The critical inclination problem — 30 years of progress

The critical inclination problem in artificial satellite theory, first discovered 30 years ago, has aroused great interest and provoked much discussion and controversy in the intervening years. It was this problem which essentially provided the seed corn for the development of the theory of the Ideal Resonance Problem (IRP). The latter theory provides good first-approximation solutions to a number of important resonance problems in celestial mechanics. It is not applicable, however, to certain other interesting resonant systems within the solar system. For these resonances a new fundamental mathematical model of resonance, in the spirit of the IRP, has recently been formulated and successfully applied.This paper reviews the history of the critical inclination problem and highlights the controversies it has generated over the years. The Problem's strong connection with the IRP is outlined with both thenormal andabnormal forms featuring. Finally, with reference to the critical inclination problem, the essential properties of the newer fundamental model are described and compared with the IRP. A strong correspondence is established between recent independent investigations of a variety of resonance problems and earlier work of Andoyer.     

Secular resonances: New results

We integrated numerically, in the frame of the four body problem Sun-Jupiter-Saturn-asteroid the orbit of the asteroid 1974 MA, an Earth-crosser, which is located in a region where three resonances overlap: the two secular resonances ₅ and ₁₆ and the mean motion resonance 5/1. The numerical integration yields a qualitative orbital evolution of this particular region.     

Reviews

OFFICE DEVELOPMENT: A Geographical Analysis by M. Bateman. 14 × 22 cm, xvi and 175 pages. Croom Helm: London 1985 (ISBN 0 7099 0697 8) $A35.95 (cloth).

ATLAS OF YOUTH UNEMPLOYMENT, 1981: The Geographic Distribution of Youth Unemployment in Australian Cities from the 1981 Census According to Birthplace and Gender by P. Matwijiw with E. Bamford and C. Maher. 21 × 29 cm, 127 pages. Australian Institute of Multicultural Affairs: Melbourne 1985 (ISBN 949890 33 2) $A12.00 (limp).

ENVIRONMENT AND HEALTH by A. J. Rowland and P. Cooper. 23 × 16 cm, vi and 205 pages. Edward Arnold: London 1983 (ISBN 0 7131 2855 0) $A27.95 (limp).

FAMINE AS A GEOGRAPHICAL PHENOMENON edited by B. Currey and G. Hugo. 17 × 24 cm, vi and 202 pages. Reidel: Dordrecht 1984 (ISBN 90 277 1762 1) Dfl 95.00, $US37.00 (cloth).

SOUTH AUSTRALIA'S CHANGING POPULATION (South Australian Geographical Papers No. 1) by G. J. Hugo. 25 × 18 cm, 71 pages. Royal Geographical Society of Australasia (SA Branch): Adelaide 1983 (ISBN 0 909112 05 03) $A4.00 (limp).

DEVELOPMENTS IN POLITICAL GEOGRAPHY edited by M. A. Busteed. 23 × 15 cm, 340 pages. Academic Press: London 1983 (ISBN 0 12 148420 3) $US42.00 (cloth).

NEITHER JUSTICE NOR REASON: A Legal and Anthropological Analysis of Aboriginal Land Rights by M. Gumbert. 22 × 14 cm, xv and 215 pages. University of Queensland Press: St Lucia 1984 (ISBN 0 7022 1746 8) $A20.00 (cloth).

RURAL RESOURCE MANAGEMENT by P. J. Cloke and C. C. Park. 14 × 22 cm, xiii and 473 pages. Croom Helm: London 1985 (ISBN 0 7099 2037 7) $A44.95 (cloth).

FARM POLICY IN AUSTRALIA by R. K. Hefford. 14 × 22 cm, xviii and 415 pages. University of Queensland Press: St Lucia 1985 (ISBN 0 7022 1698 4) $A40.00 (cloth).

TRANSPORT AND COMMUNICATIONS FOR PACIFIC MICROSTATES: Issues in Organisation and Management edited by C. C. Kissling. 14 × 21 cm, 192 pages. Institute of Pacific Studies, University of the South Pacific: Suva 1984. $A10.00 (cloth), $A8.00 (limp).

TIMES OF CRISIS: Epidemics in Sydney 1788–1900 by P. H. Curson. 15 × 25 cm, xii and 195 pages. Sydney University Press: Sydney 1985 (ISBN 0 424 00112 8). $A35.00 (cloth).

PEASANTS, SUBSISTENCE, ECOLOGY AND DEVELOPMENT IN THE HIGHLANDS OF PAPUA NEW GUINEA by L. S. Grossman. 24 × 16 cm, xxi and 302 pages. Princeton University Press: Princeton, NJ 1984 (ISBN 0 691 09406 3) $US45.50.

THE WORLD FOOD PROBLEM 1950–1980 by D. Grigg. 15 × 24 cm, 276 pages. Basil Blackwell: Oxford 1985 (ISBN 0 631 13481 6) $A58.50 (cloth).

POPULATION REDISTRIBUTION AND DEVELOPMENT IN SOUTH ASIA edited by L. A. Kosinski and K. M. Elahi. 17 × 24 cm, 243 pages. Reichel: Dordrecht 1985 (ISBN 90 277 1938 1) Dfl 120.00, $US44.00, £30.50 (cloth).

GEOGRAPHY AND ETHNIC PLURALISM edited by C. Clarke, D. Ley and C. Peach. 15 × 23 cm, xvii and 294 pages. Allen & Unwin: London 1984 (ISBN 0 04 309107 5) $A45.00 (cloth); (ISBN 0 04 309108 3) $A24.95 (limp).

SOCIAL GEOGRAPHY IN INTERNATIONAL PERSPECTIVE edited by J. Eyles. 14 × 22 cm, 295 pages. Croom Helm: London 1986 (ISBN 0 7099 0944 6) $A49.95 (cloth).

THE GENTRIFICATION OF INNER MELBOURNE: A Political Geography of Inner City Housing by W. S. Logan. 14 × 22 cm, xvi and 328 pages. University of Queensland Press: St. Lucia 1985 (ISBN 0 7022 1729 8) $A50.00 (cloth).

YELLOWCAKE AND CROCODILES: Town Planning, Government and Society in Northern Australia by J. Lea and R. Zehner. 14 × 22 cm, xxvi and 200 pages. Allen & Unwin: Sydney 1986 (ISBN 0 86861 875 6) $A24.95 (cloth); (ISBN 0 86861 843 8) $A 14.95 (limp).

THE BUNGALOW: The Production of a Global Culture by A. D. King. 20 × 25 cm, xii and 310 pages. Routledge & Kegan Paul: London 1984 (ISBN 0 7100 9538 4) $A62.50 (cloth).

THE WEST EUROPEAN CITY: A Social Geography by P. White. 15 × 23 cm, xviii and 269 pages. Longman: London 1984 (ISBN 0 582 30047 9) $A22.95 (limp).

THE SHAPING OF AMERICA: A Geographical Perspective on 500 years of History. Volume 1. Atlantic America, 1492–1800 by D. W. Meinig. 18 × 25 cm, xii and 500 pages. Yale University Press: New Haven 1986 (ISBN 0 300 03548 9) $US35.00 (cloth).

CANBERRA: MYTHS AND MODELS. Forces at Work in the Formation of the Australian Capital by K. F. Fischer. 21 × 30 cm, 166 pages. Institute of Asian Studies: Hamburg 1984 (ISBN 3 88910 009 0).

THE GEOGRAPHY OF PEACE AND WAR edited by D. Pepper and A. Jenkins. 15 × 23 cm, vi and 222 pages. Basil Blackwell: Oxford 1985 (ISBN 0 631 13559 6) $A75.00 (cloth); (ISBN 0 631 14069 7) $A23.95 (limp).

POLITICAL GEOGRAPHY: World‐economy, Nation‐state and Locality by P. J. Taylor. 15 × 23 cm, × and 238 pages. Longman: London 1985 (ISBN 0 582 30088 6) $A24.95 (limp).

THE INDUSTRIAL GEOGRAPHY OF CANADA by A. Blackbourn and R. G. Putnam 14 × 22 cm, 201 pages. Croom Helm: London 1984 (ISBN 0 7099 0622 6) $A42.50 (cloth).

THE FOODMAKERS by S. Sargent. 13 × 20 cm, 296 pages. Penguin: Ringwood 1985 (ISBN 0 14 007359 0) $A8.95 (limp).

LIMITS TO PREDICTION edited by R. B. McKern and G. C. Lowenthal. 13 × 19 cm, xiii and 163 pages. Australian Professional Publications: Sydney 1985 (ISBN 0 949416 029) $A14.95 (limp).

THE KANGAROO KEEPERS edited by H. J. Lavery. 18 × 25 cm, xxvi and 211 pages. University of Queensland Press: St Lucia 1985 (ISBN 0 7022 1875 8).

PRACTICAL ECOLOGY by D. D. Gilbertson, M. Kent and F. B. Pyatt. 15 × 23 cm, 320 pages, Hutchinson: London 1985 (ISBN 0 09 162651 X) £8.95.

BASIC BIOGEOGRAPHY (Second edition) by N. Pears. 15 × 24 cm, × and 358 pages. Longman: London 1985 (ISBN 0 582 30120 3) $A24.95 (limp).

ENVIRONMENTAL CHANGE (Second edition) by A. Goudie. 23 × 15 cm, xi and 258 pages. Oxford University Press: Oxford 1983 (ISBN 0 19 874135 9) A16.00 (limp).

MEGA‐GEOMORPHOLOGY edited by R. Gardner and H. Scoging. 16 × 24 cm, xiii and 240 pages. Oxford University Press: Oxford (ISBN 0 19 823244 6) $A48.00.

GRANITE LANDFORMS by C. R. Twidale. 25 × 17 cm, xxiii and 372 pages. Elsevier: Amsterdam 1982 (ISBN 0 444 42116 5) $A148.25.     

Flow directions in ash-flow tuffs: a comparison of geological and magnetic susceptibility measurements, Tshirege member (upper Bandelier Tuff), Valles caldera, New Mexico, USA

This study concludes that the elongation axis (K ₁) of the ellipsoid of anisotropic magnetic susceptibility (AMS) is a suitable proxy for flow axis in ashflow tuffs. 153 oriented samples (176 specimens) were studied from 18 sites in the 1.1 Ma Tshirege member of the Bandelier Tuff. These sites are distributed around the Valles caldera at distances of 5–25 km outside of the rim.K ₁ axes correlate well with postulated radial flow axes at 13 sites.K ₁ also agrees with measured geological flow indicators, mainly imbricated larger clasts, at 7 sites. At 2 of the 5 sites where significant disagreement is seen between theoretical radial flow directions and measuredK ₁ axes, theK ₁ axes correspond well with geological flow indicators, indicating that the divergence of flow from the predicted radial flow pattern is real. Two major topographic buttresses are suggested as the cause of flow divergence for the Tshirege ash flows: the San Pedro buttress northwest of the caldera, and the San Miguel buttress in the southeast. In situK ₁ axes plunge about 7° toward the source at two-thirds of the sites; therefore the plunge ofK ₁ is a plausible in situ indicator for thedirection of flow. Multiple flow zones in sections of several meters thickness indicate changes of flow direction that are both rapid and large during ash-flow emplacement. These observations raisre the question of how best to represent mean flow directions in ash-flow sheets: by eigenvector methods, by vector-sum methods, or by modes. A method for measuring imbrication of larger clasts using apparent dips in vertical joints is outlined. Imbrication, determined in this way at one-third of the sites, dips toward the source, i.e., up-flow. The minimum (K ₃) axis of the AMS ellipsoid correlates with the flow foliation rather than with the larger clast imbrication. The flow axes of ash flows correspond with theK ₁ axes, not with the declination ofK ₃ axes as suggested by some authors. Initial dip of the sampled ash flows is not large and does not affect the paleomagnetic remanence direction, which is reversed with a mean ofD=173.5°,I=-38.4°, ₉₅=3.4°N=18. This mean is not different at the 95% confidence level from that of earlier workers. The mean pole, at 098.0°E, 74.8°N,A ₉₅=3.3°,N=18, is about 15° far-sided relative to the expected time-averaged geomagnetic pole, suggesting a history of emplacement too short to adequately average secular variation.     

High pressure experimental calibration of the olivine-orthopyroxene-spinel oxygen geobarometer: implications for the oxidation state of the upper mantle

Synthetic spinel harzburgite and lherzolite assemblages were equilibrated between 1040 and 1300° C and 0.3 to 2.7 GPa, under controlled oxygen fugacity (f _{O 2}). f _{O 2} was buffered with conventional and open double-capsule techniques, using the Fe−FeO, WC-WO₂-C, Ni−NiO, and Fe₃O₄−Fe₂O₃ buffers, and graphite, olivine, and PdAg alloys as sample containers. Experiments were carried out in a piston-cylinder apparatus under fluid-excess conditions. Within the P-T-X range of the experiments, the redox ratio Fe³⁺/ΣFe in spinel is a linear function of f _{O 2} (0.02 at IW, 0.1 at WCO, 0.25 at NNO, and 0.75 at MH). It is independent of temperature at given Δlog(f _{O 2}), but decreases slightly with increasing Cr content in spinel. The Fe³⁺/ΣFe ratio falls with increasing pressure at given Δlog(f _{O 2}), consistent with a pressure correction based on partial molar volume data. At a specific temperature, degree of melting and bulk composition, the Cr/(Cr+Al) ratio of a spinel rises with increasing f _{O 2}. A linear least-squares fit to the experimental data gives the semi-empirical oxygen barometer in terms of divergence from the fayalite-magnetite-quartz (FMQ) buffer:

The effect of bulk rock composition on the stability of amphibole in the upper mantle: Implications for solidus positions and mantle metasomatism

Summary The stability of pargasitic amphibole in the upper mantle is a function of water content and bulk rock composition, and under water-undersaturated conditions, the stability of amphibole controls the solidus position. Experiments in the system Tinaquillo peridotite +0.2% H₂O, a refractory peridotite under water-undersaturated conditions, show that amphibole is stable to 1030°C and 26 kb. In contrast, pargasitic amphibole is stable to 1150°C and 30 kb in Hawaiian pyrolite, a more fertile peridotite composition. This indicates that under water-undersaturated conditions, the most fertile part of a crystallizing mantle diapir with an inhomogeneous composition will solidify first while a more refractory component will contain an alkali-rich melt which will have the ability to metasomatize adjacent regions. The relative stabilities of amphibole in refractory and fertile bulk compositions may result in increasing rather than diminishing chemical contrasts in high temperature lherzolite, i.e. a process of metamorphic differentiation. Ti, Fe, Al and Na metasomatism can therefore be considered a normal occurrence associated with the upward migration and solidification of an H₂O-bearing mantle diapir.

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Der Einfluß der Gesamtgesteins-Zusammensetzung auf die Stabilität von Amphibol im oberen Mantel: Bedeutung für Solidus-Positionen und Mantel-Metasomatose

Zusammenfassung Die Stabilität pargasitischer Amphibole im oberen Mantel ist eine Funktion von Wassergehalt und Gesamtgesteins-Zusammensetzung. Unter wasser-untersättigten Bedingungen, kontrolliert die Stabilität von Amphibol die Solidus-Position. Experimente in dem System Tinaquillo Peridotit +0,2% H₂O, einem refraktären Peridotit unter wasser-untersättigten Bedingungen, zeigen daß Amphibol bis 1030°C und 26 Kb stabil ist. Im Gegensatz dazu ist pargasitische Hornblende in einem Hawaii-Pyrolit, von mehr fertiler Peridotit-Zuammensetzung, bis 1150°C und 30 Kb stabil. Das zeigt, daß bei wasser-untersättigten Bedingungen der am meisten produktive Teil eines kristallisierenden Mantel-Diapirs mit inhomogener Zusammensetzung sich zuerst verfestigen wird, während eine mehr refraktäre Komponente eine alkali-reiche Schmelze enthalten wird, die wiederum die Fähigkeit hat, umliegende Bereiche metasomatisch zu beeinflussen. Die relativen Stabilitäten von Amphibol in refraktären und fertilen Gesamtzusammensetzungen können dazu führen, daß die chemischen Gegensätze in Hochtemperaturlherzoliten eher zunehmen als abnehmen, d. h. ein Prozeß metamorpher Differentiation. Ti, Fe, Al und Na Metasomatose können deshalb als ein verbreiteter Vorgang, der mit der Aufwärtsbewegung und Verfestigung eines H₂O-führenden Mantel-Diapirs assoziiert ist, betrachtet werden.

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With 4 Figures     

Littoral '92

Reports

Littoral '92     

Geochemistry of Gneiss-Granulite transformation in the “incipient charnockite” zones of southern India

Summary Upper amphibolite facies gneisses in the southern Indian Shield show local transformation into veins, clots and patches of orthopyroxene-bearing dry granulites (incipient charnockites). Depending upon the protolith composition, these desiccated zones are classified into ortho- and para-charnockites and have developed within rocks of distinct mineralogy and chemistry at different time intervals through the structurally-controlled influx of carbon dioxide-rich fluids. Our geochemical investigations at five critical quarry sections indicate that the incipient charnockites have undepleted chemistry and very low K/Rb values. In the paracharnockite localities, where granulite formation is characterized by consumption of garnet, biotite and quartz to produce orthopyroxene, loss of Rb and Ba and enrichment of Ti are observed. In contrast, the orthocharnockite localities show marked LILE enrichment with gain of K, Rb and Ba and loss of CaO, suggesting extensive replacement of plagioclase in the gneisses by K-feldspar in the charnockite through K-Na-Ca exchange reactions with influxing carbonic fluids. The marked depletion in Fe, Mg, Ti and P in these rocks correlates with progressive dissolution of hornblende, biotite, magnetite and accessory apatite. Our study indicates that gneiss to granulite transformation, even if on a local scale, is not an isochemical phenomenon, but attended by distinct element mobilities, although they are contrastingly different from the geochemical trends in some regional high grade terrains.

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Geochemie von Gneiss-Granulit-Übergängen in den Incipient Charnockite Zonen von Süd-Indien

Zusammenfassung Gneise der oberen Amphibolit-Fazies im Südteil des Indischen Schildes zeigen lokal Umwandlungen in Adern, and unregelmäßigen Bereichen von orthopyroxen-führenden trockenen Granuliten (Incipient Charnockites). In Abhängigkeit von der Zusammensetzung des Ausgangsgesteins werden diese Zonen in Ortho- und Paracharnockite eingeteilt. Sie entwickelten sich in Gesteinen von charakteristischer mineralogischer und chemischer Zusammensetzung zu verschiedenen Zeit-Intervallen durch die tektonisch kontrollierte Zufuhr von kohlendioxid-reichen Fluiden. Unsere geochemischen Untersuchungen an fünf strategisch ausgewählten Steinbruchen zeigen, daß die Incipient Charnockite eine nicht verarmte chemische Zusammensetzung und sehr niedrige K/Rb Werte haben. In den Paracharnockit-Lokalitäten, wo Granulitbildung charakterisiert wird durch das Verschwinden von Granat, Biotit und Quartz, aus denen Orthopyroxene gebildet werden, ist Verlust von Rb und Ba und Anreicherung an Ti zu beobachten. Im Gegensatz dazu zeigen die Orthocharnockite eindeutige LILE Anreicherung mit Zunahme von K, Rb, und Ba und Verlust von Ca0. Dies weist auf extensiven Ersatz von Plagioklas in den Gneisen durch K-Feldspat in den Charnockiten durch K-Na-Ca Austausch-Reaktionen mit zugeführten C0₂-Fluiden hin. Die deutliche Verarmung an Fe, Mg, Ti und P in diesen Gesteinen wird mit zunehmender Auflösung von Hornblende, Biotit, Magnetit und akzessorischem Apatit erKlärt. Unsere Untersuchungen zeigen, daß die Gneis-Granulit Transformation auch im lokalen Maßstab nicht ein isochemisches Phänomen ist, sondern durch charakteristische Elementtransporte charakterisiert wird. Diese unterscheiden sich jedoch deutlich von den geochemischen Trends, die in einigen regional-metamorphen high grade terrains zu beobachten sind.[/p]

     

The structural state of the former lower continental crust in Calabria (S. Italy)

In the Northern Serre (S. Italy), a continuous section through a former lower continental crust is exposed (Schenk 1984, 1985). These granulite facies rocks have not been penetratively deformed during their uplift to higher crustal levels. Therefore, they allow to study the structural state of the lower continental crust. Most rockforming minerals, among them ortho- and clinopyroxene and cordierite, show recrystallization structures. Quarz basal subgrain boundaries are developed in lower levels of the lower crust and disappear toward higher levels. In addition to dimensional orientations of the rockforming minerals, the preferred crystallographic orientations of plagioclases, cordierite, amphibole, pyroxenes and, rarely, quartz reflect the strain orientation of the prograde high-T deformation. During this deformation, the stretching direction was constant NNE-SSW throughout the exposed lower crustal section. Shear indicators are rare. This points to the fact that deformation has been homogeneous and coaxial flattening. There is only a small variation in orientation and strength of textures throughout the exposed lower crust. Therefore, neighbouring layers of different composition rather than different deformation might serve as seismic reflectors in the former lower crust.

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Zusammenfassung In der nördlichen Serre (Süditalien) ist ein zusammenhängender Bereich einer ehemaligen kontinentalen Unterkruste aufgeschlossen (Schenk 1984, 1985). Diese granulitfaziellen Gesteine sind bei ihrem Aufstieg in höhere Krustenbereiche nicht durchgreifend überprägt worden. Deshalb läßt sich an ihnen noch der strukturelle Zustand der ehemaligen Unterkruste studieren. Außer in Feldspäten, Quarz und Amphibol tritt auch in Ortho- und Klinopyroxen und in Cordierit Rekristallisation auf. In tieferen Krustenniveaus sind im Quarz basisparallele Subkorngrenzen entwickelt, die in höheren Krustenbereichen nicht auftreten. Sowohl die Gestaltregelungen der gesteinsbildenden Minerale als auch die kristallographischen Plagioklas-, Cordierit-, Amphibol-, Pyroxen- und (seltener) Quarzregelungen spiegeln die Strain-orientierung der prograden hochtemperierten Deformation wider. Während dieser Deformation blieb die Streckung im gesamten Unterkrustenbereich konstant NNE-SSW orientiert. Scherindikatoren sind selten. Beides deutet darauf hin, daß die Deformation homogen und als koachsiale Plättung abgelaufen ist. Im gesamten aufgeschlossenen Unterkrustenbereich variieren weder Intensität noch Orientierung der kristallographischen und gestaltlichen Regelungen der gesteinsbildenden Minerale wesentlich. Deshalb sollten in der ehemaligen Unterkruste Lagen unterschiedlicher Deformation weniger als seismische Reflektoren in Frage kommen als Lagen unterschiedlicher Zusammensetzung.

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Résumé Le Massif de la Serre Septentrionale en Calabre (Sud de l'Italie) représente un tronçon d'une ancienne croûte continentale profonde (Schenk 1984, 1985). Les roches du faciès granulite qui le constituent n'ont pas subi de déformation penetrative lors de leur ascension dans les niveaux plus superficiels de la croûte. Leur étude permet donc de reconstruire les caractéristiques structurales de l'ancienne croûte profonde. Non seulement les feldspaths, le quartz et l'amphibole, mais encore l'orthopyroxène, le clinopyroxène et la cordiérite ont recristallisé. Dans les niveaux les plus profonds de la croûte on observe dans les cristaux de quartz des bordures de sous-grains parallèles à la base. Celles-ci n'apparaissent plus dans les niveaux plus superficiels. L'orientation des cristaux des minéraux constitutifs des roches, de même que l'orientation des réseaux cristallins du plagioclase, de la cordiérite, de l'amphibole, du pyroxène et (mais plus rarement) du quartz réflètent la direction de contrainte de la phase de déformation prograde de haute température. Pendant cette phase de déformation, la direction d'extension est demeurée NNE-SSW. Les témoins de cisaillement sont rares, ce qui montre que la déformation s'est effectuée de façon homogène, en relation avec un aplatissement coaxial. Les textures varient très peu en orientation comme en intensité dans toute la coupe de croûte profonde exposée. En conséquence, l'existence de réflecteurs sismiques devrait refléter des différences dans les compositions minéralogiques des roches plutôt que dans leurs caractéristiques structurales.

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Coulomb-trapped particles in the electromagnetic fields of an oblique magnetic rotator

An oblique, rotating magnetized sphere emits electromagnetic waves which, for large magnetization, can quickly accelerate charged particles to very high energies. A central, attractive Coulomb force can trap particles in the region beyond the light cylinder by balancing the accelerating influence of the radiation on the particles. We sample some of the particle orbits possible under these dynamical conditions. A general feature of these orbits is that non-interacting particles started with random initial conditions in the domain of attraction of these orbits will arrange themselves on a curve corotating with the axis of magnetization. Such particle configurations can be a source of pulsed radiation. In the idealized case of no interparticle interactions the spectral index for the radiation emitted by one frequently occurring configuration is found to be –2/3, for emission from radio to -ray frequencies. The dynamical conditions in this simple model closely match those prevalent in outer pulsar magnetospheres, making it possible that part of the radiation from pulsars is emitted by trapped plasma in the region beyond the light cylinder.