Alfven's "Cosmical Electrodynamics"

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Alfven's "Cosmical Electrodynamics"

Unread post by paladin17 » Wed Nov 20, 2019 9:37 am

I've recently read this beautiful and insightful book, which seems quite far ahead of its time, and I wish to add here my own notes that I kept making while reading, so that even if you don't have time to read the book yourself (although I'd highly recommend it), still in about 1 hour you'll get a general impression of what the book is about.

This is based on the first edition (1950) - note that there is also a second edition (1963, with Faelthammar), which is noticeably different. In particular, in it most of the applied part was thrown away - and the theoretical part was expanded and corrected (as far as I can see).
I'll just give my notes mostly "as is", without too many expansions and corrections (I'll add my own comments in italics where I deem necessary, whereas direct quotes from Alfven would be just in quotation marks).


1.1 Introduction
1.2 Magnetic fields in cosmic physics

1.3 Induced electric field

At velocities, small compared to the speed of light, electric fields depend on the chosen coordinate system, while the magnetic fields don't. E.g. a rotating magnetized conductor would be electrically polarized (e.g. positive charge near the axis and negative away from it), if looked at from non-rotating system; while in the system of a conductor there would be no polarization.

1.4 Approximate equality of positive and negative space charge
Even small imbalance in +/- space charge leads to impossibly large voltages. Therefore, + and - space charges are always approximately equal.

This is a rather technical chapter. It describes some important phenomena (such as plasma drifts), but since they are pretty standard and well known, I didn't make any notes here.
2.1 Introduction
2.2 Homogeneous magnetic field
2.3 Inhomogeneous magnetic field
2.4 Dipole field: Stoermer's method
2.5 Dipole field: perturbation method
2.6 Cosmic ray orbits
2.7 Radiation losses

3.1 Introduction
Plasma scaling laws are quite non-trivial. One needs to properly balance the pressures, fields etc. Many important parameters scale up differently. (See my comment in SAFIRE topic for an example).

3.2 Mobility and conductivity
Building equivalent circuits for a gaseous discharge. In space plasmas DC is not important, since the conductivity is very high. Inductance (inertia), on the other hand, is very important, as well as capacitance (kinetic energy).

3.3 Diamagnetism of an ionized gas
Plasma in a magnetic field might be diamagnetic (have a magnetization against the external field) only in non-equilibrium state. In this case Hall currents arise which results in diamagnetism.
Flames are diamagnetic. (As well as blood).
Due to diamagnetism, plasma, expanding in inhomogeneous magnetic field would be pushed to the areas where the field is the weakest.

3.4 Constriction of a discharge
High pressures and current strengths might lead to constriction (e.g. in auroral rays). Glow discharge in low pressure - no constriction (e.g. in diffuse aurora). Constriction is the result of decline of the electric field with rising current density.
Arc discharges (with constriction) - don't obey the similarity laws (see 3.1 on scalability). As a general rule, they need more pressure. Thermal output of the current should compensate for heat losses (otherwise - thermal constriction). Plus Ampere's force - pinching effect (e/m constriction). Thermal constriction doesn't scale well, e/m constriction does.
The importance of skin effect in conductors. "It's easier to produce a current inside a dielectric than in an interior of a conductor". The situation is very different in magnetized plasmas. The current flows near the axis ("inverse skin effect").
(Note that Fig. 3.5 contradicts Don Scott's model, while in essence being the solution to the same problem).

3.5 Maximum current density in an ionized gas
A limit to maximum current depends on pressure - it is reached only in heavy arc discharges at low pressures.
Thus extinguishing of the discharge at high current is possible - e.g. due to lack of electrons or pinch effect or thermal processes ("electron gas explosion").

4.1 Introduction
4.2 Fundamental equations

4.3 Plane waves in incompressible fluid. Homogeneous fluid
"Frozen into" lines of force - p. 81.

4.4 MHD waves as oscillations of the magnetic lines of force
If conductivity is infinite, magnetic field lines cannot change, since any change leads to infinite current. Fluid is "glued" to the lines of force. Lines of force might be considered as massive elastic strings that tend to contract.
Analogy between MHD waves and e/m waves at increased permittivity. In order of reducing density: MHD waves -> ionospheric waves -> e/m waves in a vacuum.
Any state of motion in magnetized plasma is displaced with Alfven veocity (obviously, he just calls it MHD wave velocity) along the magnetic field line.

4.5 Waves of arbitrary form

4.6 MHD whirl rings
Ring, rotating around the magnetic field axis, splits in two (!) that separate and propagate along (one) and against (the other) the field.
(Reminds me of some novel theories about the electron, where it is just a photon, twisted into a ring, which then splits into an electron and positron - Alfven's analogy between MHD and e/m waves is extremely relevant here too).
If conductivity is finite, the rings would expand and "diffuse" into the surrounding medium.

4.7 Waves in inhomogeneous magnetic field; compressible fluid with variable density
Changes with density are not trivial. The pressure inside MHD ring is less than in its surroundings.
MHD waves are transverse - they may have longitudinal components, but these don't exert any force.
The presence of magnetic field in a conducting medium might change the speed of sound there.

4.8 Gravitational effect
(Alfven considers an incompressible liquid with variable density - how's that possible?..)
Rotation of the whirl, perpendicular to the magnetic field, would be accelerated until it would come into resonance with Alfven's velocity.
If the whirl is parallel to the magnetic field, the acceleration is higher as we approach Alfven velocity.
The smaller the angle between magnetic field and whirl axis, the faster is acceleration.


5.1 Introduction
Conductivity of the photosphere is about 10^(-3) of copper.

5.2 Electromagnetic properties of the Sun
Above the photosphere the cross conductivity (i.e. perpendicular to magnetic field lines) continues to decrease with decreasing density.
"In all electromagnetic phenomena the general magnetic field of the Sun is of essential importance" (another nod to SAFIRE thread).
In the corona the cross conductivity might be 17-20 orders of magnitude (!) lower than the parallel conductivity (i.e. along the magnetic field lines).
E/m effects occur as a product of plasma motions and in general tend to brake these motions.
Since ions have larger collisional cross section than neutrals, the concentration of the latter doesn't impact the conductivity unless they're 10^3 times more prevalent. But for solar electric currents it's the inductance that's important, not conductivity.
Clear observational uncertainties (in Alfven's time) in determining the solar magnetic field structure. Zeeman splitting. (Alfven clearly doesn't know yet about the solar magnetic field reversals). Most likely solar magnetic field is dipolar, with the axis well aligned with the rotational axis. (Alfven also states that the polarity is the same as of Earth's field, which is not the case in odd cycles).
Cowling argues that the solar magnetic field is a "relic" from the time of Sun's formation, and it only changes at time scales of 10^10 years. Cowling's field differs from a dipole, though his results are valid only if there's no hydrodynamic motions in the interior.
(Apparently there have been attempts to introduce a new law of nature that would explain the field's existence). Solar dipole is divergent at the center - some other structure is needed (e.g. homogeneous field). For example, it might be produced by a thin spherical shell (0.25-0.35 of Sun's radius) with current.

Solar MHD waves travel along the isolated magnetic lines of force, regardless of what the other lines are doing.
Damping of MHD waves:
a) Joule (finite conductivity - current energy transforms into heat);
b) viscosity (probably not important in the Sun);
c) gravitation (mixing of the layers with different entropy) - might also be negative (amplify the waves) if entropy falls with distance from the Sun - or positive otherwise; it only occurs when the waves (their material velocity) have a vertical component.
Velocity of MHD waves also depends on density and magnetic field (as inverse sqrt and sqrt correspondingly). If these parameters change rapidly (with respect to the wavelength), it causes rapid changes of "refractive index" (inverse of velocity), which makes reflection of MHD waves possible.
Theorem of Ferraro - each magnetic line of force should rotate with the single (for this line) average angular velocity; otherwise a very strong electric current is produced. Average velocity - because Alfven waves still might propagate. Lundquist - calculation of the Sun's angular momentum.
Following Ferraro's theorem, the magnetic axis must coincide with the axis of differential rotation, but not necessarily with the axis of resultant rotation.

Plot of angular velocty - p. 113.
Velocity above the photosphere increases (from Doppler measurements of the chromosphere) - this might happen if the state is not stationary or if the conductivity or magnetic field is very small. But corona rotates with the same velocity as the photosphere.
Since fusion depends on high powers of temperature (16 or even 18), the core should be highly turbulent and give rise to MHD waves. Convection also drives MHD waves - and vice versa. MHD driven convection might alter the temperature gradients. Other turbulent region is the photosphere (as evidenced by granules).
Heating of the corona is explained by damping of MHD waves due to decreased conductivity. Waves from the interior reflect in the photosphere. And only low frequency waves are able to get there in the first place.
In the Sun the MHD waves are balanced by centrifugal force and electric polarization. In photosphere it's impossible, so it causes discharges. Fundamentally, solar activity is caused by MHD waves' appearance at the surface.

5.3 Sunspots
(Again - Alfven makes no remark about the polarity reversals of the general solar field, even though he speaks about sunspot polarity reversals).
Whirl theory of sunspots (spots as cyclones) is problematic, because their rotation is not frequently observed, and even the magnetic field of this magnitude cannot be caused by simple rotation.
MHD theory of sunspots:
a) spots are produced by magnetic fields;
b) these fields are generated in the solar interior;
c) they are transferred to the surface by convection.

Simple solar cycle model: migration of MHD waves (which are produced by disturbance in the core) to the surface; occurring in series of pulses. Derivation of the propagation time from the butterfly diagram. It corresponds to the sphere of current with the radius 0.3 of the solar radius producing the dipole field.
Sunspots are the consequence of appearance of plasma toruses at the surface - when a torus intersects the surface, it produces two spots. (What about complex sunspot groups? Or single sunspots?).
The planes of original toruses in the core are almost perpendicular to the equator of the dipole. And perpendicular to the resulting meridian (where spots appear).
(What about the action of the solar rotation? Wouldn't it distort the ring or make it drift?)
Rings remain circular most of their passage through the Sun.
Rings are produced in two activity regions, exchanging MHD waves. The time of travel between the two = solar cycle. (Would be interesting to compare with neutrino observations; and how would polarity reversal affect this theory).

In the Sun there is a thin unstable subsurface region, unstable core and a large stable region between them.
MHD rings cannot be produced near the equator, because gravity would be acting perpendicular to their axes and they wouldn't grow. Hence they should be produced in two regions - above and below the equator.
Walen's theory: every accelerating ring gives rise to two rings, propagating in opposite directions (along and against the magnetic field). "Recoil" ring has the same rotation, so opposite magnetic polarity. Deceleration - opposite effect ("recoil" ring has opposite rotation and the same magnetic field).
I.e. damping causes partial reflection. Analogy with an electric circuit.
(That's a clever way of dealing with polarity and cycles, but is it right? In the light of polarity reversals etc.).
Intensity variability of cycles is explained by inner instabilities. Negative correlation of intensity and length of the cycle from internal considerations. Plus negative correlation between the strength of the cycle and timings of previous two cycles.
(I have an intuitive feeling some sort of "conservation law" might be at play here; e.g. "total sunspot energy" - whatever that means - is constant, but is spent differently in different cycles - I'll need to check that).
In this theory it is possible to find a connection between spots in the south and next cycle's spots in the north and vice versa. This correlation has been found.
Number of spots at the equator is 0 due to the geometry of a dipole field.
Cowling argued that MHD theory of spots doesn't work, since the MHD whirls would be damped in stable layer by gravitation. But the field line deformation (another wave traveling in sync with the ring) might solve the problem. And this process is only viable for low latitudes, which would also explain why there are no sunspots in polar areas.

Planes of rings are mostly parallel to magnetic field lines. Reflection of the ring from the surface (image principle).
Huge electric fields associated with the ring motion. E.g. 600 MV above the photosphere. Below it the fields are compensated by inductive polarization (in reality it's much more complicated).
MHD pressure of a ring (force exerted by magnetic field on the currents) is of the same order as pressure in the photosphere - therefore, the ring would expand into it. The sum of gas pressure and magnetostatic pressure needs to be constant, which causes cooling of a sunspot.
Cowling's criticism: the constant expansion is needed to keep the temperature low.

5.4 The granulation
Granulation motions cause MHD waves in the photosphere. MHD wave: magnetic energy = kinetic energy = pressure difference.
Granulation magnetic field is order of magnitude higher than the solar dipole field - 10s of mT, - so it should be seen in Zeeman effect. (Need to investigate that).
Finite conductivity causes Joule heating due to granulation waves. Plus there's a gravitational damping in the vertical direction. Low frequencies are reflected. Possible frequency range (of waves, transmitted through the photosphere) is given - p. 147.
Photospheric waves are quickly damped with depth.
Turbulence and damping in the chromosphere and corona.
MHD wave is always associated with a current.
Due to anisotropic conductivity it's problematic to calculate the Joule damping. Need to use cross conductivity for that.
Description of chromosphere is problematic, since density gradient and temperature are mutually inconsistent. It is not clear what "supports" the chromosphere - either turbulence or high temperature or something else.
About 1% of the total solar energy is in the form of MHD waves rising from the chromosphere upwards.

5.5 Theory of the corona
Coronal emission lines show high ionization, which implies very high temperature. (Robitaille provides an important observation that high ionization in the corona might be non-thermal in nature - in his opinion it is chemical; but other options are possible too). Heating up by sound waves or MHD waves. The first option ignores electromagnetism, the second ignores compressibility.
Analogy with a generator: kinetic energy is transformed into e/m energy. Joule damping of MHD waves.
Light from corona is scattered photospheric light. K-component (corona itself) and F-component (interplanetary dust).
Determination of electron density.
In the inner corona the density is enough for thermal equilibrium between molecules, but not molecules and photons.

Corona should be interpreted as atmosphere, heated to about million degrees by electric currents, associated with granulation waves. High anisotropy due to magnetic field - conductivity along magnetic field lines is much higher; MHD waves move along the lines.
Geometry of the field causes more heating in the equatorial area (closed field lines); observed ionization is indeed higher there. (Apparently that would not be the case during solar maximum, so the equatorial plasma torus would disappear). Other heating processes: prominences as electric discharges; solar activity in general.
Heating by electric currents leads to expansion of matter, which leads to diamagnetic expulsion (e.g. in CMEs - see 3.3 for the description of diamagnetic property of plasma).

5.6 Prominences
Quiescent and eruptive prominences. Size ~ solar radius. Internal motions with speeds 10-100 km/s in arbitrary directions. Frequent "attraction" downwards towards sunspots. Spectrum of prominences is similar to chromospheric spectrum.
If prominences were really erupted from below, they'd quickly cool adiabatically (just like sunspots?). Radiation pressure also doesn't explain prominences.
Earth's atmosphere is an insulator, whereas solar atmosphere is a conductor. "Hence so-called electrostatic phenomena cannot exist in the solar atmosphere". Criticism of Bruce's ideas.
Discharge theory of prominences: prominences are the result of forces generated by induction due to motions of plasma in the general solar and sunspot magnetic fields.
We might assume as an approximation that current only flows along the field lines. Then discharge would occur when the field line would intersect the surface at two points with different potential. Magnetic whirl's GV electric fields are compensated by polarization under the surface of the Sun (see 5.3), while above it it is not.
Evershed effect: upwards and outwards motions in sunspots. This should cause downwards MHD waves.

Radial voltage in a sunspot due to tangential motions (or MHD waves) ~ 10 MV.
Symmetry of global magnetic field with respect to rotation axis is necessary. (Compare to dynamo theory, where such a symmetry cannot exist - so it cannot describe e.g. Saturn's magnetic field). Differential rotation of the Sun causes electric polarization even in the rotating frame of reference. The symmetry implies that magnetic field lines are equipotential surfaces, i.e. electric fields are perpendicular to magnetic field lines and discharge doesn't occur. If the field is disturbed by a sunspot, this is no longer true - discharge is possible.
The electric potential on the surface of the Sun (due to differential rotation) is approximately 170*Sin^4(phi) MV, where phi is the latitude. Plus the voltage due to spot polarization. General polarization should be roughly constant. (But as the cycle progresses and polar fields change too, so should the polarization).
Prominences are "attracted" to sunspots, because field lines go there. Prominence as a constricted discharge.

Prominence discharge is held together by pinch forces, so the current goes only through it, even though the corona around it is less dense and more hot (conductive?). Temperature of prominences is lower because of higher density and higher radiation losses. Joule heating of prominences might heat the corona, even though prominences themselves are cooler.
Discharge magnetic field in prominences is less than 0.1 T - otherwise it would be seen in Zeeman splitting. Though in general the current strength is determined not by resistance, but by inductance.
Example calculation - p. 163.
20 nOhm resistance, 500 henry inductance - incredibly large time constants (centuries).
Caveat about circuit analogy: field lines are flexible, and currents are surrounded by conductors - there is inverse skin effect (see 3.4) etc.
(If we assume that the Sun is powered by external current, the very same inverse skin effect would probably make it pinch just the same, and it would be pretty bright - perhaps, brighter than the Sun itself).

5.7 Emission of ion clouds
Acceleration of CMEs. At speeds of 2000 km/s they should have temperature 100 MK (assuming random motion).
Diamagnetism is key. Plasma in inhomogeneous magnetic fields tends to go where it is the weakest (see 3.3).
In reality, only electrons need to be very hot. Hot electrons also demonstrate lower interaction with other particles. "Electron gas explosion". Interruption of the current in a circuit - circuit energy is dissipated at the place of interruption.

5.8 Electromagnetic conditions around the Sun
(Alfven actually underestimated (by orders of magnitude) the galactic magnetic field; solar field also doesn't decrease as fast as a simple dipole).
Interplanetary currents - problematic to calculate, since they are determined by inductance, not conductivity. "Hence if an electric field is produced, e.g. by space charge, this field is compensated by an induced field. As the induced fields are not derivable from a potential it is meaningless to speak of an electrostatic potential in the environment of the Sun".
Current + diffusion current + Hall current.
In interplanetary plasma the electric field is mostly determined by the magnetic field and the state of motion, not the electrostatic potential. In prominences most of the static voltage is compensated by induced field.

5.9 Solar noise
Solar radio noise mostly comes from sunspots. 15 MHz - 10 GHz range. Limits of ionosphere and receiver.
Calculating equivalent temperature. There is a time delay between the arrival of different frequencies (the higher, the faster). (Dispersion).
Radiowaves from sunspots are circularly polarized. In the presence of the magnetic field gaseous discharges produce "noise" oscillations. Electron gas in laboratory produces more radio noise than predicted. Galaxy is as noisy in radio as the Sun. So if these waves are from discharges, each star should be more noisy than the Sun. Or it's the noise of interstellar space itself.

6.1 Introduction
D-field - disturbance on top of Earth's magnetic field. There are 3 maxima of D-field (auroral zones and equator).
Description of Birkeland's terrella. It was an anode. (M. Mozina here claimed that Birkeland also tried cathode?..).
Stoermer's interpretation (that electrons from the Sun are key for producing the disturbance) is incorrect (magnetic field of the Sun isn't there, large space charge is present, energy is inconsistent etc.). Malmfors' interpretation is better.
Electric field theory of aurora. (Alfven seems to be the first to propose it). The main idea is the electric polarization of a CME cloud or the coronal hole stream in the solar magnetic field, which gives rise to the system of currents, driving the aurora and magnetic perturbations. (Alfven didn't know about CMEs - the way we know them today - nor coronal hole streams, but I'm using modern terminology for simplicity).
Malmfors' experiment: aurora is there even without infalling ions. CME cloud is only needed to produce external electric field. Then magnetic storm (gaseous discharge) might happen.

6.2 The electric field theory
An example model of a magnetic storm. Electron flow from the Sun is divided into encircling evening branch and far-away morning branch. And there is a "forbidden region" in between. (See scheme at p. 180).
Auroral magnetic disturbance - from auroral currents; equatorial disturbance - from ring current.
If ion temperature is much smaller, ions move just in straight lines. Hence space charges might accumulate in the forbidden region. Then these space charges might discharge through magnetic field lines and produce the aurora. (It is these discharge currents that are called Birkeland currents).
Theoretically, auroral curve is at maximum at 18h and minimum at 6h. (0h is the anti-solar point - i.e. midnight, and 12h is the sub-solar point - noon). Polar distance of auroral oval depends on electric field as the root of 8th power (!). Different auroral curves: I-curve (ideal), G-curve (geographical), M-curve (mean electric field), A-curve (actual).
As we move away from Earth, higher order corrections to dipole become negligible. Forbidden region is 5-10 Earth radii away, and that's where the storm electrons come from.
Diurnal variations of the auroral polar distance compared to observations. Auroral discharge starts from the forbidden region and generates auroral arcs. (Meaning geometric shape, not the discharge type). Calculations of auroral arcs from auroral curve correspond to observations reasonably well.

Current system of magnetic disturbance. Drift in electric field doesn't produce current. (See Chapter II for more info). Drift in inhomogeneous magnetic field does produce current - in the form of the disk of circular westward currents outside the forbidden region in the magnetic equatorial plane. (Ring current). Current density falls as r^(-4). Diamagnetic action of electrons is about 1/3 of their drift magnetic field - neglected for simplicity.
(What about gravitational drift? It should produce currents too). These currents produce equatorial magnetic disturbance with maximum at 18h and minimum at 6h.
These currents supply positive charge to the day side of forbidden region and negative to the night side. The charge accumulates and then discharges along the field lines through the atmosphere. The quasi-circular auroral current closes the circuit and produces polar magnetic disturbance. Noon and midnight points divide two current branches in the auroral system.
Calculation of the auroral current - p. 192.
(This scheme seems perfectly feasible for CME clouds, but what about coronal hole streams? Would it be just the same?..).
Plot of current strength vs. longitude. Magnetic disturbance is checked by using scale model experiment (instead of numerical integration). Comparison to observations.
Thorough description of the results of the model. Below the auroral zone the vertical disturbances are strongest at 18h. North-south disturbances are maximal at 6h. East-west are maximal at 12h.

The theory explains:
a) symmetry along 6h-18h line;
b) correlation between aurorae and magnetic disturbances - they're the same phenomenon;
c) the exact form of magnetic disturbance;
d) position of aurora in the sky.
Objections to the theory:
a) a lot of approximations;
b) magnetic moment of particles is not constant (as the velocity vector changes) - secondary effects of the discharge along the field lines are not accounted for;
c) electrons are hardly expected to reach the night side - that should introduce asymmetry;
d) inertia term of ions cannot be neglected, their drift velocity should be higher than rotation velocity, which means that extra space charge should appear;
e) Malmfors' experiment shows that aurora is produced just in an electric field, without ions at all. (In the next section Alfven shows that it doesn't really contradict the theory).

6.3 Malmfors' scale model experiment
Terrella in an electric field at low pressure + electron beam to ionize the air.
Criticism: magnetic field is too weak, so it doesn't really replicate what happens in nature. (Yet another nod to SAFIRE thread).
Ions don't behave as they should. Density is wrong etc.
Penning manometer: glow discharge happens even though the pressure is too low - magnetic field makes the mean free path longer, and ionization is more frequent.
No conflict with electric field theory of aurora.

6.4 The aurora as an electric discharge
10-100 keV electrons (necessary for the observed aurora) are predicted by the theory.
Discussion of the needed electron energy. If it's discharge all the way from ionosphere to magnetosphere, only low energy (10 eV) electrons are needed - they'd be accelerated. The aurora spectrum shows only low energy secondary electrons.
Auroral ray - discharge follows the path of higher ionization. Dissolution of auroral arc into rays = constriction of a discharge (see 3.4). Whether it's thermal or e/m - not quite clear. Seems like e/m from temperature measurements.
Auroral draperies - caused by vortical motion induced by the fluctuating potential (space charge) along the circuit.

7.1 Introduction
Electrons only comprise less than 1% of cosmic rays (CR). Latitude dependence of the flux due to Earth's field.
Total energy flux to Earth from CR is about the same as energy from starlight (Sun excluded). The flux is constant and isotropic (if you correct for pressure and magnetic storms).
(Apparently, solar cycle modulation of CR flux was still unknown at the time).

7.2 Cosmic radiation in the terrestrial and solar magnetic fields
Magnetic fields don't influence CR intensity. They just prohibit particles with certain energies and directions (forbidden cone). Forbidden cone is the shadow of the Earth. (As far as I know, neutrinos still might come "from the Earth", i.e. "from below").
Particles that can reach the Earth should have 10s of GeV energy or more. Impact of Earth and Sun's field on the motion of CR. Solar field allows particles of GeV energy to impact the Earth.
Scattering of CR by planetary magnetic fields. Earth's scattering cross section is 3 orders of magnitude larger than its absorption cross section. Time between scattering events of 1 particle ~ 160 years.
Optical analogy of CR scattering. Scattering of CR by planets allows lower energy CR to reach Earth than otherwise. If Mars had a magnetic field (Alfven assumes it does), that would decrease the lowest energy of CR at Earth some 30%.
The absorption in interplanetary plasma is very low. CR particle might move there for centuries without interaction. Though it gets deviated by electric fields of CME clouds etc. So all kinds of orbits are possible. The Sun also creates a "shadow" for CRs.

7.3 Magnetic storm variations
(Forbush's effect was discovered in 1937, but Alfven never references him).
CR flux increases some hours before the storm and then rapidly falls during the main phase. Interplanetary electric field is compensated in CME cloud by polarization. But polarization doesn't affect the CR particle, as it's not moving with the cloud.
This electric field is not potential. Double layer associated with the field accelerates positive CR and increases their flux. And it decreases the negative ones.
Scheme of a solar plasma stream - p. 218.
Electric field accelerates positive particles forward and decelerates backward, which leads to the increase of their flux before the storm onset and decrease during/after. In order to have 10% variation, the voltage in double layer should be in GV range. The numbers don't quite add up. (One reason is that Alfven underestimates magnetic field strength and actually hypothesizes that this might be the case - due to "frozen in" field lines).
CME might also accelerate CR in periodic orbits closer to the Sun and send them outwards to Earth or infinity.
CME clouds may have voltages of 10 GV.

7.4 The isotropy of CR
If we ignore magnetic fields, total energy of CR in the Universe would estimate as orders of magnitude higher than energy of starlight. But we can't ignore them. Though electric fields of reasnable strength are unimportant.
CR are getting isotropic in magnetic fields. Galactic field of 10^(-13) T would be enough to make distribution of 10^15 eV rays isotropic.
Galactic field would confine most of CR to the Galaxy - if they are produced within it in the first place. In this case the CR total energy might be much smaller than the starlight energy. E.g. if starlight travels 10^4 l.y. (before being scattered or absorbed) and CR travel 10^8 l.y., the stationary state would require 10^4 times less energy for CR (compared to starlight).
Universal isotropy hypothesis vs. Galactic isotropy hypothesis = Very large vs. very small fraction of total energy in CR.

7.5 Speculations about a galactic magnetic field
Estimates of galactic field strength. (Again Alfven underestimates solar field strength, assuming it to be a simple dipole field). Galactic field should be connected to interstellar matter rather than stars, since their fields are very localized.
Mean free path in interstellar matter (10^13 m, i.e. 100 a.u.) is small with respect to the galactic size (10^20 m), so the collision time is 10^8 s (~ 10 years). Interstellar medium might be approximated by gas at 10 kK temperature. Then conductivity would be 7 orders of magnitude higher along the field lines (and be approximately the same as in the Sun).
Discussion of timescales of existence of galactic field. Alfven velocity in interstellar medium is very small (1 m/s). In 10^10 years MHD wave travels only 100 l.y. So magnetic field doesn't affect it very much, unless the field is much stronger than assumed. (It actually is).
Magnetic pressure is 8 orders of magnitude lower than gas pressure. If additional field would be produced by current (e.g. stream of electrons), high conductivity of the medium would lead to an induced compensating current (electrons flowing backwards), so the net magnetic effect is near zero.
(This looks more like Don Scott's model of FAC).

Blackett's hypothesis of proportionality of magnetic field to angular momentum. It seems to fit 10^(-12) T field for the Galaxy. If Blackett's hypothesis is correct (it is not), Maxwell's equations need to be modified.
Slow MHD waves cannot restore the initial magnetic field fast enough - it warps due to moving matter. So it's going to be very irregular. And dragging of the field by matter is going to amplify the field too.
The fields of 10^(-10) T are already strong enough for MHD waves to traverse the Galaxy in 10 billion years. They'd lead to much more regular field structure and would impact the motion of matter in the Galaxy.
(Galactic fields are actually about 10 times stronger than that).

7.6 Origin of CR
Hypothesis of cosmological origin of CR (Lemaitre). Millikan: hypothesis of spontaneous nuclei annihilation. Klein: hypothesis of matter-antimatter annihilation.
Not really needed if we assume only galactic (not universal - see 7.4) isotropy. Nova and supernova hypothesis - OK, but doesn't account for highest energies of CR.
Bothe and Kolhoerster: acceleration by electrostatic fields. Problem: they'd accelerate all the particles. And they can't arise in the first place due to high conductance. And the energy needed to sustain them is gigantic.
Acceleration in plasma streams. Given high energy, a particle might be accelerated in the induced electric field of a moving plasma.
Example calculation - p. 226.
Multiple acceleration events in a single stream are possible. The accelerating electric field is non-potential. Acceleration depends on the stream velocity.

There is a large scale electric field, caused by the rotation of the Galaxy - around 10^12 V if we assume 10^(-13) T magnetic field. (In reality it's more like 10^16 V, since the field is ~ 1 nT). If the field is irregular, the voltage would be lower. But this field is unlikely to be able to accelerate the particles.
Stars might produce CR and accelerate them in their own electric fields. E.g. there is a GV electric field between solar poles and equator.
Swann: acceleration in changing magnetic fields (through betatron action).
Acceleration in a binary system (proposed by Alfven). "Double star generator" - produces AC voltage along the symmetry axis.
There is still a problem of high conductivity around it. "It is practically short-circuited". It would probably generate a lot of slow particles instead of few fast ones.
So we have two ways of acceleration: one needs multiple events (acceleration in moving plasma), and other needs pretty specific conditions (acceleration in changing magnetic fields).


[Note at the very end of the book:] Composition of CR is similar to interstellar matter - so they're probably indeed accelerated by electric fields in space.
Proposal of nT galactic field (the one which is actually observed) "makes the intensity problem much easier". Our CR is a local solar phenomenon. Interstellar fields might be produced by MHD waves.
Fermi: CR accelerated by variable magnetic fields of MHD waves.


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