Injection and acceleration of H+ and He2+ at Earth’s bow shock

We have performed a number of one-dimensional hybrid simulations (particle ions, massless electron fluid) of quasi-parallel collisionless shocks in order to investigate the injection and subsequent acceleration of part of the solar wind ions at the Earth’s bow shock. The shocks propagate into a medium containing magnetic fluctuations, which are initially superimposed on the background field, as well as generated or enhanced by the electromagnetic ion/ion beam instability between the solar wind and backstreaming ions. In order to study the mass (M) and charge (Q) dependence of the acceleration process He²⁺ is included self-consistently. The upstream differential intensity spectra of H⁺ and He²⁺ can be well represented by exponentials in energy. The e-folding energy E_c is a function of time: E_c increases with time. Furthermore the e-folding energy (normalized to the shock ramming energy E_p) increases with increasing Alfvén Mach number of the shock and with increasing fluctuation level of the initially superimposed turbulence. When backstreaming ions leave the shock after their first encounter they exhibit already a spectrum which extends to more than ten times the shock ramming energy and which is ordered in energy per charge. From the injection spectrum it is concluded that leakage of heated downstream particles does not contribute to ion injection. Acceleration models that permit thermal particles to scatter like the non-thermal population do not describe the correct physics.     

Solar wind contribution to the average population of energetic He+ and He++ ions in the Earth’s magnetosphere

Measurements with the ion charge-energy-mass spectrometer CHEM on the AMPTE/CCE spacecraft were used to investigate the origin of energetic He⁺ and He⁺⁺ ions observed in the equatorial plane at 3\leqL\leq9. Special emphasis was laid on the dependence of long-term average distributions on magnetic local time (MLT) and the geomagnetic activity index K_p. The observations are described in terms of the phase space densities f₁ (for He⁺) and f₂ (for He⁺⁺). They confirm preliminary results from a previous study: f₁ is independent of MLT, whereas f₂ is much larger on the nightside than on the dayside. They show, furthermore, that f₁ increases slightly with K_p on intermediate drift shells, but decreases on high drift shells (L\geq7). f₂ increases with K_p on all drift shells outside the premidnight sector. Within this sector a decrease is observed on high drift shells. A simple ion tracing code was developed to determine how and from where the ions move into the region of observations. It provides ion trajectories as a function of the ion charge, the magnetic moment and K_p. The ion tracing enables a distinction between regions of closed drift orbits (ring current) and open convection trajectories (plasma sheet). It also indicates how the outer part of the observation region is connected to different parts of the more distant plasma sheet. Observations and tracing show that He⁺⁺ ions are effectively transported from the plasma sheet on convection trajectories. Their distribution in the observation region corresponds to the distribution of solar wind ions in the plasma sheet. Thus, energetic He⁺⁺ ions most likely originate in the solar wind. On the other hand, the plasma sheet is not an important source of energetic He⁺ ions. Convection trajectories more likely constitute a sink for He⁺ ions, which may diffuse onto them from closed drift orbits and then get lost through the magnetopause. An ionospheric origin of energetic He⁺ ions is unlikely as well, since the source mechanism should be almost independent of K_p. There is considerable doubt, however, that a plausible mechanism also exists during quiet periods that can accelerate ions to ring current energies, while extracting them from the ionosphere. It is concluded, therefore, that energetic He⁺ ions are mainly produced by charge exchange processes from He⁺⁺ ions. This means that most of the energetic He⁺ ions constituting the average distributions also very likely originate in the solar wind. Additional ionospheric contributions are possible during disturbed periods.     

Helium isotopic ratio in Vulcano island fumaroles: temporal variations in shallow level mixing and deep magmatic supply

Intensive gas emanations occur throughout the island of Vulcano, Italy. Sharp fluctuations recorded in the crater gas composition suggest the presence of two separate volcanic reservoirs and continuous mixing with another source, “crustal” waters. This mixing differs between the beach and crater fumaroles. Gas samples from three crater fumaroles with temperatures ranging from 200 to 550 ° C were sampled repeatedly over a one year period. During the same interval of time, six samples from submarine and subaerial beach fumaroles and water well gases were also sampled. Gases from one crater fumarole (F5) showed variations of (³He/⁴He)_fumarole to (³He/⁴He)_air between 5 and 6 correlated with variations of several chemical species. High ³He/⁴He ratios for the beach fluids, similar to those of crater fluids, suggest the existence of a unique large magmatic reservoir at depth feeding both the crater and beach intermediate reservoirs. However, temporal changes clearly indicate variable degrees of fluids mixing, and the geographic distribution of the ³He/⁴He ratios as well as the chemical composition of the fluids suggest the existence between the magma reservoir and the surface of two intermediate different reservoirs, independently related to crater and to beach fumaroles.     

Secular variations of carbon and helium isotopes at Izu-Oshima Volcano, Japan

Secular variations in ¹³C/¹²C ratios and chemical compositions of gas samples from October 1986 to July 1992 are reported from a 92–95 °C steam well located about 3 km north of Mt. Mihara, an active volcano on Izu-Oshima Island, Japan. The δ¹³C value steeply increased from −2.97‰ (relative to PDB carbonate) in December 1986 to −1.15‰ in March 1988 and then gradually decreased to −1.75‰ in July 1992. Over the same period, the CO₂ content changed similarly with time, even though the experimental error is relatively large. These variations are consistent with helium isotope changes. Initially rapid and then slow enhancements of ³He/⁴He ratio, δ¹³C value and CO₂ content are invoked by violent eruptions of Izu-Oshima volcano from 15 November to 18 December 1986. After the eruptive activity, depletion of magmatic gas emission and subsequent mixing with crustal fluids in the hydrothermal system may produce the gradual decreases of ³He/⁴He ratio, δ¹³C value and CO₂ content. Taking into account the rates of these decreases, we suggest that helium and carbon isotope ratios will return to the situation of before the magmatic eruption within 15 years.     

Finite amplitude holmboe waves

Abstract

We investigate the evolution of a parallel shear flow which has embedded within it a thin, symmetrically positioned layer of stable density stratification. The primary instability of this flow may deliver either Kelvin-Helmholtz waves or Holmboe waves, depending on the strength of the stratification. In this paper we describe a sequence of numerical simulations which reveal for the first time the behavior of the Holmboe wave at finite amplitude and clarify its structural relationship to the Kelvin-Helmholtz wave.

The flows investigated have initial profiles of horizontal velocity and Brunt-Vaisala frequency given in nondimensional form by U = tanhζ and N ²=J sech² RCζ, respectively, in which ζ is a nondimensional vertical coordinate, J is the value of the gradient Richardson number N ²/(dU/dζ)² at ζ=0, and R = 3. Linear stability theory predicts that the flow will develop Holmboe instability when J exceeds some critical value J_c' and Kelvin-Helmholtz instability when J is less than J_c; J_c being approximately equal to 0.25 when R=3. We simulate the evolution of flows with J=0.9, J=0.45, and J = 0.22, and find that the first two simulations yield Holmboe waves while the third yields a Kelvin-Helmholtz wave, as predicted.

The Holmboe wave is a superposition of two oppositely propagating disturbances, a right-going mode whose energy is concentrated in the region above the centre of the shear layer, and a left-going mode whose energy is concentrated below the centre of the shear layer. The horizontal speed of the modes varies periodically, and the variations are most pronounced at low values of J. If J ζ J_c' the minimum horizontal speed of the modes vanishes and the modes become phase-locked, whereupon they roll up to form a Kelvin-Helmholtz wave as predicted by Holmboe (1962). When J is moderately greater than J_c' the Holmboe wave ejects long, thin plumes of fluid into the regions above and below the shear layer, as has often been observed in laboratory experiments, and we examine in detail the mechanism by which this occurs.     

Magnetic buoyancy instabilities incorporating rotation

Abstract

Recent calculations suggest that the bulk of the solar toroidal field may be stored in a thin, convectively stable region situated between the convection zone proper and the radiative zone. Determining the stability properties of such a field is therefore important with implications for both the generation and escape of magnetic flux. The plane layer, linear stability analysis of Hughes (1985) is extended to incorporate the effects of uniform rotation. Detailed studies are made of interchange, or “axisymmetric” modes and of undular, or wavelike, motions, considering modes of both low and high frequency. The force due to rotation acts to constrain the fluid motions, a feature which is strongly stabilizing for direct modes, but can, in certain circumstances, be destabilizing for oscillatory motions.

For the interchange modes we show that the instability discussed at length by Hughes (1985), driven by fields increasing with height, is still present and indeed may be enhanced by rotational effects. We also study the more conventional instabilities, discussing the transformation between direct and oscillatory modes and considering in detail some peculiar properties of the oscillatory instabilities.

The more relevant instabilities in an astrophysical context are likely to be undular modes. Previous studies of low frequency modes driven by top heavy field gradients are extended to consider modes of various frequencies for a wide range of parameter values. Of particular interest is the occurrence of two distinct modes of instability for bottom heavy field gradients. We also exhibit some of the peculiar stability boundaries which can result when none of the competing influences in the problem is dominant.     

The destabilising nature of differential rotation

Abstract

In a rapidly rotating, electrically conducting fluid we investigate the thermal stability of the fluid in the presence of an imposed toroidal magnetic field and an imposed toroidal differential rotation. We choose a magnetic field profile that is stable. The familiar role of differential rotation is a stabilising one. We wish to examine the less well known destabilising effect that it can have. In a plane layer model (for which we are restricted to Roberts number q = 0) with differential rotation, U = sΩ(z)1 _?, no choice of Ω(z) led to a destabilising effect. However, in a cylindrical geometry (for which our model permits all values of q) we found that differential rotations U = sΩ(s)1 _? which include a substantial proportion of negative gradient (dΩ/ds ≤ 0) give a destabilising effect which is largest when the magnetic Reynolds number R _m = O(10); the critical Rayleigh number, Ra _c, is about 7% smaller at minimum than at R_m = 0 for q = 10⁶. We also find that as q is reduced, the destabilising effect is diminished and at q = 10^?6, which may be more appropriate to the Earth's core, the effect causes a dip in the critical Rayleigh number of only about 0.001%. This suggests that we see no dip in the plane layer results because of the q = 0 condition. In the above results, the Elsasser number A = 1 but the effect of differential rotation is also dependent on A. Earlier work has shown a smooth transition from thermal to differential rotation driven instability at high A [A = O(100)]. We find, at intermediate A [A = O(10)], a dip in the Ra_c vs. R_m curve similar to the A = 1 case. However, it has Ra_c ≤ 0 at its minimum and unlike the results for high A, larger values of R_m result in a restabilisation.     

Origin of energetic ions in the polar cusp inferred from ion composition measurements by the Viking satellite

The magnetospheric ion composition spectrometer MICS on the Swedish Viking satellite provided measurements of the ion composition in the energy range 10.1 keV/e\leqE/Q\leq326.0 keV/e. Data obtained during orbit 842 were used to investigate the ion distribution in the northern polar cusp and its vicinity. The satellite traversed the outer ring current, boundary region, cusp proper and plasma mantle during its poleward movement. H⁺ and He⁺⁺ ions were encountered in all of these regions. He⁺ ions were present only in the ring current. The number of O⁺ and O⁺⁺ ions was very small. Heavy high-charge state ions typical for the solar wind were observed for the first time, most of them in the poleward part of the boundary region and in the cusp proper. The H⁺ ions exhibited two periods with high intensities. One of them, called the BR/CP event, appeared at energies up to 50 keV. It started at the equatorward limit of the boundary region and continued into the cusp proper. Energy spectra indicate a ring current origin for the BR/CP event. Pitch angle distributions show downward streaming of H⁺ ions at its equatorward limit and upward streaming on the poleward side. This event is interpreted as the result of pitch angle scattering of ring current ions by fluctuations in the magnetopause current layer in combination with poleward convection. The other of the two periods with high H⁺ ion intensities, called the accelerated ion event, was superimposed on the BR/CP event. It was restricted to energies \leq15 keV and occurred in the poleward part of the boundary region. This event is regarded as the high-energy tail of magnetosheath ions that were accelerated while penetrating into the magnetosphere. The cusp region thus contains ions of magnetospheric as well as of magnetosheath origin. The appearance of the ions depends, in addition to the ion source, on the magnetic field configuration and dynamic processes inside and close to the cusp.     

An important source ofHe (andHe) in diamonds

A large data base has recently accumulated on the concentrations of helium isotopes in diamonds mined from various regions. It was noted earlier (Ozima et al. (1985) [1]; Lal et al. (1989) [2]) that the frequency distribution of the⁴He concentrations is a fairly narrow one, whereas that of³He concentrations is a broad one with no pronounced peaks. The ratios ³He/⁴He, on the other hand show a broad maximum around 2 R_a (R_a equals atmospheric ³He/⁴He ratio, = 1.40 × 10⁻⁶) with a slow decrease over two orders of magnitude on either side. Does this imply that the diamonds sample a wide variety of helium reservoirs having a range of ³He/⁴He ratios but somehow attain similar⁴He concentrations? We propose that in a majority of the diamonds studied,⁴He is primarily due to implantation of radiogenic alpha particles from the host material after emplacement in the crust, usually kimberlite, and that the concentrations of⁴He in diamonds often get appreciably altered by this process. Thus the⁴He trapped in the diamond at the time of its crystallization is usually overwhelmed by the implanted helium and the measured ³He/⁴He ratios do not generally correspond to any “sources” in the mantle. However, the implanted⁴He resides in the outer 16 μm of the diamond, and the intrinsic⁴He and ³He/⁴He ratios in the diamond can be studied if its outer layers are removed.The wider implications of diamond being the “target” material for nuclear reaction products from the host material are discussed. Radiogenic³He produced in the host material is also implanted in the diamond, but this contribution is small on a gross basis. However, since the depth of implantation of³He is greater than that of⁴He, some of the very high ³He/⁴He ratios observed in diamonds could be due to the “implantation” of radiogenic³He. The radiogenic reactions in the host material can also contribute to appreciable²¹Ne in diamonds.     

Time structure of the X-ray emission of thermal solar flares

Based on observations of electromagnetic radiation, a concept of thermal solar flares has been proposed. The absence of hard X-ray emission implies no accelerated electrons. This fact is the basis of the proposed concept of thermal flares. Since the acceleration rate should not exceed the electron energy loss rate, plasma density in the acceleration range must be at least 10¹¹ cm^?3. The temperature of plasma emitting in the soft X-ray range is of the order of 10⁷ K. In the simplified problem of heated plasma hydrodynamics, we calculated the temperature profiles and their changes over time and by coordinate. The emission measure values determined from observations of the soft X-ray emission of flares is of the order of 10⁴⁵ cm^?3. The geometry of the source is an axial symmetric straight cylinder with a section of 10¹⁶ cm² and an axial coordinate determined by the depth of plasma heating. Time profiles of soft X-ray emission were calculated for different sources of plasma heating, which were simulated using the Gaussian distribution law with respect to the coordinate and time. We have considered two modes of plasma heating: single (in time) and multipulse modes with different pulse intervals. The dynamics of plasma heating and cooling was shown to control the experimentally observed time profiles of soft X-ray emission. A comparison of numerical results with observational data allows us to confirm the implications of the proposed concept of thermal flares and, in addition, to perform diagnostics of plasma parameters in the emission source.     

Primitive neon and helium isotopic compositions of high-MgO basalts from the Kerguelen Archipelago,Indian Ocean

The geochemical characteristics of mildly alkalic basalts (24–25 Ma) erupted in the southeastern Kerguelen Archipelago are considered to represent the best estimate for the composition of the enriched Kerguelen plume end-member. A recent study of picrites and high-MgO basalts from this part of the archipelago highlighted the Pb and Hf isotopic variations and suggested the presence of mantle heterogeneities within the Kerguelen plume itself. We present new helium and neon isotopic compositions for olivines from these picrites and high-MgO basalts (6–17 wt.% MgO) both to constrain the enriched composition of the Kerguelen plume and to determine the origin of isotopic heterogeneities involved in the genesis of Kerguelen plume-related basalts. The olivine phenocrysts have extremely variable ⁴He / ³He compositions between MORB and primitive values observed in OIB (∼90,000 to 40,000; i.e., R / R_a ∼8 to 18) and they show primitive neon isotopic ratios (average ²¹Ne / ²¹Ne_ext ∼0.044). The neon isotopic systematics and the ⁴He / ³He ratios that are lower than MORB values for the Kerguelen basalts clearly suggest that the Kerguelen hotspot belongs to the family of primitive hotspots, such as Iceland and Hawaii. The rare gas signature for the Kerguelen samples, intermediate between MORB and solar, is apparently inconsistent with mixing of a primitive component with a MORB-like source, but may result from sampling a heterogeneous part of the mantle with solar ³He / ²²Ne and with a higher (U, Th) / ³He ratio compared to typically high R / R_a hotspot basalts such as those from Iceland and Hawaii.     

Hydromagnetic waves in rapidly rotating spherical shells generated by poloidal decay modes

Abstract

This paper presents the first attempt to examine the stability of a poloidal magnetic field in a rapidly rotating spherical shell of electrically conducting fluid. We find that a steady axisymmetric poloidal magnetic field loses its stability to a non-axisymmetric perturbation when the Elsasser number A based on the maximum strength of the field exceeds a value about 20. Comparing this with observed fields, we find that, for any reasonable estimates of the appropriate parameters in planetary interiors, our theory predicts that all planetary poloidal fields are stable, with the possible exception of Jupiter. The present study therefore provides strong support for the physical relevance of magnetic stability analysis to planetary dynamos. We find that the fluid motions driven by magnetic instabilities are characterized by a nearly two-dimensional columnar structure attempting to satisfy the Proudman-Taylor theorm. This suggests that the most rapidly growing perturbation arranges itself in such a way that the geostrophic condition is satisfied to leading order. A particularly interesting feature is that, for the most unstable mode, contours of the non-axisymmetric azimuthal flow are closely aligned with the basic axisymmetric poloidal magnetic field lines. As a result, the amplitude of the azimuthal component of the instability is smaller than or comparable with that of the poloidal component, in contrast with the instabilities generated by toroidal decay modes (Zhang and Fearn, 1994). It is shown, by examining the same system with and without fluid inertia, that fluid inertia plays a secondary role when the magnetic Taylor number T_m ? 10⁵. We find that the direction of propagation of hydromagnetic waves driven by the instability is influenced strongly by the size of the inner core.     

An analytical model for ice-edge upwelling

Abstract

This paper presents an analytical, two-dimensional model of the wind-induced homogeneous circulation near the edge of an ice pack floating on the ocean surface. It is shown that a vertical shear layer arises under the ice edge, by which the wind-driven geostrophic motion in the open ocean is matched to the flow region underneath the ice. As in coastal upwelling models, this shear layer consists of a thin E ^1/2-layer inside a thicker E ^1/4-layer (E being the Ekman number). Under certain conditions the shear layer produces a vertical mass flux from the bottom to the surface Ekman layer. Near the surface this upwelling flux is concentrated in the narrow E ^1/2-layer. Comparison with observations of upwelling at the edge of a polar ice pack shows good agreement.     

The onset of magnetoconvection at large Prandtl number in a rotating layer II. Small magnetic diffusion

Abstract

This paper develops further a convection model that has been studied several times previously as a very crude idealization of planetary core dynamics. A plane layer of electrically-conducting fluid rotates about the vertical in the presence of a magnetic field. Such a field can be created spontaneously, as in the Childress-Soward dynamo, but here it is uniform, horizontal and externally-applied. The Prandtl number of the fluid is large, but the Ekman, Elsasser and Rayleigh numbers are of unit order. In Part I of this series, it was also supposed that the ratio thermal diffusivity diffusivity/magnetic diffusivity is O(1), but here we suppose that this ratio is large. The character of the solution is changed in this limit. In the case of main interest, when the layer is confined between electrically-insulating no-slip walls, the solution is significantly different from the solution when the mathematically simpler, illustrative boundary conditions also considered in Part I are employed. As in Part I, attention is focussed on the onset of convection as the temperature difference applied across the layer is increased, and on the preferred mode, i.e., the planform and time-dependence of small amplitude convection.     

On the spin-up of a stably stratified,electrically conducting fluid. Part 2: Spin-up controlled by the mac layer

Abstract

The linear spin-up of a stably stratified, electrically conducting fluid within an electrically insulating cylindrical container in the presence of an applied axial magnetic field is analyzed for those cases in which electric currents generated within the steady MAC layer control the fluid interior, The MAC layer is a new boundary layer first studied by Loper (1976a) which controls the fluid in the parameter range E/α² ? σS ? α²/E, α² ? 1 Where E = vωL², 2α² = σB²/pω and σS = vN²/κω;². The problem is solved using the Laplace transform and four new spin-up times are obtained. Combined into one expression they are t = ω;^?1E-½[1+(σSE/α⁶)^½ + δα^-2] [1+(σSE/α^{6 1/4}]^?1 where δ = σμv. The internal spin-up mechanisms for this problem are shown to be very similar to those discussed in part 1 (Loper, 1976b). The ten known spin-up times are summarized and their inter-relationships are investigated. It is shown how to obtain the seven hydromagnetic spin-up times from a simple torsional Alfvén wave model involving a single parameter which measures the strength of the boundary layer dissipation. Finally, the present theory is applied to the solar spin-down problem and it is found that if the magnetic field in the solar interior is at least as strong as the interplanetary field of 10^-5 gauss, then the hydromagnetic spin-down time is much shorter than the Eddington-Sweet time and is comparable to the age of the sun.     

Two-dimensional drift velocities from the IMAGE EUV plasmaspheric imager

The Imager for Magnetopause-to-Aurora Global Exploration (IMAGE) Mission extreme ultraviolet (EUV) imager observes He⁺ plasmaspheric ions throughout the inner magnetosphere. Limited by ionizing radiation and viewing close to the sun, images of the He⁺ distribution are available every 10 min for many hours as the spacecraft passes through apogee in its highly elliptical orbit. As a consistent constituent at about 15%, He⁺ is an excellent surrogate for monitoring all of the processes that control the dynamics of plasmaspheric plasma. In particular, the motion of He⁺ transverse to the ambient magnetic field is a direct indication of convective electric fields. The analysis of boundary motions has already achieved new insights into the electrodynamic coupling processes taking place between energetic magnetospheric plasmas and the ionosphere. Yet to be fulfilled, however, is the original promise that global EUV images of the plasmasphere might yield two-dimensional pictures of mesoscale to macroscale electric fields in the inner magnetosphere. This work details the technique and initial application of an IMAGE EUV analysis that appears capable of following thermal plasma motion on a global basis.     

Evaluation of radiation-damage halos in quartz by cathodoluminescence as a geochronological tool

Detailed quantitative cathodoluminescence (CL) imaging analysis was carried out for radiation-damage halos observed by CL (CL halo) created in natural quartz by implantation of 4 MeV He⁺ ions. The band of CL halo was approximately 14 μm in width and was constant for any He⁺ ion dose. The width of the halo is consistent with the theoretical range of ⁴He ions in quartz. A quantitative response of CL intensity to He⁺ ion dose was obtained, leading to the application of CL halos to geodosimetrical use. The CL intensity increases exponentially in the luminescent band from the implantation surface to the inside, until it reaches a maximum at 14 μm depth, with a rapid decrease beyond this point. This result is as predicted by Bragg's law, although we find some differences between the CL intensity and the theoretical stopping power.     

Rotational and magnetic instability in the diffusive tachocline

In this article we study the linear instability of the two-dimensional strongly stratified model for global MHD in the diffusive solar tachocline. Gilman and Fox [Gilman, P.A. and Fox, P., Joint instability of the latitudinal differential rotation and toroidal magnetic fields below the solar convection zone. Astrophys. J., 1997, 484, 439–454] showed that for ideal MHD, the observed surface differential rotation becomes more unstable than is predicted by Watson's [Watson, M., Shear instability of differential rotation in stars. Geophys. Astrophys. Fluid Dyn., 1981, 16, 285–298] nonmagnetic analysis. They showed that the solar differential rotation is unstable for essentially all reasonable values of the differential rotation in the presence of an antisymmetric toroidal field. They found that for the broad field case B _φ～sinθcosθ, θ being the co-latitude, instability occurs only for the azimuthal m?=?1 mode, and concluded that modes which are symmetric (meridional flow in the same direction) about the equator onset at lower field strengths than the antisymmetric modes. We study the effect of viscosity and magnetic diffusivity in the strongly stably stratified case where diffusion is primarily along the level surfaces. We show that antisymmetric modes are now strongly preferred over symmetric modes, and that diffusion can sometimes be destabilising. Even solid body rotation can be destabilised through the action of magnetic field. In addition, we show that when diffusion is present, instability can occur when the longitudinal wavenumber m?=?2.     

Kinematic stationary geodynamo models with separated toroidal and poloidal motions

Abstract

This paper is concerned with a three-dimensional spherical model of a stationary dynamo that consists of a convective layer with a simple poloidal flow of the S^2c ₂ kind between a rotating inner body core and solid outer shell. The rotation of the inner core and the outer shell means that there are regions of concentrated shear or differential rotation at the convective layer boundaries. The induction equation for the inside of the convective layer was solved numerically by the Bullard-Gellman method, the eigenvalue of the problem being the magnetic Reynolds number of the poloidal flow (R _M2) and it was assumed that the magnetic Reynolds number of the core (R _M1) and of the shell (R _M3) were prescribed parameters. Hence R _M2 was studied as a function of R _M1 and R _M3, along with the orientation of the rotation axis, the radial dependence of the poloidal velocity and the relative thickness of the layers for the three different situations, (i) the core alone rotating, (ii) the shell alone rotating and (iii) the core and the shell rotating together. In all three cases it was found that, at definite orientations of the rotation axis, there is a good convergence of both the eigenvalues and the eigenfunctions of the problem as the number of spherical harmonics used to represent the problem increases. For R _M1 =R _M3= 10³, corresponding to the westward drift velocity and the parameters of the Earth's core, the critical values of R _M2 are found to be three orders of magnitude lower than R _M1, R _M3 so that the poloidal flow velocity sufficient for maintaining the dynamo process is 10-20 m/yr. With only the core or the shell rotating, the velocity field generally differs little from the axially symmetric case. However, for R _M2 (or R _M3) lying in the range 10² to 10⁵, the self-excitation condition is found to be of the form R _M2˙R ^½ _M1=constant (or R _M2˙R^½ _M3=constant) and the solution does not possess the properties of the Braginsky near-axisymmetric dynamo. We should expect this, in particular, in the Braginsky limit R _M2˙R^?½; _M1=constant.

An analysis of known three-dimensional dynamo models indicates the importance of the absence of mirror symmetry planes for the efficient generation of magnetic fields.     

Magnotospheric imaging of high latitude ion outflows

High latitude ion outflows mostly consist of upward streaming O⁺ and He⁺ emanating from the ionosphere. At heights above 1000 km, these flows consist of cold and hot components which resonantly scatter solar extreme ultraviolet (EUV) light, however, the ion populations respond differently to Doppler shifting resulting from the large relative velocities between the ions and the Sun. The possibility of optical detection of the Doppler effect on the scattering rate will be discussed for the O⁺ (83.4 nm) ions. We have contrasted the EUV solar resonance images of these outflows by simulations of the 30.4 nm He⁺ and 83.4 nm O⁺ emissions for both quiet and disturbed geomagnetic conditions. Input data for the 1000 km level has been obtained from the EICS instrument aboard the Dynamics Explorer satellite. Our results show emission rates of 50 and 56 milli-Rayleighs at 30.4 nm for quiet and disturbed conditions and 65 and 75 milli-Rayleighs at 83.4 nm for quiet and disturbed conditions, respectively, obtained for a polar orbiting satellite and viewing radially outward. We also find that an imager at an equatorial distance of 9 R_E or more is in a favorable position for detecting ion outflows, particularly when the plasmapause is depressed in latitude. However, an occultation disk is necessary to obscure the bright plasmaspheric emissions.