SuperDARN studies of the ionospheric convection response to a northward turning of the interplanetary magnetic field

The response of the dayside ionospheric flow to a sharp change in the direction of the interplanetary magnetic field (IMF) measured by the WIND spacecraft from negative B_z and positive B_y, to positive B_z and small B_y, has been studied using SuperDARN radar, DMSP satellite, and ground magnetometer data. In response to the IMF change, the flow underwent a transition from a distorted twin-cell flow involving antisunward flow over the polar cap, to a multi-cell flow involving a region of sunward flow at high latitudes near noon. The radar data have been studied at the highest time resolution available (2 min) to determine how this transition took place. It is found that the dayside flow responded promptly to the change in the IMF, with changes in radar and magnetic data starting within a few minutes of the estimated time at which the effects could first have reached the dayside ionosphere. The data also indicate that sunward flows appeared promptly at the start of the flow change (within 2 min), localised initially in a small region near noon at the equatorward edge of the radar backscatter band. Subsequently the region occupied by these flows expanded rapidly east-west and poleward, over intervals of 7 and 14 min respectively, to cover a region at least 2 h wide in local time and 5° in latitude, before rapid evolution ceased in the noon sector. In the lower latitude dusk sector the evolution extended for a further 6 min before quasi-steady conditions again prevailed within the field-of-view. Overall, these observations are shown to be in close conformity with expectations based on prior theoretical discussion, except for the very prompt appearance of sunward flows after the onset of the flow change.     

Interhemispheric contrasts in the ionospheric convection response to changes in the interplanetary magnetic field and substorm activity: a case-study

Interhemispheric contrasts in the ionospheric convection response to variations of the interplanetary magnetic field (IMF) and substorm activity are examined, for an interval observed by the Polar Anglo-American Conjugate Experiment (PACE) radar system between 1600 and 2100 MLT on 4 March 1992. Representations of the ionospheric convection pattern associated with different orientations and magnitudes of the IMF and nightside driven enhancements of the auroral electrojet are employed to illustrate a possible explanation for the contrast in convection flow response observed in radar data at nominally conjugate points. Ion drift measurements from the Defence Meteorological Satellite Program (DMSP) confirm these ionospheric convection flows to be representative for the prevailing IMF orientation and magnitude. The location of the fields of view of the PACE radars with respect to these patterns suggest that the radar backscatter observed in each hemisphere is critically influenced by the position of the ionospheric convection reversal boundary (CRB) within the radar field of view and the influence it has on the generation of the irregularities required as scattering targets by high-frequency coherent radar systems. The position of the CRB in each hemisphere is strongly controlled by the relative magnitudes of the IMF B_z and B_y components, and hence so is the interhemispheric contrast in the radar observations.     

Dayside convection and auroral morphology during an interval of northward interplanetary magnetic field

We investigate the dayside auroral dynamics and ionospheric convection during an interval when the interplanetary magnetic field (IMF) had predominantly a positive B_z component (northward IMF) but varying B_y. Polar UVI observations of the Northern Hemisphere auroral emission indicate the existence of a region of luminosity near local noon at latitudes poleward of the dayside auroral oval, which we interpret as the ionospheric footprint of a high-latitude reconnection site. The large field-of-view afforded by the satellite-borne imager allows an unprecedented determination of the dynamics of this region, which has not previously been possible with ground-based observations. The location of the emission in latitude and magnetic local time varies in response to changes in the orientation of the IMF; the cusp MLT and the IMF B_y component are especially well correlated, the emission being located in the pre- or post-noon sectors for B_y < 0 nT or B_y > 0 nT, respectively. Simultaneous ground-based observations of the ionospheric plasma drift are provided by the CUTLASS Finland HF coherent radar. For an interval of IMF B_y 0 nT, these convection flow measurements suggest the presence of a clockwise-rotating lobe cell contained within the pre-noon dayside polar cap, with a flow reversal closely co-located with the high-latitude luminosity region. This pattern is largely consistent with recent theoretical predictions of the convection flow during northward IMF. We believe that this represents the first direct measurement of the convection flow at the imaged location of the footprint of the high-latitude reconnection site.     

(ϖμ/ϖT) P of the lower mantle

We estimate (/T) _P of the lower mantle at seismic frequencies using two distinct approaches by combining ambient laboratory measurements on lower mantle minerals with seismic data. In the first approach, an upper bound is estimated for |(/T) _P | by comparing the shear modulus () profile of PREM with laboratory room-temperature data of extrapolated to high pressures. The second approach employs a seismic tomography constraint ( lnV _S / lnV _P ) _P =1.8–2, which directly relates (/T) _P with (K _S /T) _P . An average (K _S /T) _P can be obtained by comparing the well-established room-temperature compression data for lower mantle minerals with theK _S profile of PREM along several possible adiabats. Both (K _S /T) and (/T) depend on silicon content [or (Mg+Fe)/Sil of the model. For various compositions, the two approaches predict rather distinct (/T) _P vs. (K _S /T) _P curves, which intersect at a composition similar to pyrolite with (/T) _P =–0.02 to –0.035 and (K _S /T) _P =–0.015 to –0.020 GPa/K. The pure perovskite model, on the other hand, yields grossly inconsistent results using the two approaches. We conclude that both vertical and lateral variations in seismic velocities are consistent with variation due to pressure, temperature, and phase transformations of a uniform composition. Additional physical properties of a pyrolite lower mantle are further predicted. Lateral temperature variations are predicted to be about 100–250 K, and the ratio of ( lnp/ lnV _S ) _P around 0.13 and 0.26. All of these parameters increase slightly with depth if the ratio of ( lnV _S / lnV _P ) _P remains constant throughout the lower mantle. These predicted values are in excellent agreement with geodynamic analyses, in which the ratios ( ln / lnV _S ) _P and ( / lnV _S ) _P are free parameters arbitrarily adjusted to fit the tomography and geoid data.     

Polar ionospheric responses to solar wind IMF changes

Auroral and airglow emissions over Eureka (89° CGM) during the 1997/98 winter show striking variations in relation to solar wind IMF changes. The period January 19 to 22, 1998, was chosen for detailed study, as the IMF was particularly strong and variable. During most of the period, B_z was northward and polar arcs were observed. Several overpasses by DMSP satellites during the four day period provided a clear picture of the particle precipitation producing the polar arcs. The spectral character of these events indicated excitation by electrons of average energy 300 to 500 eV. Only occasionally were electrons of average energy up to 1 keV observed and these appeared transitory from the ground optical data. It is noted that polar arcs appear after sudden changes in IMF B_y, suggesting IMF control over arc initiation. When B_y is positive there is arc motion from dawn to dusk, while B_y is negative the motion is consistently dusk to dawn. F-region (anti-sunward) convections were monitored through the period from 630.0 nm emissions. The convection speed was low (100/150 m/s) when B_z was northward but increased to 500 m/s after B_z turned southward on January 20.     

The elastic properties of single-crystal fayalite as determined by dynamical measurement techniques

We present new elasticity measurements on single-crystal fayalite and combine our results with other data from resonance, pulse superposition interferometry, and Brillouin scattering to provide a set of recommended values for the adiabatic elastic moduliC _ij and their temperature variations. We use a resonance method (RPR) with specimens that were previously investigated by pulse superposition experiments. The nineC _ij of fayalite are determined from three new sets of measurements. One set of our newC _ij data is over the range 300–500 K. We believe that the relatively large discrep ncies found in someC _ij are due in large part to specimen inhomogeneities (chemical and microstructural) coupled with differences in the way various techniques sample, rather than only systematic errors associated with experimental procedures or in the preparations of the specimens.Our recommendeaC _ij's (GPa) and (C _ij/T) _p (GPa/K) are: The resulting values for the isotropic bulk and shear moduli,K _s and , and their temperature derivatives are:K _s=134(4) GPa; =50.7(0.3) GPa; (K _s/T) _p =–0.024(0.005) GPa/K; and (/T) _p =–0.013(0.001) GPa/K. An important conclusion is thatK _s increases as the Fe/(Fe+Mg) ratio in olivine is increased.     

Ionospheric and geomagnetic responses to changes in IMF B z : a superposed epoch study

Superposed epoch studies have been carried out in order to determine the ionospheric response at mid-latitudes to southward turnings of the interplanetary magnetic field (IMF). This is compared with the geomagnetic response, as seen in the indices K_p, AE and Dst. The solar wind, IMF and geomagnetic data used were hourly averages from the years 1967–1989 and thus cover a full 22-year cycle in the solar magnetic field. These data were divided into subsets, determined by the magnitudes of the southward turnings and the concomitant increase in solar wind pressure. The superposed epoch studies were carried out using the time of the southward turning as time zero. The response of the mid-latitude ionosphere is studied by looking at the F-layer critical frequencies, f_oF2, from hourly soundings by the Slough ionosonde and their deviation from the monthly median values, f_oF2. For the southward turnings with a change in B_z of B_z > 11.5 nT accompanied by a solar wind dynamic pressure P exceeding 5 nPa, the F region critical frequency, f_oF2, shows a marked decrease, reaching a minimum value about 20 h after the southward turning. This recovers to pre-event values over the subsequent 24 h, on average. The Dst index shows the classic storm-time decrease to about –60 nT. Four days later, the index has still to fully recover and is at about –25 nT. Both the K_p and AE indices show rises before the southward turnings, when the IMF is strongly northward but the solar wind dynamic pressure is enhanced. The average AE index does register a clear isolated pulse (averaging 650 nT for 2 h, compared with a background peak level of near 450 nT at these times) showing enhanced energy deposition at high latitudes in substorms but, like K_p, remains somewhat enhanced for several days, even after the average IMF has returned to zero after 1 day. This AE background decays away over several days as the Dst index recovers, indicating that there is some contamination of the currents observed at the AE stations by the continuing enhanced equatorial ring current. For data averaged over all seasons, the critical frequencies are depressed at Slough by 1.3 MHz, which is close to the lower decile of the overall distribution of f_oFl values. Taking 30-day periods around summer and winter solstice, the largest depression is 1.6 and 1.2 MHz, respectively. This seasonal dependence is confirmed by a similar study for a Southern Hemisphere station, Argentine Island, giving peak depressions of 1.8 MHz and 0.5 MHz for summer and winter. For the subset of turnings where B_z > 11.5 nT and P 5 nPa, the response of the geomagnetic indices is similar but smaller, while the change in f_oF2 has all but disappeared. This confirms that the energy deposited at high latitudes, which leads to the geomagnetic and ionospheric disturbances following a southward turning of the IMF, increases with the energy density (dynamic pressure) of the solar wind flow. The magnitude of all responses are shown to depend on B_z. At Slough, the peak depression always occurs when Slough rotates into the noon sector. The largest ionospheric response is for southward turnings seen between 15–21 UT.     

High-time resolution conjugate SuperDARN radar observations of the dayside convection response to changes in IMF B y

We present data from conjugate SuperDARN radars describing the high-latitude ionospheres response to changes in the direction of IMF B_y during a period of steady IMF B_z southward and B_x positive. During this interval, the radars were operating in a special mode which gave high-time resolution data (30 s sampling period) on three adjacent beams with a full scan every 3 min. The location of the radars around magnetic local noon at the time of the event allowed detailed observations of the variations in the ionospheric convection patterns close to the cusp region as IMF B_y varied. A significant time delay was observed in the ionospheric response to the IMF By changes between the two hemispheres. This is explained as being partially a consequence of the location of the dominant merging region on the magnetopause, which is 8/12R_E closer to the northern ionosphere than to the southern ionosphere (along the magnetic field line) due to the dipole tilt of the magnetosphere and the orientation of the IMF. This interpretation supports the anti-parallel merging hypothesis and highlights the importance of the IMF B_x component in solar wind-magnetosphere coupling.     

A numerical study of the heat transfer through a fluid layer with recirculating flow between concentric and eccentric spheres

A numerical study has been made of the heat transfer through a fluid layer with recirculating flow. The outer fluid surface was assumed to be spherical, while the inner surface consisted of a sphere concentrically or eccentrically located with respect to the outer spherical surface. The recirculating flow was assumed to be driven by a gas flow creating stress on the fluid's outer surface so that creeping (low Reynolds number) flow developed in its interior. The present study solves the Stokes equation of motion and the convective diffusion equation in bispherical coordinates and presents the streamline and isotherm patterns.Nomenclature a _i inner sphere radius - a _d outer sphere radius - A ₁ defined by equation (5) - A ₂ defined by equation (6) - B ₁ defined by equation (7) - B ₂ defined by equation (8) - c dimensional factor for bispherical coordinates - C constant in equation (4) - d narrowest distance between the two eccentric spheres - E ² operator defined by equation (1) in spherical coordinates and by equation (21) in bispherical coordinates - G modified vorticity, defined in equation (22) - G ^* non-dimensional modified vorticity, defined in equation (28) - h metric coefficient of bispherical coordinate system, defined in equation (18) - k _w thermal conductivity of water - K ₁ defined by equation (9) - K ₂ defined by equation (10) - N _Re Reynolds number=2a _dU/gn - N _Pe,h Peclet number=2a _dU/ - n integer counter - q heat flux - r radius - r ^* non-dimensional radius=r/a _d - S surface area - t time - t ^* non-dimensional time=t/a _d ² - T temperature - T _o temperature at inner sphere surface - T _a temperature at outer sphere surface - T ^* non-dimensional temperature;=(T–T _o)/(T_a–T_o) - u velocity - u _r radial velocity in spherical coordinates - u angular velocity in spherical coordinates - u radial velocity in bispherical coordinates - u angular velocity in bispherical coordinates - U free stream velocity - u _r ^* =u _r/U - u ^* =u /U - u ^* =u /U - u ^* =u /U Greek symbols a ₁ small displacement - vorticity, defined in equation (17) - ^* non-dimensional vorticity, defined in equation (27) - radial bispherical coordinates - _o bispherical coordinate of inner sphere - _a bispherical coordinate of outer sphere - angular coordinate in spherical coordinates - thermal diffusivity - _w thermal diffusivity of water - kinematic viscosity - angular bispherical coordinate - spherical coordinate - streamfunction - non-dimensional streamfunction for spherical coordinates, = /(U a _d ² ) - ^* non-dimensional streamfunction for bispherical coordinates, defined in equation (26)     

Electromagnetic scattering by a perfectly conducting half-plane in a conductive half-space

FollowingDmitriev (1960) a rigorous theoretical solution for the problem of scattering by a perfectly conducting inclined half-plane buried in a uniform conductive half-space has been obtained for plane wave excitation. The resultant integral equation for the Laplace transform of scattering current in the half-plane is solved numerically by the method of successive approximation. The scattered fields at the surface of the half-space are found by integrating the half-space Green's function over the transform of the scattering current.The effects of depth of burial and inclination, of the half-plane on the scattered fields are studied in detail. An increase in the depth of burial leads to attenuation of the fields. Inclination introduces asymmetry in the field profiles beside affecting its magnitude. Depth of exploration is greater for quadrature component. An interpretation scheme based on a phasor diagram is presented for the VLF-EM method of exploration for rich vein deposits in a conductive terrain.List of symbols x, y, z Space co-ordinates - Half-space conductivity - ₀ Free-space permeability - Excitation frequency (angular) - T Time - h Depth of the half-plane - a Inclination of the half-plane - E _x x-Directed total electric field - E _x ^p x-Directed primary electric field - E _xo ^p x-Directed primary electric field atz=0 directly over the half-plane - H _y y-Component of total magnetic field - H _y ^p y-Component of primary magnetic field - H _y0 ^p y-Component of primary magnetic field atz=0 directly over the half-plane - H _z z-Component of total magnetic field - H _z ^p z-Component of primary magnetic field - J _x Surface density ofx-directed scattering current - G Green's function - k ₀,K Wave numbers - u,u ₀,u ₁,u ₂ Functions - Space co-ordinate - s Variable in transform domain - Variable of integration - Normalized scattering current - Laplace transform of - N Normalized - , ₀, ₁, ₂ Functions - t Variable of integration - Skin depth - H Total magnetic field - H ^p Primary magnetic field - H ₀ ^p Primary magnetic field atz=0 directly over the half-plane - M,Q,R,S,U,V Functions - N ₁,N ₂ Functions     

Meridian-scanning photometer, coherent HF radar, and magnetometer observations of the cusp: a case study

The dynamics of the cusp region and post-noon sector for an interval of predominantly IMF B_y, B_z < 0 nT are studied with the CUTLASS Finland coherent HF radar, a meridian-scanning photometer located at Ny Ålesund, Svalbard, and a meridional network of magnetometers. The scanning mode of the radar is such that one beam is sampled every 14 s, and a 30° azimuthal sweep is completed every 2 minutes, all at 15 km range resolution. Both the radar backscatter and red line (630 nm) optical observations are closely co-located, especially at their equatorward boundary. The optical and radar aurora reveal three different behaviours which can interchange on the scale of minutes, and which are believed to be related to the dynamic nature of energy and momentum transfer from the solar wind to the magnetosphere through transient dayside reconnection. Two interpretations of the observations are presented, based upon the assumed location of the open/closed field line boundary (OCFLB). In the first, the OCFLB is co-located with equatorward boundary of the optical and radar aurora, placing most of the observations on open field lines. In the second, the observed aurora are interpreted as the ionospheric footprint of the region 1 current system, and the OCFLB is placed near the poleward edge of the radar backscatter and visible aurora; in this interpretation, most of the observations are placed on closed field lines, though transient brightenings of the optical aurora occur on open field lines. The observations reveal several transient features, including poleward and equatorward steps in the observed boundaries, braiding of the backscatter power, and 2 minute quasi-periodic enhancements of the plasma drift and optical intensity, predominantly on closed field lines.     

Lengths and hazards from channel-fed lava flows on Mauna Loa, Hawai‘i, determined from thermal and downslope modeling with FLOWGO

Using the FLOWGO thermo-rheological model we have determined cooling-limited lengths of channel-fed (i.e. a) lava flows from Mauna Loa. We set up the program to run autonomously, starting lava flows from every 4th line and sample in a 30-m spatial-resolution SRTM DEM within regions corresponding to the NE and SW rift zones and the N flank of the volcano. We consider that each model run represents an effective effusion rate, which for an actual flow coincides with it reaching 90% of its total length. We ran the model at effective effusion rates ranging from 1 to 1,000 m³ s^–1, and determined the cooling-limited channel length for each. Keeping in mind that most flows extend 1–2 km beyond the end of their well-developed channels and that our results are non-probabilistic in that they give all potential vent sites an equal likelihood to erupt, lava coverage results include the following: SW rift zone flows threaten almost all of Mauna Loas SW flanks, even at effective effusion rates as low as 50 m³ s^–1 (the average effective effusion rate for SW rift zone eruptions since 1843 is close to 400 m³ s^–1). N flank eruptions, although rare in the recent geologic record, have the potential to threaten much of the coastline S of Keauhou with effective effusion rates of 50–100 m³ s^–1, and the coast near Anaehoomalu if effective effusion rates are 400–500 m³ s^–1 (the 1859 a flow reached this coast with an effective effusion rate of 400 m³ s^–1). If the NE rift zone continues to be active only at elevations >2,500 m, in order for a channel-fed flow to reach Hilo the effective effusion rate needs to be 400 m³ s^–1 (the 1984 flow by comparison, had an effective effusion rate of 200 m³ s^–1). Hilo could be threatened by NE rift zone channel-fed flows with lower effective effusion rates but only if they issue from vents at 2,000 m or lower. Populated areas on Mauna Loas SE flanks (e.g. Phala), could be threatened by SW rift zone eruptions with effective effusion rates of 100 m³ s^–1.Editorial responsibility: J Donnelly-Nolan     

La risoluzione dell'equazione di Laplace nel campo esterno a uno sferoide

Riassunto L'Autore dimostra che, nel sistema di coordinate polari , , , si possono determinare un numeros di funzioni della sola variabile :Q ₁,Q ₃, ....Q _2s–1 tali che la sommatoria delleQ _2i–1/^2i–1 rappresenti il potenzialeV di un geoide di rotazione. La condizione di armonicità determina ciascunaQ (che si riduce a un polinomio nelle potenze di sen ) a meno di una costante arbitraria; si dispone pertanto dis costanti che servono per soddisfare la natura dellaV sulla superficie del geoide. Come esempio l'Autore ha determinato la gravità sul geoide sferico, confermando i risultati delSomigliana, e su uno sferoide generico dove ha ritrovato la relazione diClairaut.

---

Summary The Author proofs that, in the system of polar coordinates , , , it is possible to determine a numbers of functions only of the variable :Q ₁,Q ₃ ....Q _2s–1 in such a way as to make the summatory of theQ _2i–1/^2i–1 represent the potential function of a rotational geoid. The condition of harmonicity determines, saving an arbitrary constant, each of theQ which is reduced to a polynom developed by the sin powers; therefore one disposes of a number of constants to make use for satisfing theV on the geoid. To illustrate his theory the Author determines the gravity on the spherical geoid, thus confirmingSomigliana's formulas and on a spheroidal on which he pointed outClairaut's relations.

     

Attenuation and dispersion ofSH waves due to scattering by randomly distributed cracks

The effect of randomly distributed cracks on the attenuation and dispersion ofSH waves is theoretically studied. If earthquake ruptures are caused by sudden coalescence of preexisting cracks, it will be crucial for earthquake prediction to monitor the temporal variation of the crack distribution. Our aim is to investigate how the property of crack distribution is reflected in the attenuation and dispersion of elastic waves.We introduce the stochastic property, in the mathematical analysis, for the distributions of crack location, crack size and crack orientation. The crack size distribution is assumed to be described by a power law probability density (p(a) a ^– fora _minaa _max according to recent seismological and experimental knowledge, wherea is a half crack length and the range 13 is assumed. The distribution of crack location is assumed to be homogeneous for the sake of mathematical simplicity, and a low crack density is assumed. The stochastic property of each crack is assumed to be independent of that of the other cracks. We assume two models, that is, the aligned crack model and the randomly oriented crack model, for the distribution of crack orientation. All cracks are assumed to be aligned in the former model. The orientation of each crack is assumed to be random in the latter model, and the homogeneous distribution is assumed for the crack orientation. The idea of the mean wave formalism is employed in the analysis, and Foldy's approximation is assumed.We observe the following features common to both the aligned crack model and the randomly oriented crack model. The attenuation coefficientQ ^–1 decays in proportion tok ^–1 in the high frequency range and its growth is proportional tok ² in the low frequency range, wherek is the intrinsic wave number. This asymptotic behavior is parameter-independent, too. The attenuation coefficientQ ^–1 has a broader peak as increases and/ora _min/a _max decreases. The nondimensional peak wave numberk _p a _max at whichQ ^–1 takes the peak value is almost independent ofa _min/a _max for =1 and 2 while it considerably depends ona _min/a _max for =3. The phase velocity is almost independent ofk in the rangeka _max<1 and increases monotonically ask increases in the rangeka _max>1. While the magnitude ofQ ^–1 and the phase velocity considerably depend on the orientation of the crack in the aligned crack model, the above feature does not depend on the crack orientation.The accumulation of seismological measurements suggests thatQ ^–1 ofS waves has a peak at around 0.5 Hz. If this observation is combined with our theoretical results onk _p a _max, the probable range ofa _max of the crack distribution in the earth can be estimated for =1 or 2. If we assume 4 km/sec as theS wave velocity of the matrix medium,a _max is estimated to range from 2 to 5 km. We cannot estimatea _max in a narrow range for =3.     

Planar charged-particle trajectories in multipole magnetic fields

This paper provides a complete generalization of the classic result that the radius of curvature () of a charged-particle trajectory confined to the equatorial plane of a magnetic dipole is directly proportional to the cube of the particles equatorial distance () from the dipole (i.e. ³). Comparable results are derived for the radii of curvature of all possible planar chargedparticle trajectories in an individual static magnetic multipole of arbitrary order m and degree n. Such trajectories arise wherever there exists a plane (or planes) such that the multipole magnetic field is locally perpendicular to this plane (or planes), everywhere apart from possibly at a set of magnetic neutral lines. Therefore planar trajectories exist in the equatorial plane of an axisymmetric (m = 0), or zonal, magnetic multipole, provided n is odd: the radius of curvature varies directly as ⁿ⁼². This result reduces to the classic one in the case of a zonal magnetic dipole (n = 1). Planar trajectories exist in 2m meridional planes in the case of the general tesseral (0 < m < n) magnetic multipole. These meridional planes are defined by the 2m roots of the equation cos[m()–_n^m)] = 0, where _n^m = (1/m) arctan (h_n^m/g_n^m); g_n^m and h_n^m denote the spherical harmonic coefficients. Equatorial planar trajectories also exist if (n – m) is odd. The polar axis ( = O,) of a tesseral magnetic multipole is a magnetic neutral line if m > I. A further 2_m(n – m) neutral lines exist at the intersections of the 2_m meridional planes with the (n – m) cones defined by the (n – m) roots of the equation P_n^m(cos ) = 0 in the range 0 < 9 < , where P_n^m(cos ) denotes the associated Legendre function. If (n – m) is odd, one of these cones coincides with the equator and the magnetic field is then perpendicular to the equator everywhere apart from the 2m equatorial neutral lines. The radius of curvature of an equatorial trajectory is directly proportional to ⁿ⁼² and inversely proportional to cos[m(–)]. Since this last expression vanishes at the 2m equatorial neutral ines, the radius of curvature becomes infinitely large as the particle approaches any one of these neutral lines. The radius of curvature of a meridional trajectory is directly proportional to rⁿ⁺², where r denotes radial distance from the multiple, and inversely proportional to P_n^m(cos )/sin . Hence the radius of curvature becomes infinitely large if the particle approaches the polar magnetic neutral ine (m > 1) or any one of the 2m(n – m) neutral ines located at the intersections of the 2m meridional planes with the (n – m) cones. Illustrative particle trajectories, derived by stepwise numerical integration of the exact equations of particle motion, are pressented for low-degree (n 3) magnetic multipoles. These computed particle trajectories clearly demonstrate the non-adiabatic scattering of charged particles at magnetic neutral lines. Brief comments are made on the different regions of phase space defined by regular and irregular trajectories.Also Visiting Reader in Physics, University of Sussex, Falmer, Brighton, BN1 9QH, UK     

Spatial distribution of upstream magnetospheric ≥50 keV ions

We present for the first time a statistical study of 50 keV ion events of a magnetospheric origin upstream from Earths bow shock. The statistical analysis of the 50–220 keV ion events observed by the IMP-8 spacecraft shows: (1) a dawn-dusk asymmetry in ion distributions, with most events and lower intensities upstream from the quasi-parallel pre-dawn side (4 LT-6 LT) of the bow shock, (2) highest ion fluxes upstream from the nose/dusk side of the bow shock under an almost radial interplanetary magnetic field (IMF) configuration, and (3) a positive correlation of the ion intensities with the solar wind speed and the index of geomagnetic index Kp, with an average solar wind speed as high as 620 km s^–1 and values of the index Kp 2. The statistical results are consistent with (1) preferential leakage of 50 keV magnetospheric ions from the dusk magnetopause, (2) nearly scatter free motion of 50 keV ions within the magnetosheath, and (3) final escape of magnetospheric ions from the quasi-parallel dawn side of the bow shock. An additional statistical analysis of higher energy (290–500 keV) upstream ion events also shows a dawn-dusk asymmetry in the occurrence frequency of these events, with the occurrence frequency ranging between 16%-34% in the upstream region.     

The geoelectric field at Vostok, Antarctica: its relation to the interplanetary magnetic field and the cross polar cap potential difference

The vertical geoelectric field measured at Vostok, Antarctica (78.5°S, 107°E, L=75.0) over the 13 month interval May 1979–May 1980 is correlated with the interplanetary magnetic field (IMF) components B_y and B_z at times when Vostok is connected to the dayside magnetosphere. No significant association with IMF B_x is found. The interaction of the solar wind and the Earth’s magnetic field generally results in anti-sunward plasma flow in the high-latitude, polar ionosphere driven by a dawn-to-dusk, cross polar cap potential difference pattern. Using the IZMEM model to infer the contribution of the cross polar cap potential difference to the potential difference between the ionosphere and the ground at Vostok for the measured IMF conditions, we show that this provides a viable mechanism for the IMF associations found. We demonstrate that the direct association of the geoelectric field with the cross polar cap potential difference is independent of a result (Park, 1976. Solar magnetic sector effects on the vertical atmospheric electric field at Vostok, Antartica. Geophysical Research Letters 3(8), 475–478) showing an 15% decrease in the vertical geoelectric field measured at Vostok, 1–3 days after the passage of IMF sector boundaries. Evidence is also presented supporting the Park result, for which a mechanism is yet to be confirmed.     

Determination of characteristics of steam reservoirs by Radon-222 measurements in geothermal fluids

The authors conducted a Rn²²² survey in wells of the Larderello geothermal field (Italy) and observed considerable variations in concentrations. Simple models show that flow-rate plays an important part in the Rn²²² content of each well, as it directly affects the fluid transit time in the reservoirs. Rn²²² has been sampled from two wells of the Serrazzano area during flow-rate drawdown tests. The apparent volume of the steam reservoir of each of these two wells has been estimated from the Rn²²² concentration versus flow-rate curves.List of symbols Q Flow-rate (kg h^–1) - Decay constant of Rn²²² (=7.553×10^–3 h^–1) - Porosity of the reservoir (volume of fluid/volume of rock) - ₁ Density of the fluid in the reservoir (kg m^–3) - ₂ Density of the rock in the reservoir (kg m^–3) - M Stationary mass of fluid filling the reservoir (kg). - E Emanating power of the rock in the reservoir (nCi kg _rock ^–1 h^–1). - P Production rate of Rn²²² in the reservoir: number of atoms of Rn²²² (divided by 1.764×10⁷) transferred by the rock to the mass unit of fluid per unit time (nCi kg _fluid ^–1 h^–1). - N Specific concentration of Rn²²² in the fluid (nCi kg^–1) - Characteristic time of the steam reservoir at maximum flow-rate (=M/Q)     

Typical properties of dynamic systems and the instability of hydrodynamic flows

Summary Based on Peixot's theorem of topological dynamics, the unstable behaviour of hydrodynamic flows on a two-dimensional annuloid T ² is analysed. The generating property is the curvature of the group of S ₀ Diff T ² diffeomorphisms of the (Riemannian) flow region T ² . This group is the configuration space of the ideal fluid flowing on T ² .

---

a m ma u mn u ¶rt;uauu ¶rt;am mu n¶rt;uu¶rt;¶rt;uauu nm a ¶rt; m T ² u¶rt; mu. ¶rt;au m m a m uuann S ₀ Diff T ² ¶rt;uu amu mu ( uaa) T ² . manna m uau nmam ¶rt; u¶rt;a u¶rt;mu a T ² .

     

Analysis of aeromagnetic anomalies over the central part of the Narmada-Son lineament

The Narmada-Son lineament (NSL) forms a major tectonic feature on the Indian subcontinent. The importance of this lineament lies in its evolution as well as its tectonic history. The lineament seems to have been active since Precambrian times. In order to understand the history of its evolution, it is necessary to know what igenous activity has been taking place along this lineament, and how the Deccan trap volcanics, which cover large areas along this lineament, have erupted.For the study of this problem an analysis of the aeromagnetic anomaly map lying between 76°15 to 77°30E and 21°45 to 22°50N has been carried out. Four different profiles (B ₁ B ₁,B ₂ B ₂,B ₃ B ₃ andB ₄ B ₄) have been drawn in N-S direction over this area and interpreted in terms of the intrusive bodies present within or below the surface of Deccan trap exposures. Inversion and forward modelling techniques have been adopted for interpretation purposes. An analysis of frequency spectra along the profiles has also been carried out to estimate the average depth of the different magnetic bodies. These results have been correlated with the available geological information. It has been found that most of the small wavelength anomalies are caused by dyke-like bodies within or below the Deccan trap at a depth of less than 0.5 km.