Alfven's "Structure and Evolutionary History of the Solar System"

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Alfven's "Structure and Evolutionary History of the Solar System"

Unread post by paladin17 » Fri Jan 31, 2020 10:31 am

Here I'd put down the notes I made while I was reading "Structure and Evolutionary History of the Solar System" (1975) - effectively, it's a short version of the whole book.
The authors are H. Alfven and G. Arrhenius (a grandson of Nobel laureate S. Arrhenius, so also a distant relative of Greta, he-he).
The book is based on four papers that they published in 1970-1974 and contains some important theoretical considerations regarding plasma astrophysics (especially in section 10, which I highly recommend even if you don't read anything else), as well as their own theory of Solar System formation.

I also encourage you to read my notes on two other books by Alfven at the v2.0 forum: "Cosmical Electrodynamics" (1950) and "Worlds-Antiworlds" (1966).
Just like previously, I'd make my own comments in italics, while literal quotes from the text would be given in "quotation marks".

_________________________________________


Introduction

"... many of the "generally accepted" theories lack a valid foundation".
Here Alfven describes what he calls the "first approach" and "second approach" to plasma physics - the first based on refined theory, and the second is based on experimental data - he does the same in his Nobel lecture (see p. 309) which was given around the same time (1970). See also section 10 in part III below.

"The "first approach" to cosmic electrodynamics does not describe a real plasma but a fictitious medium, a "pseudoplasma" with properties which sometimes drastically differ from those of a real cosmic plasma".
In questions of the Solar System formation one cannot neglect the magnetization and ionization of the plasma.

Even if we switch the light of the Sun off, ionization would still be present, since it comes mostly from hydromagnetic transfer of kinetic energy (produced by convection in the Sun) into e/m energy. Magnetization of interstellar clouds - hydromagnetic effects cannot be neglected.
Criticism of other theories. E.g. the concept of solid body condensation from a gas cloud in thermodynamic equilibrium.
"... we consider the most important part of our work ... to be the establishment of a framework of boundary conditions which all theories of different processes have to fit".
"... the cosmogonic conditions cannot have been drastically different from the conditions we find today".

Part I. General Principles and Observational Facts

1. Introduction and Survey

We need to use the present state of the Solar System and known laws of physics and chemistry to reconstruct the initial state.
Though again, it is yet to be proven that the Solar System even had an initial state. Strictly speaking, it cannot even be proven that it didn't exist forever.
Reliance on radiochemistry.
Most theories are centered on formation of planets. But a good theory should explain satellites too. So it should be a general theory of the formation of secondary bodies around a primary body. There is only one planetary system, but many satellite systems in it. And planets in them don't behave like the Sun, so proper solar characteristics shouldn't really matter in this theory. So we should focus on the formation of satellite systems. We'll use the term "hetegony" (formation of the companion).

Observations of other systems with possible planets. Importance of plasma phenomena.
Actualistic principle (Hutton): sequentially progressing backwards in time to find an initial state instead of postulating and initial state and progressing forward.
Planetesimal approach. Stages of evolution (Fig. 1.1): a) plasma condenses around a central body and angular momentum is transferred to it; b) chemical differentiation and formation of grains; c) accretion of grains into larger bodies; d) fine and dynamical effects (tidal, resonant etc.).
So we need to progress through these stages backwards.

2. The Orbits of Planets and Satellites

Nine parameters describing a body (position, velocity, spin). They change - we need to find invariants.
Typical orbits are circles in a certain preferred plane. Radial oscillations (in a plane) - orbit becomes elliptical. Axial oscillations (perpendicular to the plane) - orbit becomes inclined. We'll consider elliptical orbits as perturbations of circular orbits.
Angular momentum. Derivation of oscillation forces. Relation between frequencies of orbital oscillations and orbital frequency.
Finding properties of perturbed motion. In the orbiting system the perturbed body moves in an elliptical "epicycle".

Equatorial bulge of the central body introduces an additional perturbing (non-Coulomb) force.
Here a "Coulomb force" means a central gravitational force, falling as an inverse square of distance.
It causes the prograde precession of pericenter and retrograde precession of nodes. To estimate the average perturbations from planets we need to smear their mass along the orbit and then calculate the gravitation from that ring. Important invariants - absolute values of angular momentum and spin. Though their direction might change.
Specific angular momentum (per unit mass). Parameters of planets and satellites - see p. 16 and further.
Definitions of some other parameters (grazing satellite, time of escape etc.).

Prograde satellites most likely experienced angular momentum transfer from their central body. Retrograde satellites are captured ones.
Moon is also a captured satellite.
We assume the accretion idea and estimate the plasma density (before accretion) in a certain region by using the observed mass there.
But the general "flat" structure remains unexplained. Alfven talks about condensing tori, but what about the higher inclinations? I.e. where's the flatness coming from? Is it just the spin of the central body? UPD: it is mentioned later on.
The graph of density at p. 23 looks like discharge volt-amp characteristic.

Laplacian model does not predict such non-trivial density variations.
"... try to look at Figure 2.6 without centuries of Laplacian brainwashing".
There have been two clouds with a gap (asteroid belt) in between. Similar groupings in satellite systems - see p. 26.
Criticism of Titius-Bode's "law". It doesn't work and it's not based on anything.

3. The Small Bodies

For masses over 10^(-13) kg gravitation dominates - see chart at p. 28.
Perturbations: a) mass-independent (precession of nodes and pericenter); b) mass-dependent (light pressure, Poynting-Robertson effect) - become insignificant for 10^2 kg; c) viscosity (collisions).
10^(-18) to 10^(-13) kg - radiation pressure is important. It depends on size and composition. Zodiacal light and gegenschein. Lifetimes of 10^7 s (years). For masses less than 10^(-18) kg e/m forces dominate.

"... a solid body in space is usually electrically charged".
Two competing effects: photoelectric (gives positive charge) and ambipolar diffusion (gives negative charge). The first dominates if the radiation is strong and plasma density is low; the second - if radiation is weak and density is high.
"... the result is usually a charge of the order of a few volts" (for a dust grain).
"There is little direct evidence that the small particles really behave as they are supposed to".

Production of small bodies: a) by fragmentation of larger bodies; b) by accretion.
We might study the distribution of their orbits or their size distribution. Radiation pressure analysis. Viscosity analysis. Importance of both increases as the mass decreases. So with the more dispersed matter (in the past) viscosity should have played a bigger role. In the asteroid belt viscous effects might be present even today. It seems they cannot be neglected for bodies smaller than 10 km.

Interaction between dust grains is often described by a wrong model: scattering of a beam of particles by a medium at rest. In reality dust grains are not at rest. On average they move in a prograde sense around the Sun. It also leads to reduction of a spread of velocities (due to collisions) rather than its increase.
"... general result of viscosity is to make the orbits of particles more similar".
Focusing effect of gravitational Coulomb field. If the orbiting body emits particles, they form a torus enveloping the orbit - jet stream.
Mean free path in a jet stream is long compared to its dimensions, which is different in Laplacian theory's rings. Plus jet streams may be as eccentric as we like.
Jet stream is sustained by inelastic collisions, but there are also dispersive forces. If these are quicker, jet stream would fall apart. If they are small enough, jet stream might accrete into a single body.

Collision of a grain with a jet stream leads to its integration into it. And the jet stream parameters would slightly change (towards the orbit of a grain). In the long run the jet stream would form a larger body.
Non-Coulomb perturbations lead to disruption of the jet stream. So it would stick together only if the viscosity is strong enough. So Coulomb focuses grains into jet streams which are sustained by viscosity (inelastic collisions). Jet streams tend to contract and to capture other grains. In the stream they'd form larger bodies, which then might leave the stream.

Size distributions. Estimation for three simple models: a) all the particles are consumed by larger body and its accretion is non-gravitational; b) same but gravitational; c) fragmentation is also possible.
a) gives constant distribution at all sizes; b) gives an r^(-2) distribution (the larger the size, the smaller the number); c) gives a power law dependence too. Piotrowski's law.
The result of fragmentation is that most mass remains in the larger bodies, but smaller particles are responsible for most of the cross-section.

Statistical distribution of asteroids. Gaps at Jupiter and Mars resonances. Plus Jupiter trojans, Hilda group etc.
"There is no well-defined limit between the orbits of comets and of asteroids".
Comets evaporate gases which form their tails. Collisions between asteroids and smaller grains.
Hirayama - families of asteroids with same orbital parameters (i, a, e). To get rid of secular variations we introduce "proper elements" - see p. 46.
Identification of other families through proper elements - e.g. Flora family.
If all the elements coincide, the bodies are members of a jet stream. Tables with families and jet streams - see p. 48 and further.

Since the time of spreading of the parameters of the jet stream is 10-100 kyr, there should be a mechanism that kept the observed jet streams intact. Viscosity or something else.
Maybe they're simply younger than that.
We might assume the existence of subvisual (invisible) asteroids. But we know nothing about their size distribution.
"... if the orbits of the hyperbolic comets are corrected for planetary disturbances, all of them become nearly parabolic".
Hypothesis of Oort cloud - see p. 53.
Short period comets - mostly prograde. They are hard to explain. Russell's theory: they are long-period comets captured by Jupiter. It doesn't explain their large number. An idea that they might brake due to cometary jets also doesn't hold merit.

About half of all observed meteors do not belong to any known stream - sporadic meteors.
"There is a convincing correlation between cometary orbits and some meteor showers".
But it doesn't necessarily mean that they are parts of a disintegrated comet. Because the comet itself is hard to explain. Perhaps the comets form from jet streams, and meteoroids are parts of the same jets streams that partly accreted into comets.
It is highly unlikely that collisions in the asteroid belt might lead to production of Earth-crossing asteroids.

4. Resonance Structure

Analysis of a pendulum problem.
A thing to think about - average velocity of a pendulum is zero.
Simple case of orbital resonance. Resonant satellites tend to separate longitudinally until a maximum (180 degrees) is reached.
Oscillations around this equilibrium (librations) are possible, and orbits might precess. This broadens the resonance ("near-commensurability").
Many periods in the Solar System are commensurable. Resonances seem to be very important for stability, since they might be maintained indefinitely long.

Two possibilities: a) planets formed and then resonances were established (through tidal forces etc.); b) planets were forming already under the influence of resonances.
Orbit-orbit and spin-orbit resonances.
I don't quite understand why in asteroids the resonant orbits are "forbidden", whereas for planets they are claimed to be the most stable. It makes no sense to me.
Resonance in Saturn and Jupiter satellites. Saturn's rings don't demonstrate resonant gaps - satellite masses are too small for that.
And here Alfven questions the same thing as I just did - the problem of resonant gaps (Kirkwood gaps) in the belt.
Perhaps Kirkwood gaps are produced due to viscosity (collisions), and not gravitation.

Spin of Venus cannot be easily explained. If the Sun braked its rotation, it couldn't have been retrograde in the end. Resonance with Earth is strange too, since Earth's field is too weak to be of such importance.
Difference between near-commensurability and exact resonance. The former gives much higher perturbations, and positions are not locked. They might be important in retrograde satellites capture.
Criticism of the tidal theory of resonances: it doesn't explain low libration amplitude of certain satellites, and is also not applicable to planets due to large distances. So it seems resonances (except spin-orbit resonances of Mercury and Venus) are the relic of the accretion period.

5. Spin and Tides

Derivation of the height of the tides. The deformation is smaller for the central body (in terms of fraction of its size) than in a satellite in all cases.
Tidal braking - transfer of angular momentum from spin to the orbit. Tidal braking probably doesn't work for solid bodies.
On Earth tides from the Moon should cause waves and the recession of the Moon too.
"This theory ... has very little to do with reality".
"Instead, the tidal waves one observes have the character of standing waves excited in the different oceans and seas which act as resonance cavities".

"... the Moon is a captured planet, brought to its present orbit by tidal action".
Capture of the Moon might be another realistic scenario for planetary catastrophes in the past.
Triton seems also to be a captured body. The angular momentum of giant planets' satellites probably didn't alter their own spins. The Earth is the only case where we can definitely say that solar tides exist.
Whether they played a role in Mercury and Venus' spin-orbit resonance is impossible to say. It seems that except Moon and Triton no other satellite orbit was significantly altered by tides.

Similar periods of spin of most bodies in the System - asteroids, large planets etc. About 10 h. Law of isochronic rotation.
Neptune is slower due to braking by Triton.
Earth before lunar capture should have had a period of about 6 h.
If we exclude all the tidal systems, the only exceptions from isochrony would be Pluto, Mars and Icarus.
What about Venus? And wasn't Charon already discovered back then? It is clearly a tidally locked system too. UPD: it wasn't.

Isochronism cannot be explained by any reasonable forces acting today; it cannot be explained by rotational instability. So it's a hetegonic feature. Braking by viscosity wasn't important, since asteroids spin with the same periods as large planets. Breaking up of a planet cannot explain the asteroid belt, since we'd expect (due to energy equipartition) faster rotation in smaller asteroids and slower in larger ones.

6. Post-Accretional Changes in the Solar System

Longitudes of perihelia and ascending nodes vary monotonically, whereas eccentricity and inclination demonstrate secular variations. Semi-major axis is the most stable parameter (due to angular momentum conservation - there's just no other body to exchange it with).
Angular momentum can be changed due to tidal action and resonances, though the latter's contribution is usually negligible. Just enough energy to sustain the locking itself gets transferred.

"A proportional change in the periods of all the orbiting bodies in a ... system will not alter the resonances".
"... if once an exact resonance is established, the bodies will remain in resonance indefinitely, the existence of near-commensurabilities exclude larger changes in the orbits".
E.g. period of Jupiter is constrained by near-commensurabilities with Saturn and Uranus (2/5 and 1/7) and period of Uranus is constrained by near-commensurabilities with Saturn and Neptune (3 and 1/2). Same is true for satellite systems. Except for Earth and Neptune. Tidal effects are negligible for Jupiter, Saturn and Uranus systems.
So that's where tectonics come from?..

What did change due to tidal forces is the spin of satellites. In giant planets the spin of the primary body is more than an order of magnitude higher than the total satellite angular momentum. Earth is understandable, but other terrestrial planets seem to spin too slow. Solar tides?..
"... a series of dramatic events four or five billion years ago produced the Solar System".
"Drastic changes in the orbits of planets and satellites ... are unacceptable".
Except Moon and Triton satellite orbits didn't change much. These two were independent planets, captured and brought to where they are by tidal forces. Small bodies (including retrograde satellites) may have changed their orbits due to viscosity.
Martian satellites are unlikely to be captured asteroids, because it would have been nearly impossible to circularize their nearly parabolic initial orbit.
But the same can be said about the Moon and Triton then.

Part II. Accretion of Celestial Bodies

7. Formation of Celestial Bodies

Spitzer: problem with stellar accretion hypothesis - rotational momentum and magnetic flux oppose the contraction. Even worse for planets: thermal motion alone would counteract it (for the masses and sizes that we observe). Still even worse for satellites: gravity of the main body would suppress their accretion.
The problem with spin: if we assume contraction of a planet, we get a radius of the initial cloud (assuming constant angular momentum) much smaller than the distance between planets. So an unknown braking mechanism is needed. Plus the asteroids have the same spin anyway etc.

Alternative - gradual accretion of solid bodies (embryos) from smaller grains and then collecting these bodies together to form a planet. "Accretion by impact". This is the only way to explain law of isochronism - same mechanism of formation over orders of magnitude of sizes.
Energetic particle tracks in chondrites and the lunar samples are different. So chondrites have been irradiated from all sides, whereas the Moon itself protected its surface from half of the sky.

Usual objection to this scenario is fragmentation due to collisions. But the formation of jet streams, focused by the Coulomb gravitation and viscosity, would prevent that by minimizing the impact velocities. Other effects that help: partial melting during impact, condensation of impact gases, electrostatic bonding, loose aggregation of particles that leads to absorption of impact energy. Then gravitation takes over.
External resonances help accretion. E.g. Jupiter trojans or Hilda group may be accreting into something bigger right now. Since collisions are partially inelastic, the average impact energy would decrease over time, facilitating accretion.
Accretion needs to explain: a) orbital elements; b) spacing of the orbits; c) the observed spins and their isochronism (where tidal effects can be ignored).

Systems akin to Saturn's rings could have formed even outside Roche limit. Initial grains could not have moved in circles around the equator, and their orbits should have been eccentric. Estimates of minimal eccentricity, given the observable orbital spacings.
Asteroid belt as an example of a system in intermediate accretion stage. Size distributions support this idea.
The idea of exploded planet is supported by high-temperature minerals and diamonds in meteorites from the belt (so we need a large body to produce that). But - diamonds might be formed in plasma-gas processes at low pressure.
That's interesting; maybe that's a way to fund Plasma Universe experiments.
And high temperatures might be caused by impacts.
Asteroids haven't accreted yet due to lower density in this area. It would take orders of magnitude more time for them to produce a single planet. It may even fail altogether.

8. Spin and Accretion

Changes in spin velocity and angular momentum after the collision. Non-gravitational accretion from circular orbits in the same plane gives a slow retrograde spin. But gravitation cannot be neglected. If we take gravitation into account, angular velocity of the accreted object tends to a constant value regardless of the radius of the body. This explains isochronism.
Giuli's theory of accretion. Accretion from circular orbits produces retrograde spin. Eccentric orbits - prograde spin.
Seven bands of particles that can accrete to the embryo. And seven more with semi-major axis less than that of an embryo.
Statistical theory of accretion. The problem is that large grains (3% of embryo's mass or more) can alter the rotation of the embryo significantly. The result might be anomalous rotation axis (Uranus) or slow rotation (Mars). Perhaps applicable to asteroids too.

9. On the Accretion of Planets and Satellites

Problems of planetesimal accretion:
a) Neptune couldn't have yet accumulated all the mass in its area. And we should see many asteroids at its orbit. Only in BB cosmology, that is.
b) large relative velocities (see asteroid belt) prevent accretion;
c) existence of gas giants.
Jet streams might solve the problems of accretion theory. Two stages: formation of the jet stream; accretion of the jet stream.
Mass and energy balance of the jet stream. Compariso of accretion time in different planets. Temperature distribution in the accreted body. High temperature layer between two low temperature layers. On average the temperature is proportional to the mass.

Gas giants seem to have at least one hot layer. The one in Jupiter is at half its radius from the center. The one in Saturn is further out. The ones in Uranus and Neptune are close to the surface. Venus should have a hot layer closer to the center (in comparison to Earth). On Mars it should be very close to the surface. But perhaps it's not there at all. Same is for Moon and Mercury.
"Accretional heat front", sweeping through the interior of a body from the inside out. Melting of the material - partial chemical segregation (heavy elements sink down, light elements float up). Perhaps radioactive materials migrated closer to surface because of that.
Are they lighter or something?.. Seems unreasonable.

Part III. The Plasma Phase

10. Plasma Physics and Hetegony

"Models of the Laplacian type have been made obsolete by magnetohydrodynamics. Furthermore they are in conflict with observations".
In previous sections the accretion from grains to jet streams and large bodies was analyzed. Here the preceding stage is considered.
Development of plasma physics: experimental (gaseous discharges with many anomalies and complications), theoretical (extention of gaseous laws to ionized gases, experimental anomalies are ignored).
Chapman-Ferraro and Chapman-Vestine theories as an example of the second.

Table with differences in approaches to plasmas in space (see p. 119).
"... no real scaling of cosmic phenomena down to laboratory size is possible, partly because of the large number of parameters involved which obey different scaling laws. Hence, laboratory experiments should aim at clarifying a number of basic phenomena of importance in cosmic physics rather than trying to reproduce a scaled-down version of the cosmic example".

Lehnert: 32 types of plasma instabilities.
Electrostatic double layers (DL) might exhibit strong electric fields. They might be stable, but they can also oscillate.
NB: DL are independent of magnetic fields and cut the frozen-in field lines. If the current flows through a DL (perhaps producing the DL in the first place), the DL might cut it off. The voltage across DL might reach any value necessary to break the circuit (10s of GV in solar flares). Then the discharge is disrupted and high vacuum is produced.

Pinch effect - production of filaments. Therefore, homogeneous models are often not applicable. Horror vacui vs. amor vacui.
Critical ionizing velocity - when kinetic energy is enough to ionize the neutral gas.
The transition from weak to full ionization is often very sharp. You pump the energy in slowly, and at certain point the ionization jumps from 0.1% to 100%.
Regarding Don Scott's model debate - Alfven mentions the external field in figure description explicitly, see p. 122.
Lindberg: phenomenon of flux amplification. If the toroidal magnetic field in a plasma ring is stronger than the poloidal one, the poloidal field is increased and toroidal field is decreased.
Solar cycle?
It happens through kink instability.

When a plasma moves parallel to magnetic field and reaches a bend in the field lines, it might turn in the opposite direction than the lines do (see picture at p. 124), violating all expectations. This happens due to an electric field transmitted backwards by fast electrons.
Shock and turbulence phenomena need to be studied in a laboratory. As well as magnetic conditions at neutral points. Condensation of plasma and saturated gas are different due to optical (thermal) and chemical differences.
Chemical diversity in space plasmas - need to study plasma condensation experimentally.

Pre-MHD models (Laplace, Berlage, Cameron) and "first approach" theories (Hoyle) are of little interest.
Extrapolation is also important to understand the past. E.g. transfer of angular momentum from a rotating magnet to a surrounding plasma. Extrapolation from magnetospheric physics and solar physics (sunspots and prominences). Scheme of a discharge around a sunspot (its rotation separates the charges) - see p. 126.
Prominences are filamentary currents that drag the plasma inwards through pinching. They have much higher density than their surroundings. And also currents of 10^11 A.

"... the solar situation merely represents a high-current and high-density variation of the magnetospheric situation".
"... the hetegonic situation generally implies very high currents".
Hetegonic magnetosphere is similar to the present day solar corona. Rotating magnetized body with a network of prominence-like filaments. General scheme of building an astrophysical understanding (p. 127).
Required properties of a model (to produce the grains for the accretion). Non-uniform density etc. Hydromagnetic effects must be important.
Gravity of the central body cannot be counteracted by magnetism alone (if the density is the same as now), so density of primordial plasma must be lower. And the material must be constantly added from outside and removed (in the form of particles and condensation into grains).

Alfven considers some other theories (in some detail) while making a general objection that they are all highly speculative and not based on any evidence.
Hoyle's theory is incorrect, because it assumes frozen-in field lines. Plus evidence from Lundquist that a system with large stored toroidal magnetic energy is unstable.
I wonder how the current data on the heliosphere looks in this light. Since in its outer reaches the field is almost exclusively toroidal. Alfven says that it is because in this case kinetic energy is larger than magnetic energy. Anyways - maybe that might explain the solar cycle? See picture on p. 130.

11. Model of the Hetegonic Plasma

The need of an ad hoc assumption: the central body in hetegonic system is magnetized.
Problem of angular momentum in Laplacian theories - central body should have the most of it. But the observed momentum of satellites (per unit of mass) is much larger. Transfer of angular momentum through hydromagnetic forces is the answer.
Criticism of Ferraro's isorotation law. It assumes infinite conductivity and frozen-in lines.
In reality electric fields parallel to magnetic fields may arise for two reasons: anisotropy of velocities of plasma + magnetic field; or field-aligned currents (which tend to produce double layers). Block - a review with some evidence of DL in ionosphere and magnetosphere.
Such fields lead to decoupling of the plasma from the magnetic field, and far regions might rotate slower than the magnetized central body.

Idealized system of a rotating magnetized conductor. Potential difference in non-rotating system. If there is no isorotation, a current would arise, trying to establish it (picture at p. 135). Surface fields of 1 mT are enough to produce the needed angular momentum transfer in ~ 100 Myr.
Analogous estimates for the Sun are given. If the currents are filamentary (pinched), the needed current and magnetic field are much smaller.
Hydromagnetic waves also might decrease the needed currents. But we also omit the possible large contribution from volatile substances.
What if Mercury's perihelion precession is also caused by Alfven's mechanism?! Or the equinox precession even.
How do we counteract the gravitation until the angular momentum is transferred? By toroidal current, for example. But it requires a very strong magnetic field of the central body.
And an explanation of where the current would come from.
So it doesn't work.

So plasma needs to be constantly injected into the system. And its average density at each given moment (while condensation is happening in the background) is about the same as density of the corona.
What if planets condensed from solar wind plasma then?.. But that wouldn't explain the satellites.
Infalling gas reaches critical ionization velocity and gets ionized, then receives some angular momentum from the central body. Then condensation into grains occurs in fields of 10-100 uT. Then grains are focused into jet streams and form larger bodies.
Illustration of the whole process (see p. 142).

"Hetegonic nebula" instead of "solar nebula". Primordial supercorona.
Superprominences (pinched currents) that transfer angular momentum.
Kreutz comet's jet stream - what does it look like? Maybe some relation might be established?
The whole sequence of hetegonic processes (see p. 144 and 146).
Irradiation of grains (and even nuclear reactions) is explained by acceleration of charged particles by e/m fields.
Need to enhance the theory in the future to include the gas behavior.

The advantage is that we don't need to know how the Sun formed. It's too hypothetical anyway. "Stellesimal accretion" is one possibility.
The importance of studying jet streams. Explanation of short period comets etc. Difference between the planetary system and satellite systems: planets have most angular momentum compared to the Sun; whereas satellites don't (compared to their planets).
This is not the case for the Moon, obviously, but it's a quasi-satellite anyways.

12. Transfer of Angular Momentum and Condensation of Grains

Ferraro corotation + Kepler -> plasma is centrifuged outwards, producing lower density near the body.
Lower density produces double layers which impede further angular momentum transfer. "Partial corotation" is established (only gravitation and inertia matter). It might be transient or steady depending on various parameters.
Examining partial corotation geometrically (see p. 149). The appearance of toroidal current due to gravitation-centrifugal balance.
Kinetic energy of partial corotation state is 2/3 of kinetic energy of circular Keplerian motion at the same distance (table at p. 150).
The rest 1/3 is compensated by the toroidal current which gives an Ampere's force in the magnetic field.
Diamagnetic expulsion (see "Cosmical Electrodynamics", link at the beginning) would reduce the 2/3 factor somewhat, but it's only important for high temperatures.
Alfven's derivation of temperature here is suspicious. It's the "first approach" derivation, in his own terms.

Condensation and recombination of plasma would make the toroidal current disappear, and the orbit turn into an ellipse with 1/3 eccentricity. Considering a simplified case of such condensation (figure at p. 153). The embryo that would result from that would spiral inwards while growing. And it would be situated in the equatorial plane in a circular orbit.
As a general rule, the resulting orbit is 2/3 of the size of the region of condensation. Transfer of angular momentum is accompanied by the release of heat in the plasma.

13. Accretion of the Condensation Products

Examining the condensation of plasma into grains in more detail. We need to explain three observed systems: a) Saturn's rings; b) asteroid belt; c) jet streams.
General result of inelastic collisions is that the eccentricity and inclination decrease over time (figure at p. 156). This seems to explain the rings and groups of planets/satellites. Asteroids seem to be in an intermediate stage.
Discussion of Roche limit. It is probably not directly applicable to Saturn's system, but some modified version of it might be.
So the outer edge of Saturn's rings represents the boundary between the region where accretion is suppressed by tidal forces and where it is possible (so satellites might form).

Inside the Roche limit the model leads to the formation of a thin disk, whereas outside - to a series of jet streams.
Structure of Saturn's rings (figure at p. 161). Gaps. Thickness of 2 km. Keplerian motion of separate rings.
Analysis of the misconception that gaps are caused by resonance with satellites. Differences between the asteroid belt (Kirkwood) gaps and ring gaps is due to the mass ratios (Jupiter is 0.1% mass of the Sun, and Saturn's satellites are lighter with respect to it).

If rings aren't explained by resonances, they might be primordial. Hetegonic situation before the accretion of rings (figure at p. 167) - we need to enlarge their orbits by 3/2 to see the region where the matter came from. Turns out that Cassini division then maps at the present Mimas orbit, and inner boundary of B ring onto the outer boundary of C ring.
Cassini's division as a "hetegonic shadow" of Mimas (figure at p. 165). Same story with Janus.
This is brilliant.

Accretion beyond the Roche limit is harder to figure out, because it should have involved a longer chain of processes.
Asteroid belt might give some clues about intermediate processes. Accretion didn't happen there because of lower density. And may never happen.
Differences between the belt and Saturn's rings: a) far outside Roche limit; b) low density - rare collisions; c) rings did not accrete because of Roche, and the belt because of low density; d) resonance gaps are present in the belt, but not in rings.
Hetegonic mapping of asteroid orbits (figure at p. 168). Jupiter's hetegonic shadow limits the asteroid belt to 2/3 Jupiter distance.

Groups of satellites and planets. Inside a group the spacing is never above 2 (one slight exception - 2.01 for Saturn-Uranus), which is the aphelion-perihelion ratio for plasma grain condensation (eccentricity = 1/3). Between the groups it's always above 2.
So the grains produced in between those groups could not accrete onto neither of them. Ergo, these were the regions of low density initially. Perhaps to this day there are microscopic dust particles in satellite systems in these regions (miniature asteroid belts).
Interesting to study Pluto system in that regard.

Scheme of condensation sequence vs. distance (see p. 171). Inadequacy of Laplacian theories.
There is still a problem of volatiles - how to explain "gas giants" and how do gases behave in general during accretion. We might assume that the atmosphere is collected from interplanetary medium.
It is now assumed the reverse - the escape of atmospheres. Plus Alfven talks about the minimum mass, but what matters is the acceleration. And e.g. at Mercury it is larger than at Mars, yet Mercury doesn't have an atmosphere.
Primordial atmospheres might have accumulated right near the jet streams themselves.
The case of Jupiter: for it (and other giants) grain accretion might not be applicable at all - a serious revision of the model may be needed.

Part IV. Chemical Differentiation. The Matrix of the Groups of Bodies

14. Chemical Compositions in the Solar System

Failure of Laplacian hypotheses - different densities, different chemical compositions etc.
Observational data on chemistry and bulk composition. For bodies larger than few hundred km the interior should be very different (layered etc.) than their surface. The importance of electric charge and vapor deposition during grain formation (pictures at p. 181-182). Electrostatic growth leads to high porosity (low density) - p. 180.
Fluffiness of material may lead to better accretion at high impact velocities (compared to compact dense bodies). Martian satellites demonstrate signs of such fluffiness, judging by crater shapes. Tables with data on some bodies (p. 184-185). In Earth oxygen seems to be the most important element down to the core. The core is either different (conducting) phase of silicates or an iron-nickel alloy.

Four ways to get a metallic core: a) accretional heating; b) gravitational separation (and heating) after accretion; c) differentiation in the jet stream; d) differentiation during gas condensation.
Mercury, Venus and Earth have similar densities. Moon and Mars are a separate group with other densities. Asteroids have even lower density.
Extra heat from the interior of Jupiter plus some doubts on the idea of solid metallic hydrogen in it (otherwise conduction would do the heat transfer). Magnetic fields also add many uncertainties. Jupiter trojans might give more hints about the initial composition.
Densities of Uranus and Neptune are similar and much larger than the density of Saturn. Triton is a captured planet, even more dense. Large uncertainties with Pluto.
It does seem that Charon wasn't even known then.
Plots of densities of inner and outer planets vs. mass (p. 192). Densities of satellites also vary noticeably.

Homogeneous models of the Sun may be completely misleading. It is highly structurized even at smaller scales.
NB: Solar magnetograph measurements are seiously in error; solar magnetic fields derived from magnetograms do not obey Maxwell's equations.
High fluctuations in elements emitted from the Sun. Its composition may be different altogether due to various selection/fractionation processes.
Type I chondrites as a proxy for the initial composition of the Solar System. Plots on p. 196-197.
Meteorites are quite different in composition with respect to solar particles.
It seems that elemental abundances should vary with gravitational potential around the central body (because of critical ionization velocity in plasmas). Plots at p. 199-201.
Density falls with distance, then rises again. Possible role of solar radiation.
But we have the same picture in planetary satellites too - ?..
The general conclusion is that an assumption about homogeneous composition of the primordial Solar System is wrong.

15. Meteorites and Their Precursor States

Unclear origins of meteorites. They cannot form from condensation in thermodynamic equilibrium, as assumed - since in space the grain would have a different temperature with respect to the surrounding gas.
"Exploding planets" is an even worse idea. Not clear how a differentiated body (larger than the Moon) might explode. And not damage its parts at the same time.
Jet streams as origin of meteor streams. We still don't know where meteorites come from, and the idea that they might come from the belt needs to be proven. Plus the sample of meteorites on Earth is not indicative, since we have a huge cutoff due to the atmosphere. Meteors are sometimes associated with comets, but their chemical composition differs.

Estimates of sizes of parent bodies.
"It is doubtful if a body larger than about a thousand kilometers in size can ever be blown apart by collision using any other body in the Solar System as a projectile".
"... meteorite parent bodies are unlikely to have been more than some kilometers or possibly some ten kilometers in size".
Parent bodies as result of jet streams condensation. Heating is the result of gas friction. Cohesion by electrostatic bonding and vapor deposition. In ferromagnetic solids (e.g. magnetite) magnetic cohesion might also play a role.
Grain picture (at p. 208). Magnetite crystal picture (at p. 209).
"The observed magnetization cannot derive from planetary fields".
Remnant magnetization of the order of 10^(-4) T. Particle track records: not only solar wind (1 keV) and flares (1 MeV), but also particles accelerated in primordial plasmas. Chondrules and crystals show irradiation from all sides (picture of irradiated chondrules at p. 211).

At some point disruptive processes prevailed. After that the accumulative processes took place (diagram on p. 214).
Most likely chemical differences in meteorites are related to chemical differences in their parent jet streams. Using decay (Rb-Sr, I-Xe) to measure ages. Other methods: amount of gas (He), cosmic ray dose.
Problems: material collected and dispersed over time, so there were periods of both exposure and shielding etc.

16. Mass Distribution and the Critical Velocity

Laplacian theories assume uniform density. But this is not what is observed. Two other possible explanations: ejection of mass from the central body or infalling of mass on it.
The second option is more reasonable. Particles fall until their kinetic energy is enough for ionization. Then they're stopped by magnetic field. The final distance from the central body is determined by this process. There seem to be three bands of bodies in the Solar System (diagram on p. 221).
To initiate hetegony one needs a rotation and a magnetic field. Earth and Neptune probably lost their satellites because of capture of the Moon and Triton. The mentioned band structure: "... groups of bodies are formed in regions where the specific gravitaitonal energy has values in certain discrete ranges".
Due to hetegonic properties, synchronous orbits are the natural lower limit for satellites to form. Only Phobos orbits below it. Outer limit is Lagrangian points.

Comparing satellite systems. To get rid of uncertainties of the young Sun we need to consider satellite formation first.
Simple model: satellites are formed from the same jet stream that formed the central body. Gas cloud from the jet stream infalls onto the central body (picture at p. 224). Ionized material is stopped by magnetic field, so only neutrals and dust continue to fall.
Infalling gas at high enough velocities would ionize in contact with plasma, so it will again be stopped by magnetic field. This will increase the overall density. Ionization might assume an avalanche-like character.

Analogy with gaseous discharges. Electric field induced by the magnetic field of the central body increases the ionization. The radius at which ionization occurs depends on ionization potential of an element. All the important elements fall in one of three bands (table at p. 227 and plot at p. 228). Most energetic (smallest distance) I band - H and He. II band - Li-F. III band (least energetic) - heavier elements.
I should note that the idea of a key role of ionization potential is also used by Larin in his hydridic Earth concept - e.g. see this book; the idea is from 1968, so it precedes Alfven-Arrhenius' book, therefore it is possible that they took this idea from him; on the other hand, Alfven has published many papers in the 50's and 60's stating roughly the same ideas, so perhaps it was the other way around.

In the actual discharge most of the energy is radiated, so the real energy needed for ionization is sometimes 10 times larger than the theoretical one. Experiments: there exists a limiting voltage (see p. 230) that gives the same ionization result.
NB: An experiment of Angerth with field of 1 T and cylindrical electric field. Relevant to accretion problem in terms of scaling. In this experiment the axial magnetic field and radial electric field produce plasma rotation, which makes ionized matter move with respect to neutral matter - check of critical ionization velocity. When critical velocity is attained, no increase in velocity follows (with increase in voltage above the limiting one). Instead what changes is the degree of ionization.
Like temperature during phase transitions. Until all the ice melts, temperature is zero (in equilibrium state).
Scheme of the circuit (see p. 231). It seems that the electrons are accelerated until they ionize everything.

Plots with experimental results (see p. 232-233). Experiment of Danielsson (scheme at p. 234). Plasma is shot into a neutral gas cloud. If their relative velocity is below critical, there is almost no interaction. If it's above critical, strong interaction occurs, and gas becomes partially ionized (plots at p. 235-236). So even if collisions are negligible, strong interaction might still occur, which would cause heating of electrons, ionization and slowing down of plasma.
Space experiments: crashing of the lunar module produced a cloud of particles that interacted with solar wind and produced suprathermal electrons. Theoretical explanation of critical velocity phenomenon is highly problematic. Analogy with Franck and Hertz's experiment.
Consideration of elemental separation in light of that. Consequential formation of A, B, C, and D clouds (from a single cloud) with different elements. Relative positions of clouds (p. 240). Same process occurs around planets (figure at p. 241).

Molecules add complexity to the picture. Most likely the critical velocity for molecules is close to the velocity of the element with lowest ionization potential in this molecule. In some compounds of metals this is not the case, and ionization potential is increased there.
Discussion of inhomogeneous models (figures at p. 244-245) . Infalling gas might be trapped and ionized by previously infalling cloud. This might explain the discrepancies. Ablation of dust grains provides another mechanism of element transfer between the clouds.
Six different processes leading to the accretion with chemical differentiation.
If the plasma is not at rest with respect to the central body, but in a state of corotation, ionization of infalling neutrals would occur at 4/3 of the distance (due to extra relative velocity). If one takes condensation into account (which happens at 2/3 of distance), the effective distance becomes 0.89 of the theoretical one.

17. The Structure of the Groups

Picture with critical velocity sphere (see p. 249).
Energy released during momentum transfer goes into ionization (about 5%) and heating of the electrons and radiation (95%).
It means that the degree of ionization depends on the ratio between orbital period of plasma and spin period of the magnetized central body.
Complete ionization happens when orbital period is much larger than the spin period. Resulting mass distribution calculation and figure (see p. 253).
Effects of partial ionization: the outer limit of secondary bodies is displaced inward (picture at p. 254).
Changes of spin of central bodies - very small for giant planets, very large for the Sun. Serious uncertainties here (with the Sun). We don't know how much its radius changed etc.
The ratio plotted for secondary bodies (see p. 256). Systematic trend between mass distribution and orbital distance (normalized to ionization distance) - picture at p. 258.
What implications this critical velocity has for comets/asteroids?

Table with periods and normalized periods for secondary bodies (see p. 261). Lunar maria may have formed when initial satellites of Earth were destroyed by the Moon.
"Before the capture of the Moon the Earth had a much more rapid spin. A reasonable value for the spin period is 4 h".
There are only two cases where matter orbits inside synchronous distance: a) Phobos (possible if for some unknown reason Mars slowed its rotation or gained a lot of mass, or if Phobos is a captured satellite, which is doubtful due to low eccentricity and inclination - somehow it's not doubtful in case of the Moon - ?..); b) Saturn's rings.
Overall, more observational data is needed.

Summary and Conclusions

Hetegonic theory - need to explain secondary bodies in general (planets and satellites).
General method is to move backwards in time, from more certain to less certain eras.
Respect for laws of physics:
a) e/m is included;
b) lack of thermodynamic equilibrium between grains and surrounding plasma is acknowledged;
c) electrostatic effects leading to accretion are recognized;
d) need to introduce a concept of jet streams.

Summary of the formation processes:
a) emplacement of plasma (critical velocity, chemical differentiation);
b) transfer of angular momentum through magnetic field - partial corotation;
c) condensation into grains, which are focused into jet streams, where embryos grow;
d) further slow evolution.
The theory seems to work well.

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JP Michael
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Re: Alfven's "Structure and Evolutionary History of the Solar System"

Unread post by JP Michael » Fri Jan 31, 2020 1:29 pm

Thanks for posting this summary, Eugene. I probably don't have time to read the whole book right now so having this 15 min read was a good primer until I have time to read the book itself.

Out of curiosity, what do you think of David LaPoint's 'bowl' magnetism as a potential answer to self-sorting spacings in orbital dynamics (as per here: Primer Fields; watch the second video in the OP, especially from the ~18 minute mark)?

As far as i am aware, LaPoint also discovered elemental transmutation in his plasma device like SAFIRE does to its anode (they turned that same iridescent metallic rainbow colour), the difference being that LaPoint's exhibited dichotron instability 'scarring' at the poles of his magnets, around about where one would see auroras if it were Earth's sphere.

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paladin17
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Re: Alfven's "Structure and Evolutionary History of the Solar System"

Unread post by paladin17 » Sat Feb 01, 2020 1:56 pm

JP Michael wrote: Fri Jan 31, 2020 1:29 pm Thanks for posting this summary, Eugene. I probably don't have time to read the whole book right now so having this 15 min read was a good primer until I have time to read the book itself.

Out of curiosity, what do you think of David LaPoint's 'bowl' magnetism as a potential answer to self-sorting spacings in orbital dynamics (as per here: Primer Fields; watch the second video in the OP, especially from the ~18 minute mark)?

As far as i am aware, LaPoint also discovered elemental transmutation in his plasma device like SAFIRE does to its anode (they turned that same iridescent metallic rainbow colour), the difference being that LaPoint's exhibited dichotron instability 'scarring' at the poles of his magnets, around about where one would see auroras if it were Earth's sphere.
Thanks for reading. Writing this wasn't in vain after all.
I've watched LaPoint's videos some years ago, and the problem I have with them is the apparent lack of any theory/understanding. The impression I got was that his "primer fields" are simply (and solely) some geometric intuition - again, without any explanation or a mechanism of how and why it works. So if he gets a planetary arrangement pattern (for some reason I couldn't find it in the videos), there are still questions: what produces such fields (?) around the Solar System (?), how exactly they arrange planets, why aren't they observed etc.

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