energetics. Finally, a discussion is given of the relevance of these phenomena to a variety of magnetized plasma experiments.

Convective instabilities in the plasmasphere

According to observations, the averaged slope of the equatorial plasma density distribution is nearly constant ( d ln n / d L = - 0.724 ) during very quiet geomagnetic activity from L = 2 to L > 7 , and even smaller ( d ln n / d L = - 1.5 ) during more typical quiet activity. These slopes are steeper than the threshold values for which magnetostatic plasma density distributions in the equatorial regions become unstable with respect to transverse and translational interchange motion in the Earth's gravitational and magnetic fields. When the effects of a centrifugal force due to corotation of the plasma with the angular velocity of the Earth are taken into account, these convective instability thresholds are significantly affected, at least in the vicinity of and beyond geosynchronous orbit. Nevertheless, for L < 6.6 , neither instability criterion is satisfied (i.e. corotating plasma should be convectively stable inside geosynchronous orbit) for the observed density slope as well as for that corresponding to a rigidly corotating plasmasphere in magnetostatic equilibrium. This conclusion holds under the assumption that the unperturbed magnetic field lines are straight (i.e. not curved, as are geomagnetic field lines). However, this assumption is not realistic and the effects associated with the magnetic curvature are largely dominant over the effects of the effective gravity in the equatorial regions of the plasmasphere and of the magnetosphere in general. When the effect of magnetic field tension (due to the curvature of the dipole magnetic field lines, and B-field gradient) is properly taken into account, the thermal plasma confined in the Earth's dipole magnetic field cannot remain in magnetostatic equilibrium but becomes convectively unstable for smaller L, i.e. much deeper inside the equatorial plasmasphere. In other words, the equatorial region of the plasmasphere becomes convectively unstable at much lower altitudes when the curvature of dipole magnetic field lines is taken into account. Thus the existence of a plasmaspheric wind is supported by our theoretical result: i.e. the equatorial plasmasphere is not in magnetostatic/barometric/diffusive equilibrium, but is convectively unstable at L = 2 and beyond. The picture of a static equatorial plasmasphere seems to be at odd, even in a saturated stage following a long period of quiet geomagnetic conditions.

Mechanism and scaling for convection of isolated structures in nonuniformly magnetized plasmas

Large-scale radial advection of isolated structures in nonuniformly magnetized plasmas is investigated. The underlying mechanism considered is due to the nonlinear evolution of interchange motions, without any presumption of plasma sheaths. Theoretical arguments supported by numerical simulations reveal an inertial scaling for the radial velocity of isolated structures in the ideal limit. This velocity increases as the square root of the structure size relative to the length scale of the magnetic field. The magnitude of the radial advection velocity, as well as the dynamical evolution of the structures, compares favorably with recent experimental measurements of radially propagating blob structures in the scrape-off layer of magnetically confined plasmas.

Self-organization observed in numerical simulations of a hard-core diffuse Z pinch

A hard-core Z-pinch plasma (metal conductor on axis) with an unstable pressure profile can rearrange itself through m=0 interchange motions to produce a stable pressure profile. In this paper the self-organization process is demonstrated in numerical simulations of an experimental plasma formation process, using a two-dimensional compressible two-fluid magnetohydrodynamic code. The stabilization process results in m=0 turbulence, which has a level of kinetic energy that is saturated typically at a few percent of the plasma thermal energy. Using idealized initial conditions for simulations with an axial sinusoidal density perturbation, it is possible to observe in detail the development of instability and then turbulence. At first a coherent Rayleigh–Taylor type motion grows exponentially, with localized isentropic heating and cooling associated with the motion. Then the bubble and spike structure breaks up and incoherent m=0 turbulence develops.

Line assignments and global analysis of the tunneling–rotational microwave absorption spectrum of dimethyl methylphosphonate

Line assignments were carried out for about 600 Fourier-transform microwave transitions for dimethyl methylphosphonate involving levels of all six symmetry species in the G 18 molecular symmetry group appropriate for three large-amplitude motions and covering J and K values of 1 ⩽ J ⩽ 6 and 0 ⩽ | K | ⩽ 3 . The assignments are based on combination–difference loops, variations in line shape for different symmetry species caused by the small internal-rotor splitting patterns of the third, high-barrier methyl top, and agreement with theoretically expected positions. A global fit of 609 lines to a phenomenological tunneling–rotational Hamiltonian with 54 constants was performed, yielding a standard deviation of 8.0 kHz, which is close to the experimental measurement uncertainty. The A/ E tunneling splitting for the lowest barrier methyl group internal rotation motion was determined indirectly to be about 34 GHz. The much smaller tunneling splitting for the methoxy interchange motion was determined (with some assumptions) to be 3.3 MHz.

Application of Permutation–Inversion Group Theory to the Interpretation of the Microwave Absorption Spectrum of Dimethyl Methylphosphonate

The G36 permutation–inversion group theoretical tunneling–rotational formalism originally developed for the methanol dimer has been modified (for the subgroup G18) and extended (to the larger group G54) for application to dimethyl methylphosphonate, CH3P(O)(OCH3)2, which has three large-amplitude methyl top internal rotation motions and one large-amplitude methoxy interchange motion. Energy levels of this chiral molecule are conveniently labeled by symmetry species corresponding to a mixed set of irreducible and reducible representations of G18 denoted by A1, A2, E, E1sep, E2sep, and Gsep. The separably degenerate species (with subscript sep) consist of pairs of irreducible representations of G18 whose energies are degenerate for Hamiltonians invariant to time reversal. All characters of these separably degenerate representations are real. Comparison of the group-theoretically derived splitting patterns with Fourier transform microwave and ab initio results from the preceding paper permit drawing a semiquantitative energy level diagram showing how a given Ka=0 level splits into A1⊕A2⊕2E⊕E1sep⊕E2sep⊕2Gsep components when the large-amplitude motions are turned on in the following order: (i) low-barrier methyl top internal rotation, (ii) medium-barrier methyl top internal rotation, (iii) top–top interaction, and (iv) methoxy interchange motion. (Internal rotation of the high-barrier methyl top is ignored.) Spectral splitting patterns observed for Ka=1–1 transitions are also quite regular, being either the same as, or mirror images of, the Ka=0–0 patterns. Theoretical work on Ka>0 splitting patterns is in progress.

Survey of thermal ions in the Io plasma torus with the Galileo spacecraft

The densities, temperatures, and bulk flow velocities are reported for a series of six passages of the Galileo spacecraft through Io's torus in Jupiter's magnetosphere. These observations were gained with the plasma analyzers on December 7, 1995, and July 1–2, August 12, September 14, October 11, and November 25, all of the latter in 1999. These plasma analyzers provided high‐resolution measurements of the energy/charge (E/Q) spectra of the three‐dimensional velocity distributions of the thermal ions that included determinations of the mass/charge (M/Q) of the primary ions with a mass spectrometer. The four dominant ions in the hot torus were two populations of ions with M/Q = 16 and two smaller populations with M/Q = 8 and 32, respectively. The identification of these four ions was based upon a best fit to the E/Q spectra of the measured three‐dimensional ion velocity distributions. The two distributions with M/Q =16 were characterized by two different temperatures, in the ranges of 20 to 30 eV and 60 to 80 eV, respectively. On the basis of expectations of higher temperatures with higher masses for the pickup ions the cooler population is identified as O+, and the hotter as S++. The two smaller populations with M/Q = 8 and 32 are identified as O++ and S+, respectively. The temperatures were ∼20 eV for the O++ and 60 to 80 eV for the S+. The densities and temperatures of the ions in the hot torus remained constant during the period July through November 1999. However, the ion densities during the initial passage on December 7, 1995, were greater by factors of ∼3, which support the presence of long‐term density variations of the torus plasmas but with relatively small fluctuations in the temperatures. A complete survey of System III longitudes was acquired with the set of six passages. The presence of an “active sector” at longitudes in the approximate range of 180° to 230° as originally found with remote observations of the torus brightnesses is confirmed with these Galileo measurements. In addition, further evidence for the importance of interchange motions for radial plasma transport was also evident in several of the Galileo passages, a dynamical process which was first identified in fields and particles measurements during the first passage through the torus on December 7, 1995. A persistent lag with an average in the range of ∼2 to 4 km/s in the azimuthal flows relative to that for rigid corotation was detected and supports the previously proposed System IV coordinate system that has a slightly slower rotation rate relative to that for System III.

Quasi‐interchange modes and interchange instability in rotating magnetospheres

Adopting the widely held view that plasma transport in rotating magnetospheres, like those of Jupiter and Saturn, proceeds through the interchange of magnetic flux tubes, we study the physical characteristics and stability properties of interchange motions. We start by examining a broader category of motions containing all the modes driven by buoyancy forces of gravitational or magnetic nature; these modes, known as quasi‐interchanges, fall into two types: type 1, to which the familiar interchange mode belongs, and type 2, in which the plasma moves essentially along magnetic field lines. In the second part of the paper, we focus on the interchange mode, with the purpose of deriving formal analytical expressions for both its dispersion relation and its stability threshold.

Observations of plasmas in the Io torus with the Galileo spacecraft

On December 7, 1995, the Galileo spacecraft passed through the Io torus near the magnetic equatorial plane of Jupiter. High– resolution measurements of positive ions and electrons in the energy/charge (E/Q) range of 0.9 V to 52 kV were acquired over the jovicentric radial distances of 5.6 to 7.8 Rj. At radial distances beyond Io's orbit at 5.9 Rj the plasma instrument (PLS) observed intense magnetically field‐aligned beams of electrons with average energies of hundreds of eV to several keV. The directional energy fluxes at the spacecraft position ranged from ∼1.5 to 90 erg cm−2S−1sr−1 in directions parallel and antiparallel to the magnetic field. The corresponding range of energy fluxes into Jupiter's ionosphere was ∼9 to 560 erg Cm−2s−1, sufficient for the production of auroral emissions at far‐ultraviolet wavelengths with brightnesses in the range of 0.06 to 3 mega‐Rayleighs. The largest energy fluxes were observed at ∼7.8 Rj and were comparable to those observed during the close flyby of Io. The torus plasmas were observed to rigidly corotate with Jupiter out to a radial distance of ∼7 Rj and are slower at greater radial distances. Fluctuations of the bulk ion speeds and densities were found to be superposed upon the general pattern of corotation and are suggestive of interchange of magnetic flux tubes in the plasma torus. For an isolated field‐aligned electron beam, the radial component of plasma flow was directed toward Jupiter at a speed of ∼4 km s−1. The other electron beams also occurred coincidentally with the fluctuations in the radial component of flow. The observations of these low‐energy electron beams are consistent with the absence of magnetically field‐aligned acceleration of electrons into Jupiter's ionosphere. The electron acceleration appears to be due to intense heating of the ionospheric plasmas associated with large currents driven by the interchange motions in the torus plasmas.

Magnetic Flux Accumulation at the Galactic Center and Its Implications for the Strength of the Pregalactic Magnetic Field

We study the inflow of disk gas toward the Galactic center during the lifetime of the Galaxy and its effect on magnetic field lines frozen-in to the interstellar plasma. While compression leads to a large amplification of the "vertical" magnetic field (pointing perpendicular to the disk), ambipolar diffusion efficiently removes from the disk magnetic flux components oriented parallel to the Galactic plane. Turbulent interchange motions of nearly parallel vertical field lines at the Galactic center enhance the efficiency of magnetic reconnection of neighboring regions of oppositely directed vertical field. This suggests that the sign of the present-day vertical field at the Galactic center is uniform. If the Galactic-center field originates in the entrainment of a pregalactic field B0 in radially inflowing interstellar plasma, then observations of the vertical flux through the central 200 pc of our Galaxy yield a measure of the pregalactic field that depends on the total mass accreted into the central 200 pc during the Galaxy's lifetime. If this mass is 3 × 109 M☉ and if the surface density of disk gas is roughly constant over the lifetime of the Galaxy, then B0 ≳ 2 × 10-7 G, regardless of the angle of the pregalactic field with respect to the Galactic plane. The abundance of mechanisms for radial accretion of disk gas suggests that strong magnetic fields should be a generic feature of the centers of spiral galaxies. We also note that cosmic-ray confinement in the strong vertical field at the Galactic center is expected to be poor.

Magnetohydrodynamic waves and gravitational/centrifugal instability in rotating systems

Interchange motions of magnetic flux tubes are customarily regarded as one of the main contributors to radial plasma transport in planetary magnetospheres, particularly in those magnetospheres, like the Jovian and Saturnian ones, where the centrifugal force is known to play an important role. However, so far, interchange motions have been treated only under a variety of simplifying assumptions which are not always justified. In this paper, we present a rigorous treatment of the interchange instability within the broader context of magnetohydrodynamic waves. After reviewing the existing work on the magnetospheric interchange instability, we derive the full wave equation for magnetohydrodynamic perturbations in the presence of external forces, magnetic field curvature, and overall rotation, and we proceed to a detailed examination of their dispersion relation and stability condition in the one‐dimensional case when the equilibrium parameters vary in a single direction normal to the magnetic field. We then focus on the so‐called “quasi‐interchange” modes, which, by definition, represent all the modes driven by gravitational or magnetic buoyancy (or a combination of both), including, in particular, the interchange mode. We demonstrate that they leave the total pressure virtually unchanged, slightly perturb the plasma density and the magnetic field, and generally give rise to motions both perpendicular and parallel to the background field lines.

Centrifugally driven instability of a rotationally dominated magnetodisc

The dynamics of a rorationally dominated magnetodisc is considered on the basis of linearized MHD. The treatment is prompted by the concern that the dominant theoretical view on this subject is based on the reduced framework of interchange motion, in which changes in magnetic field are suppressed. A realistic perturbation of a magnetodisc generally does not satisfy this constraint, and the changing magnetic field is expected to stabilize any small‐amplitude perturbation. We reexamine the problem in an idealized slab magnetodisc geometry but with dynamical terms fully installed in the MHD equations. We find that the traditional interchange instability, essentially a centrifugal buoyancy regulated by the ionosphere, is not a proper solution for a thin magnetodisc. For short‐wavelength modes the actual situation of instability comes to resemble what is known in the literature as magnetic buoyancy, i.e., a centrifugally driven motion moderated by the strong local magnetic field. Physically, the instability results as the rotational effects couple the Alfvén and slow modes; density perturbations formed by the latter are in turn driven radially by centrifugal buoyancy. The instability is manifest even for a perfectly uniform density distribution and for the characteristic parameters near the Io torus, dominates over the contribution from a radial density gradient. The theory of centrifugally driven radial diffusion is considered with this instability as the mechanism of eddy formation. This consideration gives a mass transport rate of ∼ 103 kg/s and a density profile n ∼ L−4 near the Io torus, both in good agreement with observations. Further computational works need to be carried out to compare our model with more detailed in situ observations.

The Nitric Acid−Water Complex: Microwave Spectrum, Structure, and Tunneling

Eight isotopic derivatives of the complex HNO3−H2O have been observed by microwave spectroscopy. The spectra are consistent with a structure in which the nitric acid forms a near-linear, 1.78 Å hydrogen bond to the oxygen of the water. A second, presumably weaker hydrogen bond is formed between a water hydrogen and one of the HNO3 oxygens. The resulting cyclic structure adopts a planar configuration except for the non-hydrogen bonded proton of the H2O. In complexes containing DOH, only the isomer with the deuterium in the plane is observed, confirming the contribution of the secondary O···H interaction to the overall stabilization of the system. Strong evidence for complex internal dynamics involving the water subunit is also presented. The a- and b-type transitions of the H2O and D2O containing species exhibit a doubling which disappears in the DOH complex, providing direct evidence for the existence of a proton interchange motion in the system. Moreover, c-type rotational transitions do not appear at their predicted rigid rotor positions, even for the DOH species, providing indirect evidence for a second motion which is interpreted as a large amplitude wagging of the non-hydrogen bonded proton of the water.

Coriolis influences on the interchange instability

Previous treatments of rotationally driven interchange motion assume rigid corotation and incorporate centrifugal force into an effective gravity. When the ionospheric acceleration time is short, this approximation is acceptable, but in remote regions of the Jovian magnetosphere, the constraining influence of the ionosphere is increasingly ineffective. Conservation of angular momentum then governs local dynamics, and the Coriolis force is an essential part of the perturbation analysis. If the ionosphere is absent, the result agrees with earlier studies of magnetized Couette flow. If the ionosphere is merely very ineffective, the interchange criterion is not changed, but the instability growth rate is significantly reduced from earlier calculations.

Enhanced whistler‐mode emissions: Signatures of interchange motion in the Io torus

During the Galileo inbound pass through the Io torus the plasma wave instrument detected intervals of enhanced whistler‐mode emissions. Over two of these intervals in the inner torus (L &lt; 6.5), for which energetic particle data is also available, the flux and pitch angle anisotropy of resonant electrons exhibited a simultaneous enhancement consistent with inward adiabatic transport from a source region in the outer torus. The enhanced electromagnetic emissions are interpreted as a modulation of cyclotron whistler‐mode instability above the normal marginally stable state of the plasma. This suggests that the enhanced emissions are a sensitive indicator of rapid inward transport associated with interchange motions in the Io torus.

Galileo evidence for rapid interchange transport in the Io torus

Anomalous plasma signatures were detected by the Galileo particles and fields instruments during the initial transit through the Io torus. These unusual events are characterized by abrupt changes in the magnetic field, enhanced levels of broadband low frequency electromagnetic waves and a pronounced change in both the flux and pitch angle anisotropy of energetic particles. Here we present a coordinated study of one of the events which occurred near 6.03RJ just after 17:34 UT on December 7, 1995. The available data are consistent with the concept of rapid inward transport, and this is interpreted as the first evidence for the predicted interchange motions in the region exterior to the orbit of Io. Theoretical arguments indicate that the interchanging flux tube is characterized by substantially reduced plasma density, a spatial scale comparable to 10³ km, and an inward radial velocity comparable to 10² km/s.

A note on the interchange stability criterion

The correct stability criterion of interchange motions in the magnetosphere has been a question of some controversy. Many researchers hold the view first espoused by Gold [1959]. For a low‐β plasma in a dipole magnetic field, Gold argued that the gradient of pVγ, where p is the plasma pressure, V is the unit flux tube volume, and γ is the adiabatic polytropic index, determines the interchange stability. This notion was further developed by Chandrasekhar [1960]. This common belief was questioned by Cheng [1985], who was subsequently questioned by Rogers and Sonnerup [1986] and Southwood and Kivelson [1987] on the issue. Is Gold's criterion the necessary and sufficient condition for interchange stability? We shall demonstrate that the answer is “no” and provide a more accurate criterion for the dipole magnetic field. We shall also discuss the interchange instability in a plasma distribution with a longitudinal gradient.

Effect of Hall conductivity on time‐dependent convection

Magnetospheric convection can be seen as a form of interchange motions, but unlike in an ideal MHD system, is subject to the ionospheric boundary condition. For general time‐dependent interchanges, the Hall current in the ionosphere generates a field‐aligned current independent of any background gradients. The effect of the Hall conductivity on time‐dependent convection is isolated through a simple box model where pressure gradient and field line curvature are suppressed. Mathematical analysis suggests that the Hall conductivity can destabilize interchange modes with long longitudinal wavelength. The finding comes at the expense of a high degree of geometrical idealization. More realistic computations are needed to test the theory.