THE NATURE AND ORIGIN OF PLANETARY MAGNETIC FIELDS

by

CONSTANTINE THOMAS

Submitted as a Final Year Project for the Physics of Planetary Interiors course, Exploration Geophysics BSc (Upper Second Hons), UCL, 1994

INTRODUCTION

Many of the planets in the Solar System possess magnetic fields, and almost all have possessed them in the past, with the probable exception of tiny distant Pluto. The origin and nature of these planetary magnetic fields is a major topic of research in planetary science today.

There are three main types of planetary magnetic field, coincidentally corresponding to the three classes of planets in the Solar System:

The first group is that of the Terrestrial Worlds - those small solid bodies (including the Earth and its Moon (Luna)) orbiting near the Sun. Of the terrestrial worlds, Earth and Mercury are the only ones that now possess a magnetic field, while Mars and Luna may once have possessed a field which has since collapsed. Venus is unusual in that it too may have once possessed a magnetic field which has disappeared, but which may re-appear in the future. The magnetic fields of the terrestrial planets are believed to be generated in their convecting molten iron cores, and are the smallest in magnitude in the Solar System.

The second and third groups are technically subdivisions of the Jovian Worlds - huge balls of hydrogen and helium gas. These worlds form in similar ways, beyond the 'Frost Line' where Ices and volatiles dominate over rocky material. The difference between the two sub-types is a result of the distance at which they formed from the Sun.

The first sub-type, referred to here as the Large Gas Giants (LGG's), are Jupiter and Saturn. These are the largest of the four Jovians in the Solar System, and are located nearest the Frost Line. Their magnetic fields are very large in magnitude, and are believed to be generated in a shell of liquid metallic hydrogen surrounding their rocky cores.

The final sub-type of magnetic field are those of the Icy Giants, Uranus and Neptune. These Jovians are similar in size, being around 50,000 km across, but both share unusually displaced and tilted magnetic fields. Their field strengths are intermediate between the LGGs and the Terrestrials, being 50 and 25 times as strong as the Earth's respectively. Their magnetic fields are believed to originate in an ionized convecting molten ice mantle.

Magnetic fields are by no means static phenomena - they display many variable characteristics, not least of which is the possibility of complete reversal in direction over a short period of geological time (on the scale of 105 yrs). In addition, the smaller planets (ie. Mars and Luna) seem to have completely lost their 'active' magnetic field, although there is evidence (at least on Luna) that 'remnant magnetism' can still be found in the surface rocks of the planet.

This report will summarize the primary characteristics of planetary magnetic fields, and theories on their possible origin.

NOTE: The nomenclature used in this report has been previously defined in my 'Uranus and Neptune' report (pages 9 -11, 'Magnetic Field Geometry 101') - this explains the terms used in this report, such as 'magnetosphere', 'magnetotail', 'solar wind', and 'bow shock'.

PART 1: THE ORIGIN OF MAGNETIC FIELDS

The mechanism that sustains planetary magnetic fields is well understood. In all cases, the magnetic field is driven by what can be approximated to a self-exciting dynamo.

In all dynamos, an electrically conducting material rotates through a magnetic field, which generates a current. An example of a normal dynamo is one that drives a bicycle light - the faster one pedals, the brighter the light. This is caused by a metal disc, rotating between two (permanent) magnets. As it rotates, free electrons are forced towards the centre of the disc, creating a potential difference between the edge and the centre, which produces a current. In the case of the bicycle, the pedals turn the disc, which in turn generates the current which powers the light.

However, it is also possible to construct a self-exciting dynamo, which replaces its permanent magnets with electromagnets. This type of dynamo uses the current it generates to power its electromagnets, creating a magnetic field through which the metal disc rotates, which in turn generates the current to power the magnets. Thus, all that is required is a current to initially start the dynamo, and the magnetic field set up as a result will create the current to drive it - thus, the field is self-sustaining, and requires no further outside input. It is the principle behind these self-exciting dynamos that is believed to drive planetary magnetic fields.

Planetary magnetic fields are believed to be generated in convecting, electrically conducting fluids located near the planetary core - the three different types of magnetic field are generated in different electrically conducting fluids. As long as these fluids are convecting, the magnetic field can be sustained.

The mechanisms that drive the three field-types are present in the following sections.

Dynamo Origins: Dynamo generation in all the planets initially occurred as a result of heat-flow convection. All planets (Terrestrial and Jovian) generate (and lose) heat in some way, whether through radiogenic heating (in the former) or contractional cooling (in the latter). This manifests itself as a heat flux, which can be transported in one of several ways, depending on the level of flux.

If the conductive adiabatic cooling rate of a planetary interior (Fcond,ad) is greater than the cooling rate of its core (Fc), then the 'excess' heat flow (ie. Fc - Fcond,ad) will be transported convectively - ie. convection will occur in the core fluid (when Fc > Fcond,ad). If the cooling rate of the core is less than the conductive adiabatic cooling rate (ie. Fc < Fcond,ad), then convection cannot occur since large-scale motions of fluid in the core are not possible in these conditions. Mantle convection (and heat loss) also restrains the core heat flux, since the core cannot cool faster than the mantle.

It is believed that, above a certain convective velocity, a magnetic field is 'induced' in the fluid as a direct result of the rapid motion of the electrically conducting fluid, which in turn creates a current which also drives the dynamo. In a purely thermal system (ie. the initial state of all the planets after formation), this critical convective velocity can be represented by the heat flux Fd (the total heat flux required to generate enough convection to drive a dynamo (this includes Fc)). If Fd is sufficiently greater than Fcond,ad (ie. if Fd - Fcond,ad reaches a critical value), then a dynamo will be generated.

In a system where only heat flow is important, there are thus three possible 'regimes' under which the planetary interior can develop - which path the planet follows depends on its heat flux. The parameters used below are Fcond,ad, Fc, Fd (all defined on the previous page) and F (the actual heat flux of the planet):

(1) If F < Fcond,ad, the heat flux is conductive, and there is insufficient energy to drive convection (thus no dynamo is present).

(2) If Fcond,ad < F < Fd, the temperature profile is adiabatic, and convection can occur. This means that Fc > Fcond,ad, so there is both conductive heat flow (through Fcond,ad) and convective heat flow (ie. Fc - Fcond,ad). However, since Fd - Fcond,ad is not large enough, no dynamo is generated (even though convection is present).

(3) If F > Fd, convection occurs as described above, but Fc - Fcond,ad now exceeds Fd - Fcond,ad, allowing the creation of a dynamo.

The difference between Fd and Fcond,ad is known to be much smaller than Fcond,ad itself. Thus, it is highly unlikely that Regime (2) would occur in a given planet. Knowing this, it is most probable that any given world will initially satisfy either Regime (1) or (3) - ie. there will either be no core convection at all, or there will be convection and a dynamo.

Dynamo evolution: While there is no clear evolution that can apply to all the planets (they are all too different for a single 'evolutionary law' to apply), the following sequence of events is the most probable.

Once the dynamo is initially generated through heat-flow convection, the magnetic 'seed' field is small in magnitude, but the 'self-exciting' capability of the dynamo will gradually increase the field strength. The growing magnetic forces eventually overcome the Coriolis (rotational) forces that initially constrain the convection, causing the flow to become more vigorous. The field strength peaks at a stable value near an 'optimal value' related (among other things) to the density and velocity of the convecting fluid.

The heat flow in terrestrial worlds drops off after the planet's formation, as a result of the decay of short-lived radioisotopes in the core (see 'Terrestrial Worlds'). However, around this point solidification of the core begins, and the dynamo is now maintained by compositionally driven convection currents which result from the solidification of the core (see 'Terrestrial worlds'). The dynamo is sustained as long as convecting fluids are present. Eventually, the dynamo system will collapse if there is insufficient heat flow to drive convection or if the core completely solidifies - both of which occur as a result of the planet's evolution.

In Jovians, heat-flow convection remains as the planet cools through contraction (see 'Jovian Worlds'). The internal heat flux does not drop below the critical value required for dynamo generation until much later in the planet's evolution (this has not occurred in the 4.6 billion years since the Jovians formed, and it can be assumed that the lifetime of the Jovian dynamo is at least a few billion years longer than this). Thus, Jovians can maintain their magnetic fields for much longer than the slowly solidifying Terrestrial worlds.

Presumably there will come a time (several billion years hence) when the Jovian has lost so much heat that thermally driven convection cannot continue. Since there is probably no material in these planets (except perhaps in the Icy Giants) that can solidify to drive compositional convection, the dynamo will collapse at this point.

This exact evolution may not apply for all planets, but the general sequence of events is the same for all worlds - the dynamo forms, grows, peaks, and then gradually dies.

Non-dynamo origins: There have been many suggestions of possible non-dynamo origins for the magnetic fields, including the possibility that a planet's magnetic field is induced by the magnetic field of the Sun, or that a rotating ferromagnetic body can create its own magnetic field simply by the fact that it contains free electrons which also rotate with the body. However, the magnitude of the predicted magnetic fields set up as a result of these non-dynamo models falls far short of that of the observed magnetic fields - while it is possible that these may contribute a very small part to the total magnetic field, it is not likely that they are responsible for the gross magnetic fields of the planets.

The rotation of the planet itself can also create convection currents in its fluid core. Simultaneously, these rotational currents can serve to disrupt the initial creation of heat-flow convection in the core, as it sets up turbulence in the flow. Nevertheless, convective flows that have a strong rotational influence appear to be much more likely to satisfy the dynamo criteria stated above than 'non-rotating' flows.

Tidal forces from nearby satellites may also influence the dynamo, but both tidal and rotational effects are much less important than heat-flow convection.

TERRESTRIAL WORLDS

The main property of terrestrial planetary dynamos is the fact that their electrically conducting fluids will ultimately solidify. The exact composition of these electrically conducting core fluids is different for all the terrestrial planets - however, in all cases the predominant constituent is iron, with varying degrees of sulphur and/or oxygen impurities. These impurities are important, as they lower the freezing point of the core fluids.

While this fluid is a very good electrical conductor, it must be kept molten in order to generate the magnetic field. However, the interiors of most of the terrestrial worlds are slowly cooling - their cores are solidifying (ie. freezing), separating out into a molten outer core and a solid inner core.

The mechanism that actually generates the magnetic field of terrestrial worlds today is believed to be this solidification of the inner core. Being impure, the core fluids cool eutectically - ie. as cooling continues, pure material (iron) solidifies from an increasingly impure melt, until the eutectic point is reached and the very impure liquid solidifies.

This eutectic cooling occurs in the centre of the planet, so that a solid iron inner core forms in situ. The impure melt which forms as a result of this cooling appears immediately above the solid iron - thus there is a chemical discontinuity in the overlying fluids since the more impure melt is overlain by unaltered core fluid. Being less dense, the more impure melt rises through the overlying core fluid, which results in the initiation of compositionally driven convection currents that can drive the planetary dynamo. The inner core continues to grow, until it (theoretically) solidifies completely, collapsing the planetary magnetic field.

It is important to note that this compositional convection can only occur once the heat flux has dropped to such an extent that the core can begin to solidify. In the time between the planet's formation and the initiation of core solidification, the heat flow convection described in the previous section is the primary generator of the magnetic field. It is quite possible for the dynamo to collapse at the time that the heat flow convection ceases if core solidification criteria are not met - this is believed to have occurred in Venus. There are other ways in which a dynamo may not be maintained after the initial thermal-convection stage of a planet's evolution - these will be discussed in the second part of this report.

While it is certain that planetary magnetic fields are maintained by dynamos, there are two different models that can explain the lack of a magnetic field. The first model states that the core has completely solidified, as defined above. The second states that the core is in fact completely fluid, yet stably stratified - ie. there is no convection within the core. Without this convection, no magnetic field can be generated.

In general, the latter model appears to be more accurate - the timescale required for complete core solidification appears to be too large to fit the observed magnetic fields. The only way to be sure would be to determine the internal structure of the planets by using seismic data. This would reveal whether the planet has a solid or liquid core, and would also indicate the presence of a solid inner core.

Both models allow a planet to possess a magnetic field early in its history, which would then disappear at some later stage. The core-freezing hypothesis states that by default there must have been a period when the planet's core was partially molten, and that the continuing solidification of the inner core (and the associated compositional convection) would allow the existence of a magnetic field in that period. Once the core is completely solid, the field can no longer be generated, so disappears.

The stable-fluid core models use the thermodynamics described on page 2 to provide the means of convection - ie. if Fc > Fcond,ad, heat will be transported convectively in the core fluid. If Fc < Fcond,ad, convection cannot occur since large-scale motions of fluid in the core are not possible in these conditions. Current theories on planetary formation suggest that the terrestrial planets were initially homogeneous - ie. composed of the same material throughout, from surface to core - and that they later differentiated into Mantle and Core. Assuming that all the planets initially contained the same amount of radioactive isotopes, more heat will be generated through radioactive decay in the early history of the planet.

This is because of the presence of short-lived radioisotopes, which rapidly decay and release their heat. Enough heat is generated in the initial stages of a planet's evolution by the combined decay of short-lived and long-lived radioisotopes to create a core heat flux that is far greater than the conductive adiabatic heat flux (Fcond,ad), so that convection can occur early in planetary evolution. This convection can generate a planetary dynamo and so sustain a planetary magnetic field.

However, as the planet continues to evolve, the short-lived isotopes decay completely and so cease to provide the extra heat - thus, the heat flux will drop to such a level that convection cannot be maintained (when Fc < Fcond,ad), collapsing the planetary magnetic field.

The magnetic fields of specific terrestrial worlds will be discussed in the second part of this report.

JOVIAN WORLDS

The Jovian magnetic fields are all much larger in magnitude than those of the Terrestrial planets. Although undoubtedly driven by the self-exciting dynamo process described on page 2, the fields of the Jovian worlds originate in different electrically-conducting fluids to the Terrestrial worlds. This is because the Jovians are very unlike the Terrestrial planets in internal composition and structure.

All Jovians are composed primarily of hydrogen and helium gas. In the Large Gas Giants (LGG's - Jupiter and Saturn), hydrogen plays a very important role in magnetic field generation. However, the magnetic fields of the Icy Giants (Uranus and Neptune) are believed to originate in their molten icy (H2O, CH4, and NH3) mantles. This difference arises primarily as a result of the size contrast between the two classes of Jovian. The LGG's, as their name suggests, have large diameters - Jupiter is around 143,000 km across, while Saturn is about 120,000 km in diameter. The Icy Giants (Uranus and Neptune) are much smaller, having diameters of 55,118 km and 49,528 km respectively.

In all Jovian worlds, core solidification is not a factor in dynamo generation. In these planets, the dynamo is created and maintained by heat-flow convection. All Jovians have large internal heat sources, although Uranus' heat appears to be trapped in its interior and so cannot escape. This heat originates as a result of the Kelvin-Heimholtz mechanism, in which the gaseous planets contract over time, cooling (ie. emitting heat) as they do so. There is certainly enough heat flux to drive convection in the Jovians' electrically conducting fluids and to initiate dynamo systems within these worlds. In addition, there may be other effects which drive the dynamo - these will be discussed later when specific planets are discussed.

LGG's: The larger diameters of the LGG's enable greater atmospheric pressures to develop in their interiors, as a result of the overlying mass of their huge molecular hydrogen and helium atmospheres. The internal pressures in these worlds are great enough to compress the 'atmospheric' hydrogen and helium gas into liquid molecular (hydrogen and helium) fluid. Beneath this thick molecular fluid ocean, pressures are sufficiently great (around 2 to 3 million bars!) to instigate a phase change from liquid molecular fluid into liquid metallic fluid. This fluid is a very good electrical and thermal conductor due to its metallic properties, and is the location of the LGG planetary magnetic field dynamo.

Icy Giants: The Icy Giants are much smaller than the LGG's, so cannot generate as high internal pressures as the latter - thus their hydrogen and helium cannot be compressed into either molecular or metallic phases. Much more importance is placed on (H2O, CH4, and NH3) ices in the Uranian and Neptunian interiors (as described in my previous report). It is believed that these worlds consist of a very small rocky core, overlain by a thick molten ice mantle which constitutes most of the planetary mass. The outermost region of the planet is the atmosphere, composed largely of H2 and He gas.

Uranus and Neptune possess appreciable magnetic fields, so there must be an some form of dynamo present in these worlds. Since they are not massive enough to possess a liquid metallic hydrogen layer, it is believed that the molten 'Ice' mantle of these planets is under enough pressure to induce ionization in at least the H2O component, which increases its electrical conductivity and allows the generation of the magnetic field.

Alternatively, pressures near the rocky core of these worlds may be large enough to convert the deepest part of the ice mantle into a metallic (or partially metallic) phase, which would be a much more suitable for the generation of a magnetic field. Either form of dynamo may account for the unusual fields (and offset) that these Icy Giants possess.





PART 2: THE MAGNETIC FIELDS OF THE PLANETS.

This section focuses on the origins and properties of the magnetic fields of specific planets. It begins with the inner Terrestrial worlds (Mercury, Venus, Earth, Luna, and Mars), and then goes on to discuss the fields of the Jovian Worlds (Jupiter, Saturn, Uranus and Neptune).

Pluto (the outermost (and smallest) planet) is believed to have a stably-stratified fluid (or completely solid) core - its heat flux was probably never large enough to drive a dynamo, so it is likely that Pluto has never possessed a magnetic field.



TERRESTRIAL WORLDS

MERCURY: Mercury is the smallest (and innermost) terrestrial planet (with a radius of 2240 km), being heavily cratered with no appreciable atmosphere. Before Mariner 10 observed Mercury in 1974 and 1975, it was not believed to possess an appreciable magnetic field. Indeed, it was theorized that the Mercurian core had completely solidified, and that all that would remain was some remnant magnetism on the surface. However, Mercury does possess a sizeable magnetic field - one that is too large to be explained by purely remnant magnetism - and may be the only terrestrial world other than the Earth to currently possess a magnetosphere.

Mercury has a high density (almost as great as Earth's), which implies that it has a truly immense iron core, occupying about 70% - 80% of the planet's radius (and a similar proportion of the planet's mass)! If current models of solar system formation are correct, this core consists largely of pure iron. These models suggest that higher-temperature material (refractory minerals and iron) will concentrate in the region nearest the forming Sun (ie. in the vicinity of Mercury's orbit). It is likely that the refractory materials (aluminium and calcium oxides) did not settle in the core of the planet after differentiation occurred, leaving an almost pure iron core. However, there must be some impurities (probably sulphur) in this core, which are very important for the creation of the Mercurian dynamo.

Being a small world, heat loss would be rapid on Mercury - indeed, if the Mercurian core consisted of pure iron then it would have completely solidified billions of years ago. There is evidence on the surface of radial contraction (ie. global compressional faulting), which is probably the result of inner core freezing (the core contracts as it freezes, creating compressional stresses in the overlying mantle and crust). However, the very existence of a Mercurian magnetosphere implies that there is certainly some dynamo activity occurring in its interior, which in turn means that the core cannot be completely frozen.

The presence of a very small amount of sulphur impurities in the core would be sufficient to prevent the complete freeze-out of the core. A sulphur abundance of only 3% (one-tenth of the solar abundance) would yield a 300 km layer of fluid molten Iron over the solid iron core, in which compositional convection currents would be set up by inner-core solidification. These currents would be sufficiently vigorous to drive a dynamo, which would explain the magnetic field seen today. This level of impurity is certainly possible, even given Mercury's distance from the Sun.

The interior of Mercury probably consists of a huge solid iron inner core about 1500 km in radius, overlain by a thin (300 km) vigorously convecting fluid Fe/S outer core in which the Mercurian dynamo is maintained. Above this lies a solid (probably convecting) mantle and a thick crust.

Magnetosphere: The Mercurian magnetosphere is well defined, with a noticeable bow shock. However, it has only been observed by one vehicle (Mariner 10), so little is known about its geometry and properties. What is known is that it has a magnetic dipole moment (roughly equivalent to the 'absolute field strength') of about 3 x 1022 Gm³, less than 1/2500th that of the Earth. However, being smaller in radius (and with dynamo generation occurring so close to its surface), the actual surface strength of the Mercurian field is about 1/150th that of the Earth.

Because of its proximity to the Sun, the Mercurian magnetosphere is very compressed on the sunward side, due to the high intensity of the incident solar wind. The magnetotail extends for at least 10 Mercury Radii away from the sun. Since the dipole moment is so small, it is unlikely that radiation belts (such as those found around Earth and Jupiter) would be stable in the planet's magneto-sphere. Since dynamo generation occurs so near the surface of Mercury, it is believed that the Mercurian magnetic field is actually highly complicated in structure, with very visible quadrupole and octupole structure. The only way to verify any of this information would be to send another vehicle to orbit Mercury and map out its magnetic field.

In summary, Mercury appears to be the only other terrestrial world (apart from the Earth) that currently possesses an active dynamo, which is best described as a 'thin shell dynamo'. Its fluid outer core must at best be relatively thin, and since inner-core solidification must be continuing it would seem that Mercury is nearing the end of its active magnetic lifespan.


VENUS: Magnetically, Venus is an unusual world. Venus is similar in size to the Earth (only 321 km smaller), but is less dense - as a result, Venus is 0.815 as massive as the Earth. Surface conditions are very hostile, with a 90 bar CO2 atmosphere and surface temperatures of around 700 K (the melting point of lead!).

The internal structure of Venus is very different from Earth's. This is largely due to its higher internal temperatures and lower internal pressures, which are a result of the planet's smaller mass. The higher temperatures result from the high surface temperatures, which change the thermal structure of the mantle (and thus also the core) accordingly - effectively, the centre of the planet 'knows' that the surface is hot! The lower pressures (2.9 Mbar in the centre of Venus, as opposed to 3.65 Mbar in the Earth's centre) result from the planet's lower mass. These lower pressures also limit inner-core solidification, which has important implications for the Cytherean dynamo.

Venus has no intrinsic magnetic field, although it does have an induced field, created by the interaction between the solar wind and the planet's ionosphere (the uppermost region of the atmosphere where solar radiation ionizes atoms and molecules in the atmosphere, creating an electrically conducting layer). This ionosphere serves to deflect the incoming solar wind around the planet, creating a noticeable (but weak) bow shock.

However, the magnetic field does not have any overall structure, consisting only of the bow shock and the 'ionotail' (the 'shadow' caused by the ionosphere in the solar wind). If there is any intrinsic field, its dipole moment must be extremely small in magnitude (1/80,000th that of the Earth at most).

It is believed that Venus currently has a completely fluid molten iron core, with roughly the same proportion of sulphur and oxygen impurities as the Earth. Venus' different internal pressure and temperature structure have prevented any core solidification, which in turn has precluded any dynamo generation.

Cytherean magnetic evolution is believed to have occurred as follows: After formation, there was sufficient heat-flow convection in the core to drive a planetary dynamo and thus create a magnetic field. However, this ancient field is unlikely to be preserved in surface rocks today, since the ambient temperatures are so high. Around 1.5 billion years ago, the heat flux dropped to levels that were insufficient to drive this dynamo, thus collapsing the intrinsic magnetic field. Since then (until the present day), Venus has not been capable of sustaining a dynamo - however, the ionosphere of the planet provides enough protection from the solar wind to create a bow shock and magnetotail around Venus.

In the future (probably millions of years hence), the Cytherean interior will have cooled to such an extent that core-solidification can begin. This will drive compositional convection in the fluid (outer) core, thus initiating dynamo action. Thus, Venus may yet possess a magnetic field which will probably be much like the Earth's today. Billions of years from now, it is entirely possible for Venus to be the only terrestrial world to have an active magnetic field, since all the others may have long since lost their fields through total core-solidification.

Today, Venus can be best described as being in an 'inter-dynamo' phase - too cool for thermal convection to drive a planetary dynamo, but too hot for core-solidification to occur. Effectively, Venus is in magnetic 'limbo'.


EARTH: The Earth's magnetic field is of course the most well understood of all the planets. The Earth (Terra) is the largest of all the terrestrial worlds, with a radius of 6371 km, and a density 5.517 times that of water. Seismic data has shown that the Terran internal structure consists of a solid iron inner core 1221 km in radius, surrounded by a liquid iron outer core 3485 km in radius, overlain by a silicate mantle at least 2800 km thick and a thin crust 70 to 100 km in depth.

The driving force sustaining the Terran dynamo is the solidification of the inner core. Inner core freeze-out is believed to have commenced about 2 billion years ago - prior to this, a magnetic field driven by thermal convection was present, probably since the planet's formation. It is important to realise that present-day outer core convection is the direct result of inner-core solidification - had this not begun, the thermally driven convection would have collapsed about a billion years ago and the Earth would not have a magnetic field today. The initiation of core freezing would have dramatically increased the strength of the intrinsic (thermally driven) field, as large amounts of gravitational and latent heat energy was released by the freeze-out.

It is also important to note that mantle evolution has significantly affected the evolution of the Terran dynamo (and probably the other terrestrial worlds as well), since the core cannot lose heat faster than the mantle can transport it. Core freeze-out is continuing today because the mantle itself is slowly cooling, which in turn causes the core beneath it to cool and solidify.

Terran Magnetic Variation and Reversals: The Terran magnetic field is not a static phenomenon - it has been shown to vary over all timescales, from geologic to diurnal. The daily variations are caused by the changing strength of the solar wind, which alters the shape of the magnetosphere.

On a longer (decade to millennium) timescale, the (dipole) magnetic axis has been decreasing since 1960, before which it was stable at 11.5° for at least the previous century - it is currently tilted at 10.8° to the rotational axis. The dipole has also drifted westwards by at least 40° over the past 400 years, although this drift rate has not been constant. The dipole strength has also dropped by 17% over this period, and the rate appears to be accelerating as time goes on - at present, the Terran dipole moment is 7.9 x 1025 Gm3.

Clearly, the Terran magnetic field is going through an unstable phase at the (geological) moment. This is not unprecedented in the evolution of our planet - palaeomagnetic studies have revealed a long history of magnetic reversals preserved in the oceanic crust, going back several hundred million years. These studies examine the remnant magnetism of the spreading basaltic crust, which preserve the magnetization vector (ie. field direction) of the region at the time the rock cooled. The data shows that the magnetic field vector has completely reversed direction hundreds of times throughout the Earth's history, and that the frequency of these reversals has been steadily increasing over the past 100 Ma - they now occur once every few hundred thousand years.

It is interesting to note that between 165 and 125 Ma, the polarity of the Terran magnetic field was rather unstable, changing frequently. Between 125 and 70 Ma, there followed a period when the field was very stable, polarized in the same direction as today - indeed, between 85 and 120 Ma, no reversals are recorded at all. Between 55 and 70 Ma, the field was fairly stable, changing polarity every few million years. For the past 55 million years or so, the field vector has been highly unstable (more so than during the Jurassic and Early Cretaceous), reversing polarity hundreds of times with each change enduring for only a fraction of a million years.

The mechanism behind magnetic reversals is still not fully understood. One suggestion is that the normally stable convection currents in the core gradually develop into cyclonic spirals as a result of Coriolis forces produced by the Earth's rotation. These cyclones remove the radial symmetry from the convective system within the planet, as they rotate in opposite directions in the northern and southern hemispheres. Eventually, stable convection resumes as one cyclonic cell dominates over the other - the convection in this cell may be in the opposite direction to the previous fluid motion, thus reversing the field.

A more recent model proposes that the reversal process is at least partly controlled by mantle topography and convection. Indeed, the present decay of the Terran field strength described above may be a precursor to such a reversal, although it is equally likely that the field will fully recover without reversing polarity. In this model, the dipole field vector reverses via an intermediate quadrupole field. This reversal process is shown in the diagram below.


Fig 1: A possible mechanism for magnetic field vector reversal, via an intermediate quadrupole field.

It is suggested that all reversals originate in the same low latitude region of the southern hemisphere, deep within the Earth near the core-mantle boundary.

A related model suggests that there may be an indirect link between plate tectonism and magnetic reversals, since mantle convection may play a key role in driving both processes. It is proposed that the thicknesses of the boundary layers either side of the core-mantle boundary affect convection in both the outer core and the mantle. In the region above this boundary, heat pulses are released into the mantle. These thermal pulses rise along paths influenced by mantle convection cells, eventually reaching the lithosphere and creating hotspots on the surface (eg. Hawaii). Below the core-mantle boundary, cold thermal pulses are sent into the outer core. These 'cold plumes' affect outer core convection, and so influence the magnetic reversal rate. This coupling between core and mantle is regulated by the thickness of the thermal boundary layers (in which the pulses originate) on either side of the core-mantle boundary.

Magnetosphere: The magnetosphere of the Earth has been intensely studied by the huge number of satellites in orbit around the planet. The bow shock stands at about 15 Earth Radii (RE) to the sunward side of the planet, with the magneto-pause itself located at a distance of 10 RE. The magnetotail extends in the antisolar direction for at least 1000 RE.

The magnetosphere holds a variety of energetic charged particles, collectively known as plasma. These are supplied by various sources, including the solar wind itself, the ionization of the atmosphere, and cosmic rays from beyond the Solar System. There are two regions within the magnetosphere in particular in which this plasma is trapped - these are the Van Allen belts, located at 1.5 and 5 RE. Substorms occur as a result of a buildup of magnetic flux within the magnetotail through the interaction of the solar wind and magnetosphere. Eventually, the energy is released, driving the aurorae and disturbing the ionosphere.



LUNA: Luna (the Moon) is the nearest planetary body to Terra, yet its magnetic evolution is very poorly understood. If current theories of Lunar origin are correct, it may be the most difficult world in the entire Solar System to model.

Luna is the smallest terrestrial world, with a radius of 1738 km. It also has an anomalously low average density of 3.3 kgm-3, well below that of the Earth. This has been explained in several ways, but the most convincing argument so far has been that the material that would eventually form the moon was blasted out from the Earth in a cataclysmic impact soon after the planet's formation and subsequent differentiation. The impactor was a Mars-sized body (about 6000 km across), which is assumed to have already differentiated into a mantle and core. The impactor struck a 'glancing blow' on the newly formed Earth, and was completely destroyed. The impactor's core was incorporated into that of the Earth (possibly having implications for Terran bulk composition), while the majority of both planets' mantles were vaporized and ejected into orbit around the Earth. Being composed of mantle material, this ejecta was deficient in iron, but enriched in refractory (high-temperature) material. Most of the volatiles were lost to space as the debris formed into a circumplanetary disk around the Earth, which later coalesced into the Moon within a few tens of millions of years.

This model may not be completely accurate, but it is currently the most favoured. If it is indeed correct, then it will be extremely difficult to model the lunar interior, since the thicknesses of the lunar mantle and core would depend on what parameters are used for the giant impact.

Luna no longer possesses an active intrinsic magnetic field, although there is considerable remnant magnetism in its surface. The evidence available suggests that there may be a small metallic (probably FeS) core whose radius cannot be greater than 500 km. However, the existence of this core is by no means certain, as it is neither required nor excluded by lunar moment of inertia calculations. The state of this core is still uncertain, but it is probably partially fluid, with continuing inner core-solidification. However, there is insufficient energy available (by a factor of three) to drive any compositional convection currents. The heat flux is also too low to drive thermal convection - thus, Luna may be the only world undergoing core-solidification that cannot generate enough convection to drive a dynamo, possibly satisfying Regime (2) on page 3.

Palaeomagnetic data from the surface rocks suggests that there was an intrinsic magnetic field between 3.9 and 3.0 Ga. The origin of this field is not clear - it may have been the result of thermal convection in the completely fluid core, but it could equally have been formed because compositional convection currents created as a result of core-solidification were strong enough to drive a dynamo at this time.

The Moon interacts with the solar wind as if it was an inert (though slightly conducting) body. Luna casts a shadow in the stream of charged particles, creating a conical plasma umbra (ie. deep shadow) which is completely devoid of any matter - this may be the most perfect vacuum in the entire solar system.


MARS: The existence of an intrinsic Martian magnetic field is unverified at present. If one is present, then it must be very weak, with a maximum possible dipole moment of about 1022 Gm3 (1/8000th that of the Earth). Mars possesses an induced bow shock and magnetotail similar to that found at Venus, which may be created by the interaction between the planet's ionosphere and the solar wind. Whether or not this bow shock is the result of an intrinsic field remains to be seen, since probes sent to the planet have not been sufficiently sensitive to detect one.

Internally, Mars probably possesses a metallic core enriched in sulphur. This enrichment is probable because sulphur is a volatile element, which becomes more abundant in the solar nebula as distance increases from Sol. Since Mars is located in a further orbit than any other terrestrial world, it is likely to contain more sulphur. The high core sulphur abundance lowers its melting point considerably, which means that the core may still be completely molten. If this is true then heat-flow convection should have ceased 3.5 billion years ago, with no subsequent inner-core solidification. Thus, Mars may be internally similar to Venus. However, another source of evidence suggests that the core may actually be completely solid today.

This evidence is provided by the SNC meteorites. These are meteorites found on Earth that may have originated on Mars. Geochemical evidence suggests that these are fragments of a Martian lava flow erupted 1.3 Ga ago, which was struck by an impacting body some 180 Ma ago. The debris from this impact was ejected at sufficiently high velocity to escape from the Martian gravitational field, and eventually found its way into the Earth's sphere of influence and onto the surface of our planet. Palaeomagnetic studies indicate that these rocks cooled in a surface field of between 0.001 and 0.1 Gauss in strength. If this is true, then it suggests that a substantial Martian dynamo existed as recently as 1.3 Ga ago (for comparison, the strength of the Earth's magnetic field at its surface is 0.3 G). This implies that core solidification was occurring, since a thermally driven Martian dynamo in a completely fluid core should have collapsed around 3.5 Ga ago - if this is the case, the present lack of a magnetic field may be explained by the fact that Mars now has a completely solid core (despite the presence of sulphur). This could only occur if the mantle is rich in volatiles, which lowers its viscosity and aids heat transfer away from the core through mantle convection. Alternatively, current estimates of the sulphur abundance within the core may be too high, so that the core actually solidifies at lower temperatures than previously considered.

In summary, Mars currently does not possess an intrinsic magnetic field. If the SNC meteorites are truly examples of Martian crust, with preserved (unaltered) magnetism, then they imply that the Martian core is now completely frozen and that the mantle is richer in volatiles than previously suspected. If these meteorites did not originate on Mars, then it is equally likely that the core is completely fluid and not convecting - the high core sulphur content would have prevented inner core freeze-out from occurring after thermal convection ceased 3.5 Ga ago.



JOVIAN WORLDS

JUPITER: Jupiter is the largest planet, with a radius of 71,372 km - it also possesses the most powerful, complex and extensive magnetic field of all the planets. Its dipole moment is 1.5 x 1030 Gm3 (about 20,000 times that of the Earth), while the field strength at its equator is 4.2 G! The magnetosphere itself is huge, extending at least 650 million km downwind of the planet, and has been detected as far as the orbit of Saturn! On the sunward side of the planet, the bow shock stands at an average distance of 80 Jupiter Radii (RJ), although this varies as the strength of the solar wind fluctuates - the magnetopause lies at a distance of between 60 and 70 RJ. At the magnetopause, the energetic particles that make up the solar wind are decelerated so abruptly that they are heated to phenomenal temperatures (between 300 and 400 million K!!).

Beyond 20 RJ, the Jovian magnetosphere is forced into a single plane that lies roughly within the planet's magnetic equator - in this region, huge electrical currents flow in a current sheet which holds about 300 million amps!

Within 20 RJ are immense radiation belts similar in nature to the Terran Van Allen belts, but over 10,000 times as powerful. Highly energetic particles are trapped within these belts - Pioneer 10 (the first spacecraft to fly through the belts) was very heavily irradiated, receiving a total dose of over 250,000 rads from the protons and electrons therein. For comparison, a whole body dose of 500 rads would be fatal for a human. These belts were so intense that they seriously jeopardized the Pioneer 10 mission, damaging several circuits and darkening optics. As a result, subsequent missions had to be redirected to bypass the radiation belts.

The Jovian magnetosphere contains a variety of unique features, not least of which are the Io flux tube and plasma torus. All of Jupiter's Galilean satellites lie within the magnetosphere and are constantly bombarded by high energy protons and electrons, which erode their surfaces. However, this erosion is particularly intense on Io (the innermost Galilean satellite), creating a huge cloud of (neutral) sodium, potassium and magnesium that stretches along Io's orbit. In addition, the volcanoes on the highly active moon eject vast amounts of dust and sulphur dioxide that become ionized and accumulate along the orbit, to form the plasma torus.

It is believed that Jupiter and Io are connected by a 'flux tube' of ions and electrons, which carries an immense current of 5 million amps at a potential difference of 400,000 volts - the power generated by this flux tube (about 2 x 1012 watts) is over 70 times the combined generating capacity of all the nations of the Earth! This energy may also contribute to the heating of Io's interior, sustaining its volcanic activity.

The presence of a Jovian magnetic field was first suggested in 1955 by the detection of naturally-generated radio waves emanating from the planet. There are three types of radio emission, two of which are originate in the Jovian magnetic field. The first type has frequencies of between 425 kHz and 40 MHz, corresponding to wavelengths of 700 m to 7.5 m respectively - because emission predominantly occurs at wavelengths measured in tens of meters, it is known as decametric radiation. These emissions are not continuous, but are characterized by strong bursts at irregular intervals - they are believed to originate through the interaction of Io with the Jovian magnetic field.

In addition, decimetric (centimetre-band) radio emissions were also detected at Jupiter, originating from a toroidal region encircling the planet. Unlike decametric emissions, these are continuous and non-sporadic in nature. Decimetric emissions are produced by synchrotron radiation, in which electrons are accelerated at relativistic velocities in helical paths around magnetic field lines - under these conditions, the electrons emit polarized radiation pointing along the direction of the particles' motion. Examination of this synchrotron radiation can yield information on the obliquity and polarity of the Jovian magnetic field.

The Jovian field is aligned at an angle of 10.8° to its rotational axis, and is currently 'reversely' polarized - ie. its south magnetic pole is located near its north geographic pole, and vice versa (it is probable that the magnetic fields of all Jovian worlds periodically undergo reversals like the Earth, but their frequency is uncertain).

Beyond a distance of 2 RJ, the Jovian magnetic field is dipolar in geometry - within this distance, the field is much more complex with quadrupolar and octu-polar components. The Jovian magnetic field appears very similar to that of the Earth, although at a much larger scale - however, the mechanism driving the former is very different to that driving the Terran field.

Jupiter's dynamo is certainly driven by thermal convection within its fluid interior. As described on page 6, the pressures within the LGGs are great enough to transform gaseous hydrogen and helium into liquid molecular fluid and (at greater depths and pressures of 2-3 Mbars) liquid metallic fluid. While dynamo generation certainly occurs within the electrically conducting liquid metallic layer, it may also extend to the deep molecular fluid since at high temperatures and pressures the molecular hydrogen is likely to be a good semi-conductor. Above a large rocky core which occupies the innermost 20% of the planet's volume, the metallic layer extends between 0.2 RJ and 0.75 RJ, with the overlying semiconducting molecular region (if it exists) extending out to 0.9 or 0.95 RJ. Thus, the region of dynamo generation may occupy up to 75% of the planet's radius!

In summary, the magnetosphere of Jupiter is the most powerful of all the planets in the solar system. It contains many unique features, some of which (the plasma torus and flux tube) originate through the presence of Io, its volcanic satellite. Jupiter also emits radio signals at a variety of frequencies - these too are generated in the magnetic field. The Jovian dynamo is believed to be generated in a huge region of liquid metallic hydrogen and helium, occupying over 55 % of the planet's volume - if the overlying liquid molecular fluid is compressed to such a degree that it behaves as a semiconductor, then dynamo generation may extend up to 0.95 RJ



SATURN: Saturn is the second largest planet in the Solar System, with a radius of 60,000 km. It too is a radio source, although its emissions were too weak to detect from Earth-based observations. These emissions are very low frequency, (a few hundred kHz, corresponding to the kilometre wavelengths) and seem to originate in a small area at a latitude of about 80° - emission only occurs once this region crosses the noon meridian. The origin of this signal is unknown, but is certainly linked with the planetary magnetic field.

The Saturnian magnetosphere is much smaller than that of Jupiter, but is very peculiar. It is aligned at an angle of about 0.1° to the rotational axis, and is highly spin-axisymmetric (ie. symmetrical around the rotational axis). The magnetic centre is displaced northwards along the axis by about 0.04 Saturn Radii (RS). The magnetic field is weaker at the equator that the Earth's, with a strength of 0.21 G, although the dipole strength is considerably stronger (4.3 x 1028 Gm3 (about 600 times that of the Earth)).

The high degree of spin-axisymmetry of the Saturnian magnetic field is unusual, and difficult to explain with conventional dynamo theory. Indeed, it is believed that a dynamo cannot regenerate if the magnetic field and fluid motions in the planet's interior are axisymmetric. However, this only applies within the dynamo region itself - it does not prevent another mechanism from altering the field into an axisymmetric configuration outside this region.

It is suggested that the interior of Saturn is made up of a rocky core occupying about 0.25 RS, overlain by a convecting liquid metallic layer of hydrogen and helium fluid up to 0.45 RS. However, immediately above this convecting liquid metallic shell lies a thin non-convecting metallic layer. This layer originates through helium rainout, in which helium separates out from hydrogen at the temperatures and pressures of the Saturnian interior (this is not believed to occur at Jupiter, since that planet is much warmer than Saturn). The consequence of this rainout is that the atmosphere is depleted in helium, while the core is enriched in that element - between the two regions is a layer across which is an increasing helium gradient as depth increases. As a result of this gradient, this layer is stable (ie. non-convecting), probably occurring at such depths that it is composed of metallic fluid - thus, while the core and liquid molecular 'mantle' may convect, there is no communication between the two through this non-convecting region.

As a result of this helium rainout, the Saturnian dynamo is driven by a combination of thermal and compositional convection currents below the stable metallic layer. The axisymmetry of the magnetic field can be explained if the stable layer undergoes differential rotation as a result of deep-seated equator-to-pole thermal winds. To an external observer, this rotation would have the effect of 'filtering out' any non-axisymmetric components produced in the dynamo below.

Externally, the Saturnian magnetosphere is much less extensive that Jupiter's. The bow shock stands at a distance of about 30 RS from the planet, with the magnetopause at around 20 RS, although this distance varies considerably. Saturn's largest satellite, Titan, orbits at the boundary of the magnetopause - since the distance varies, it sometimes lies within the magneto-sphere, and sometime lies beyond it. As a result, there is a torus of ionized and neutral material (similar to that found at Io) that has been stripped from the moon's thick atmosphere by the solar wind when it lies beyond the magnetopause.

Within about 7 RS, there is another torus composed of ionized hydrogen and oxygen particles - this represents the Saturnian radiation belt.

Saturn's satellite system also has an unusual effect on plasma within the magnetosphere - they filter out electrons so that only those above a certain energy can migrate inwards towards the planet. As a result, those electrons located within the innermost satellite orbits have very high energies, of around 1.6 MeV. The satellites also absorb inwardly-migrating protons, so that there is a nearly total absence of low energy protons near the planet. Those protons that are found in this region have energies exceeding 100 MeV - these are more likely to have originated from the decay of neutrons bombarded by cosmic rays in Saturn's upper atmosphere than to have survived the migration from the outer magnetosphere.

Saturn's extensive ring system also plays an important role in plasma containment - at the outer edge of the system, the charged particle population drops dramatically as they are absorbed by the ring particles. As a result, the volume interior to this cut-off is one of the most efficiently shielded regions in the Solar System.


NOTE: Since the Uranian and Neptunian magnetic fields have already been described in greater detail in my previous report, a brief summary of these worlds' fields is presented below.

URANUS: The Uranian magnetic field is approximately 50 times more powerful that the Earth's, and is unusual in many ways. Most obviously, the magnetic field axis is tilted at an angle of 58.6° to the planet's rotational axis, and offset by a distance of about 8000 km (0.3 Uranus Radii (RU)) from the centre of the planet, towards the north polar region. In contrast, the Earth's magnetic field is currently tilted 10.8° to its rotation axis, and offset by 462 km.

Another unusual feature of the Uranian magnetic field is the varying shape of its magnetosphere over the course of a Uranian day and year. The magnetic field orientation changes dramatically as the planet rotates (being inclined at a large angle to the rotational poles), and the planet in turn changes its orientation relative to the Sun (and the solar wind) throughout its 84-year long orbit. During the 1986 Voyager 2 encounter, the south rotation pole of Uranus was pointing towards the Sun, and magnetic field was tilted a further 58° below the Sun-Uranus plane (the ecliptic). Over the course of a Uranian day, the solar wind 'blows' the magnetic field downwind of the planet - however, the planet's rotation also twists this field into a complex helical 'corkscrew' shape, with each turn of the magnetotail separated by about 70 million km.

As Uranus continues in its orbit, the orientation of the magnetic field evolves relative to the rotational poles. Twice during its orbit, (at the 1986 Voyager encounter (and 42 years later)), the magnetotail 'helical axis' is parallel to the rotational axis of the planet - at these points, one of the rotational poles points more or less at the Sun. One-quarter of an orbit (21 years) later, the rotational equator will be facing the Sun, and the magnetotail will stretch approximately at right angles to the rotational axis (away from the Sun). Uranus has one of the largest variations of this type in the Solar System.

NEPTUNE: Neptune's magnetic field is about half as powerful as Uranus', making it approximately 25 times as strong as the Earth's. However, the magnetic axis is tilted at an angle of 47° to the rotational axis, and it is offset by a huge distance of about 13600 km (0.55 RN)!!

The combined tilt of the rotational and magnetic axes creates a magnetic field orientation unique in the Solar System - for part of the Neptunian day, the magnetic south pole points almost directly at the sun (into the solar wind). Usually, a magnetic field in the solar wind has two polar cusps, where the magnetic poles intersect the magnetopause - however, since only one pole faces the solar wind for part of the Neptunian day, the magnetic field at these times has only one cusp. When the magnetic axis is not in this orientation, the Neptunian field has two polar cusps, so appears similar to the magnetic fields of other planets.

Both Icy Giants have similar internal structures, consisting of a very small rocky core (less than half the mass of the Earth) overlain by a thick molten ice mantle which constitutes most of the planet's mass. The outermost region of the planet is the atmosphere, composed of H2 and He gas with some icy material enrichment (CH4, H2O, and NH3). The magnetic fields of these worlds are believed to originate in a region located far from the planetary centre, in the molten ice mantle. The energy source driving the planetary dynamo is contractional cooling, which creates thermally driven convection currents in the planet's mantle. The field itself is generated through the compression (and ionization) of H2O in this mantle, which increases its electrical conductivity so that a magnetic field may form. However, the thermal and electrical conductivities of this ionized ice are not as good as that of metallic hydrogen or iron, being more akin to the semi-conducting molecular hydrogen described on page 16. This may account for the unusually tilted and offset fields that these Icy Giants possess.



CONCLUSION

In conclusion, there is a bewildering variety of planetary dynamos in the Solar System. While they can be broadly divided into three classes (Terrestrial, LGG, and Icy Giant), it is clear that each magnetic field has its own unique qualities within this classification.

Dynamo generation occurs in convecting electrically conducting layers within the planetary cores. These layers vary in composition, depending on the type of dynamo, and can convect either as a result of heat-flow or through compositional differentiation.

The Terrestrial worlds (Mercury, Venus, Terra, Luna, and Mars) all possess some form of metallic iron-rich core in which dynamo generation has taken place (or is still continuing). Mercury and Terra still have active dynamos that are driven by inner-core solidification, which sets up compositional convection currents in the still fluid outer core. Venus may be presently in an 'inter-dynamo' phase, with internal temperatures too cool for thermal convection to occur, and too hot for core-solidification to commence. Luna and Mars once possessed active dynamos, but these have long since collapsed as their cores have cooled. In Luna's case, core solidification may be continuing, with the resulting convection being too weak to drive a dynamo. Mars may have either a completely fluid core (in which case it is similar to Venus) or it may have a completely frozen core, depending on which evidence is believed.

The Jovian worlds all have extensive magnetic fields, driven by thermal convection as they contract. The inner Jovians (Jupiter and Saturn) are known as the Large Gas Giants (LGG's), and are large enough to possess substantial liquid metallic hydrogen layers in which convection and dynamo generation can occur. Intense radiation belts occur around Jupiter, and there is much interaction between the magnetic field and the innermost Galilean satellite Io. Powerful natural radio signals are also emitted by the Jovian magnetic field. The Saturnian field is very symmetrical around the rotational axis, and is slightly weaker than expected. This is probably because of an intermediate stable metallic layer in the planet's interior which filter out the non-axisymmetric components of the field (generated in the conducting metallic layer below). The Saturnian field is probably driven by a combination of thermal and compositional convection, since helium can differentiate from the hydrogen in the planet and sink towards the core (creating the stable layer).

The Icy Giants (Uranus and Neptune) have very similar magnetic fields, which are both highly tilted relative to the rotational axis and are noticeably offset from the centre of the planet. These are believed to be generated in a thick fluid ice mantle, which is sufficiently compressed to become ionized and thus electrically conducting. However, this fluid is a poor substitute for the metallic hydrogen and iron of the other planets, resulting in unusual field configurations around these worlds.

BIBLIOGRAPHY

(Uranus and Neptune - the Outer Jovians, Constantine Thomas, 1994)

The New Solar System, Beatty and Chaikin (eds.), 1990

The Atlas Of The Solar System, Garry Hunt and Patrick Moore, 1983

Planetary Magnetic Fields, DJ Stevenson, Rep. Prog. Phys., 46, 555-620, 1983

Magnetic Fields of the Outer Planets, JEP Connerney, Journal of Geophysical Research-Planets, 98, Issue E10, 18659-18679, 1993

Magnetic Fields of the Terrestrial Planets, CT Russell, Journal of Geophysical Research-Planets, 98, Issue E10, 18681-18695, 1993



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