Flux Tube Volume Research Articles

Particle drift and loss rates under strong pitch angle diffusion in Dungey's model magnetosphere

Strong pitch angle diffusion so thoroughly randomizes the first two adiabatic invariants of charged‐particle motion that it conserves (as a first approximation) the surrounded phase space volume Λ ≡ p3Ψ0, where Ψ0 = ∮(ds/B) is the flux tube volume per unit magnetic flux and p is the common scalar momentum of the particles involved. (This conservation law is widely used in plasma physics. Its nonrelativistic form is usually derived from the adiabatic gas law but is not really a “fluid” result. Since the conservation law does not couple particles with different energies in the same flux tube, such particles can have different values of Λ.) Here the flux tube volume Ψ is computed for selected field lines in Dungey's model magnetosphere (dipole moment μE ≈ −30.2 μT−RE3 plus uniform southward ΔBz ≈ −9.0 COS6Λ* μT, Λ* being the invariant latitude of the quiet time auroral oval, which maps outward to a circular neutral line at radial distance b = (μE/ΔBz)1/3 in the equatorial plane). The integral ∮(ds/B) is fitted within 0.2% at all L values by the expression Ψ0 ≈ (L4a4/μE){(32/35) − [2.045 + 1.045(r0/b)3 + 0.095(r0/b)6 + 0.075(r0/b)9] ln [1−(r0/b)3]}, where r0 (equatorial radius of the field line) is obtained by solving the cubic equation (r0/b) = (La/b)[1 + (1/2)(r0/b)3]. The particle lifetime τ against strong pitch angle diffusion is given in turn by τ ≈ [4ΨBnBs/(Bn + Bs)(1 – η)](m/p), where Bn and Bs (which can differ in an offset‐dipole field model) are the field intensities at the northern and southern foot points of the field line, m is the relativistic mass, and η is the backscatter coefficient. The same expression for Ψ thus enters both the quasi‐adiabatic Hamiltonian (to whose derivative with respect to 1/L the ensemble‐averaged gradient‐curvature drift rate is directly proportional) and the particle loss rate 1/τ (by which the phase space density ƒ = J4π/4πp2 is exponentially attenuated along the ensemble averaged drift trajectory). This construction provides a means of numerically simulating kinematical aspects of electron motion in the outer magnetosphere and precipitation in the diffuse aurora, as well as ion motion in part of the plasma sheet (regarded as a source of the ring current). Its use in magnetospheric plasma simulations should save computer time and reveal analytical structure relevant to magnetospheric dynamics.

Azimuthal hot plasma pressure gradients and dawn-dusk electric field formation

Abstract The effects of hot plasma pressure gradients in the high latitude magnetosphere are analysed. It is shown that such a mechanism may in fact be responsible for Region 1 field-aligned currents and for the dawn-dusk electric field. The estimated azimuthal gradients in the plasma pressure may account for the observed field-aligned currents and also give the opportunity to determine the day-night plasma pressure changes along isosurfaces of magnetic flux tube volume. These pressure changes are then compared with experimentally measured pressure distribution and it is shown that the day-night plasma change, in the high latitude magnetosphere, may be high enough to sustain Region 1 currents. The closure of these currents in the high latitude magnetosphere may in turn be responsible for the dawn-dusk electric field and the dawn-dusk potential drop in the inner plasma sheet regions. The influence of the IMF on the magnetostatically equilibrium inner magnetospheric currents may qualitatively explain the IMF control of the dawn-dusk electric field and magnetospheric activity.

The inner magnetosphere source of dawn-dusk electric field and magnetospheric dynamics

The qualitative theory of the formation of inner magnetosphere dawn-dusk electric field based only on the assumption of the magnetostatic equilibrium in the asymmetric plasma trap was developed. The theory associates the generation of Region 1 field-aligned currents with the topology of magnetic field in the transition region where the magnetic field lines change from dipolar in the deep inner magnetosphere to stretched in the magnetotail. The mechanism of the plasma pressure gradients can be used to explain qualitatively the inner magnetosphere source of dawn-dusk electric field and the dynamics of substorm electric fields and currents. The antisunward stretching of the magnetic flux tube volume isolines in the equatorial plane during substorm growth phase brings to the increase of Region 1 field-aligned currents formed by the azimuthal plasma pressure gradients. The disruption of the cross-tail current and the dipolarization of the magnetic field lines causes the increase of magnetic flux tube volumes in the limited plasma sheet region. That makes possible to explain the formation of the nighttime pressure hole and the substorm current wedge.

Formation of density troughs embedded in the outer plasmasphere by subauroral ion drift events

A dynamic global core plasma model (DGCPM) is used to investigate the effects of subauroral ion drift (SAID) events on the formation of trough density profiles in the outer plasmasphere during periods of high magnetic activity. The DGCPM includes the influences of convection on the changing flux tube volumes, as well as daytime refilling and nighttime draining of plasma, to calculate the plasma tube contents and equatorial plasma density distribution versus time throughout the magnetosphere. SAIDs are regions of latitudinally narrow westward flow of plasma equatorward of the auroral zone. We present DGCPM results for various presumed SAID locations and durations relative to enhanced substorm convection onset and decay, to parametrically elicit the formation of plasmaspheric density trough structures resulting from SAID effects. It is found that imposing a SAID event in the dusk‐evening sector for 30 min leads to the formation of a narrow (less than 1 RE near the equatorial plane) embedded plasma density trough in the dusk bulge region. The modeled plasmasphere density profiles with troughs generally resemble plasmasphere density profiles observed from DE 1 measurements.

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.

Details of current disruption and diversion in simulations of magnetotail dynamics

Properties of current disruption and diversion are investigated on the basis of resistive MHD simulations which include the inner tail region with the transition toward a dipole field and the dynamic formation of a thin current sheet in the inner tail. As in earlier simulations, magnetotail instability leads to reconnection and plasmoid formation and ejection, accompanied by features of the substorm current wedge. In contrast to earlier simulations of the breakup of a thick current sheet, the presence of the thin current sheet leads to a much faster evolution on the timescale of few minutes and to larger electric fields (up to 20 mV/m), concentrated mostly in the dipolarizing region earthward of the reconnection site. The fast growth is relatively insensitive to the resistivity model used. The current “disruption” is largely a consequence of an expansion of the near‐Earth current sheet, associated with the dipolarization. It starts well earthward of the reconnection site in association with a pileup of magnetic flux and propagates tailward. Field‐aligned currents of region 1 type (toward the Earth on the dawnside and away on the duskside) at the near‐Earth boundary are found to increase both during the driven phase of the thin current sheet formation and during the energy release and current disruption phase. They result from a diversion of perpendicular into parallel currents, which is associated with a gradient of the magnetic flux tube volume directed away from midnight at the flank edges of the dipolarization region. Locally, the current diversion takes place earthward of the reconnection site, predominantly in shear layers above and below the neutral sheet rather than close to the neutral sheet. The peaks of the field‐aligned current densities associated with the substorm wedge do not follow field lines very closely, because of the presence of strong perpendicular currents, so that care must be taken in using these features for a mapping between the Earth and the equatorial plane.

On the selection of a coordinate system for high latitude radiation

A preliminary analysis of the question about selection of a coordinate system for studies of high latitude processes in the Earth's magnetosphere is given. Calculations of magnetic flux tube volumes, W, based on the empirical Tsyganenko (1987) model were made for geomagnetic latitudes exceeding 50°, with different K p-values. The equal volume magnetic flux tube isolines and angle coordinate isolines were mapped in the dipole geomagnetic coordinate system. The changes of isoline shapes were considered corresponding with changes of the geomagnetic disturbance level.

On the formation of electric fields and currents in the three-dimensional magnetosphere

One of the main still unresolved problems of the Earth's magnetosphere physics is the problem of dawn-dusk electric field formation and interplanetary magnetic field ( IMF) control of its value. Analyzing the configuration of magnetic flux tube volume isosurfaces and tail current distribution it became possible to show that the existence of azimuthal plasma pressure gradients and thus field-aligned currents is the intrinsic property of magnetospheric trap connected with its day-night asymmetry. The IMF control of Region I currents can be explained by IMF control of magnetopause and tail currents.

The magnetostatic equilibrium in high latitude magnetosphere and the selection of coordinate system for high latitude processes description

The coordinate system employing isosurfaces of magnetic flux tube volume as the coordinate surfaces was used for the reconstruction of azimuthal magnetospheric plasma pressure gradients on a basis of the data of large scale field aligned currents distribution and the Tsyganenko magnetic field models. The integral plasma pressure changes are compared with the satellite measurements of plasma pressure. It was shown that Region I and Region II currents can be maintained by azimuthal hot plasma pressure gradients. The localization of the Region I currents in the inner magnetosphere creates the mechanism of dawn-dusk electric field formation which does not require the reconnection or viscous interaction of the solar wind with the magnetosphere.

Formation of thin current sheets in a quasistatic magnetotail model

Observations suggest that thin current sheets forming in the near‐Earth magnetotail late in substorm growth phases may be a crucial part of substorm evolution. In a simple theoretical model the current density was shown to become singular for suitable external perturbations. Here, we address the same problem in a more realistic model based on the adiabatic MHD ‐ theory developed by Schindler and Birn [1982]. We show that under suitable conditions the formation of a thin current sheet in the near‐Earth tail is an intrinsic aspect of flux transfer to the magnetotail. The mechanism is based on the strong variation of flux tube volume with the magnetic flux function.

Particle drift in the Earth's plasma sheet

We generalize the derivation of the average gradient/curvature‐drift for a flux tube filled with an isotropic distribution of particles at specified kinetic energy. The present treatment is restricted to a two‐dimensional magnetic field with zero electric field, but it includes all chaotic and Speiser orbits, which do not correspond to the simple picture of gradient/curvature drift. We assume that particles are evenly distributed throughout the regions of phase space allowed by their energy and canonical momentum. This assumption is closely related but not exactly equivalent to the assumption of isotropic pitch‐angle distribution. Our derivation assumes that the maximum Larmor radius is small compared to the scale length for equatorial variations in the flux tube volume, but it does not involve any restrictions on the curvature of the field line. The resulting expression for the drift rate is valid for situations where the particle drift velocity is comparable to the thermal speed in some regions. The apparent implication of this generalized treatment is that the existence of very complex non‐adiabatic particle trajectories in the plasma sheet may not invalidate previous estimates of the average rate of particle drift out the sides of the tail, estimates that were made under the assumption of simple guiding‐center drifts.

Plasma convection and ion beam generation in the plasma sheet boundary layer

Because of the dawn‐dusk electric field Edd, plasma in the magnetotail convects from the lobe toward the central plasma sheet (CPS). In the absence of space or velocity diffusion due to plasma turbulence, convection would yield a steady state distribution function ƒ = V−2/3 g(υ²V2/3), where V is the flux tube volume. Starting with such a distribution function and a plasma beta which varies from β > 1 in the CPS to β ≪ 1 in the lobe, we study the evolution of the ion distribution function considering the combined effects of ion diffusion by kinetic Alfvén waves (KAW) in the ULF frequency range (1–10 mHz) and convection due to Edd×B drift in the plasma sheet boundary layer (PSBL) and outer central plasma sheet (OCPS). Our results show that during the early stages after launching the KAWs, a beamlike ion distribution forms in the PSBL and at the same time the plasma density and temperature decrease in the OCPS. Following this stage, ions in the beams convect toward the CPS resulting in an increase of the plasma temperature in the OCPS. We also discuss the effects on the polytropic index γ by simultaneous convection and wave‐induced diffusion, both in the PSBL and CPS. We find that γ is less than the adiabatic value in the OCPS but approaches the adiabatic value in the CPS and in the PSBL.

Ionospheric outflow of plasma and compression relationship in the plasma sheet

We are concerned in this article with the curious finding of Huang et al. [1989] which suggests a polytropic index of plasma compression of about 0.7 in the quiet time central plasma sheet. We show that the reduction of this index from its adiabatic value (=5/3) can be achieved through an ionospheric outflow of plasma which lowers the plasma temperature by virtue of energy partition. The observed correlation between the plasma temperature and density is best reproduced by an ionospheric source of ∼5×1025 ions/s, consistent with independent experinental estimates and smaller than the average solar wind source by a factor of two or more. Despite the change in the polytropic relationship, we find that the global energy equation PV5/3=constant (V=volume of a unit flux tube) still holds approximately (in the absence of other energy‐loss mechanisms).

Distributions of He+ at middle and equatorial latitudes during solar maximum

Observations of ionospheric composition made by DE 2 in the mid‐latitude ionosphere, show that during the solar maximum period of 1981, at altitudes near 900 km during the nighttime, the dominant light ion species is He+. Conditions may arise in which He+ is the dominant ion species, exceeding the O+ concentration by a factor of 2. This observation is contrasted by those at the same altitude near the dip equator. Here a deep minimum in the He+ concentration accompanies observed maxima in the O+ and H+ concentrations and O+ is always the major ion species. Calculations are used to illustrate that the distribution of neutral species at solar maximum, together with the appropriate ionization rates can easily account for the dominance of He+ at mid‐latitudes. The relative abundance of the ionospheric species is a sensitive function of local time and the associated evolution of the topside O+ concentration profile. Factors such as E×B drift may easily effect the precise nature of the observation. At the dip equator the existence of an E×B drift motion of the plasma is required to explain the He+ minimum. Here the E×B drift is such that plasma observed near 900 km during the night, has resided at altitudes below 600 km during the day. Thus the He+ concentration is only that which is produced in one day against the chemical loss process. This is contrasted with the situation at mid‐latitudes where the large flux tube volume provides a reservoir in which the He+ can accumulate each day.

Representations of currents and magnetic fields in isotropic magnetohydrostatic plasma

We develop the theory describing electric currents in magnetized plasma for the case of static equilibrium with isotropic pressure. The current density is determined by pressure balance and charge conservation. We show that the current density can be expressed as the sum of the current density determined by plasma pressure gradients, Jp = c▽F × ▽P, and the force‐free current density, Jf = gB, where F = ∫ ds/B is the flux tube volume per unit flux measured from a surface at which the normal component of Jp vanishes, P is the scalar pressure, and g is a field line constant. The expression explicitly satisfies charge conservation, and its perpendicular component is the usual perpendicular current density. In the absence of force‐free currents, J is a curl; in this case it is possible to introduce a magnetic scalar potential, ψ, that satisfies the equation ▽²ψ = −4π▽ · P▽F; the magnetic field can then be determined from B = −▽ψ −4πP▽F.

Plasma pressure in the environment of Jupiter, inferred from Voyager 1 magnetometer observations

A spherical harmonic model of Jupiter's planetary magnetic field is combined with a self‐consistent model of the Jovian magnetodisc. The sets of parameters of both models are determined simultaneously by using a generalized inverse technique. Assuming that the pressure P in the middle (and outer) magnetosphere is related to the unit flux tube volume V through PVγ = const, the fit yields a value of 0.88 for γ. If the hot (30 keV) plasma is transported adiabatically inward under the interchange instability triggered by the centrifugal force of the heavy torus ions, losses are not sufficient to account for such a low value of γ beyond L = 10 (as compared to γ ≈ 5/3 that would be expected for adiabatic transport of monoatomic gas). Closer to the planet, as the outer edge of the Io plasma torus is approached (at distances between 7 and 9 RJ from Jupiter), PVγ is found to decrease inward, as expected from the particle measurements, which identified an inner boundary of the particle fluxes in that region. At the magnetic equator, our pressure estimates were compared with the ones obtained from direct particle measurements (low‐energy charged particle (LECP) experiment). Assuming a mixture of O+ and H+ at the same temperature (or with the same spectral power law exponent), consistency between those two independent determinations of the pressure would require that the pressure produced by H+ constitute 18–36% (at most) of the total pressure, at distances between 13 and 21 RJ. Finally, as concerns the internal field coefficients, despite an overall consistency, a slight variability is found between the present estimates and previous ones derived from the same data set, which puts some limitation on the accuracy with which internal coefficients can be determined from the Voyager 1 encounter alone.

A numerical investigation of the formation and evolution of magnetospheric irregularities by the interchange of magnetic flux tubes

The formation and evolution of magnetospheric irregularities by interchange of tubes of force, is studied through the solution of the electron and ion heat, and ion density equations. These calculations indicate that interchange of magnetic flux tubes may cause irregularities in the ionosphere and protonosphere. Ionospheric irregularities result from disturbance of the F-layer through electrodynamic movement vertically while the protonospheric irregularities result from variations in flux tube volume. It has been found that the temperature profile plays an important role in the variation of irregularity magnitude along flux tubes and that irregularities will persist for many hours at night. After several hours a small growth of the irregularities has been observed.

Hydromagnetically Stable Periodic Magnetic Field

Results of the analysis of a class of periodic magnetic fields which have the property that the flux tube volume can decrease in the θ = 0 plane and increase in the θ = ½π plane. By symmetrizing the system with connecting regions between semistable units, closed surfaces of flux tube volume with negative gradient are obtained. Quadrupole and quadrupole-octupole stabilization is considered. Realizable current configurations are proposed for stabilizing a periodic mirror system.