Peratt's "Physics of the Plasma Universe"

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Peratt's "Physics of the Plasma Universe"

Unread post by paladin17 » Mon Feb 15, 2021 12:50 pm

These are my notes on "Physics of the Plasma Universe" (2nd ed., 2015) - effectively a short version of the whole book.
The book is going to be useful for anyone who wants to get a scientific opinion on electric currents and electric fields in space, behavior of plasma filaments and such. A noticeable portion of the book is devoted to computer modeling and high energy experimental techniques, which don't really interest me much, so the notes are pretty sparse in these sections.

In general, I have to note that compared to Alfven's books that I covered here previously this book is just horrible in terms of writing quality and overall vibe (to my taste anyways). It is tainted with a certain type of sickly textbook dryness and "consider this equation and a hundred following ones, though I wouldn't tell you why". This was the reason I started reading it a year ago (right after reading Alfven) and couldn't finish right away. But now I forced myself through it.
Hopefully these notes would save you some time if you don't want to go through this process yourself. I tried to capture all the important points.

Just like previously, I'd make my own comments in italics, while literal quotes from the text would be given in "quotation marks". Every now and then I give the number of the page where the following statements are found (just in case).

______________________________________________________________


Preface

Purpose- to address the growing recognition of the need for plasma physics in astrophysics.

Prologue

"To be sure, nothing expected was ever encountered; only the unexpected but readily recognizable from the standpoint of HEDP in astrophysics and cosmology"
(HEDP - high energy density plasma).
The terms "plasma universe" and "plasma cosmology" were first used to describe Starfish Prime experiment in 1962.
"We coined these names in the mid- and late 1980's".
Computer simulations. "None of the results were ever expected".

1 Cosmic Plasma Fundamentals

1.1 Plasma

p. 1
The book is mostly about energetic or highly ionized plasmas.
NB. It was Einstein who started calling the equations "Maxwell-Hertz's". Before that they were known as Hertz-Heaviside's.
p. 2
Complex plasma behavior. Separation into cells divided by charged particle sheaths.
"Plasmas need not be neutral" - study of purely electron plasmas etc.
Plasma filamentary structures. Higher conductivity than metals. Wide range of possible densities and temperatures (graph on p. 3).

1.2 Physical Sizes and Characteristics of Plasmas in the Universe

Various plasmas on Earth and in its surroundings. Plasmas in the Solar System.
p. 8
NB. Peak magnetic field strength in comet Halley was stronger than Earth's (0.7 G vs. 0.5 G). See my comment below.
Hydrogen plasma torus around Saturn 15-25 radii from the planet.
Transition regions between plasmas with different parameters.
p. 11
Photosphere is only weakly ionized: 10^(-4) or about so.
p. 12
Interesting footnote on solar corona heating vs. thermodynamics. Peratt claims the disparity is caused by the fact that corona is made of plasma rather than regular matter. He also says that heating may be caused by electrons accelerated by double layers (DL) in coronal loops or by electron beam instabilities.
NB. "Protons accelerated inward collide with ions in the Sun's atmosphere to produce nuclear reactions, whose gamma rays and neutrons have been detected from spacecraft".
Maybe that's the answer for the solar gamma ray problem?
p. 13
Solar wind magnetic field strength can reach 0.2 G.
Really?.. That's a lot. Looks suspicious (just like with Halley above). I think it should be uG instead of mG in the text.
Solar wind flow is twisted into Archimedean spirals.
p. 15
Current sheet at minimum is shown.
What about the maximum when the sheet is highly tilted?
Plasma filaments at the Galactic center.
Other galaxies etc.

1.3 Regions of Applicability of Plasma Physics

p. 17
"Even weakly ionized plasma reacts strongly to electromagnetic fields" - due to the strength of e/m interaction itself.
p. 19
"Most of our knowledge about electromagnetic waves in plasmas derives from laboratory plasma experiments where the gases used have a low degree of ionization, 10^(-2)-10^(-6)".
Criterion for neglecting magnetic properties of plasma: Lundquist parameter is much less than unity.
Conductivity of known plasmas varies for about 4 orders of magnitude (10^2 to 10^6 S/m), and magnetic field varies for about 18, so it's the latter that is most important for Lundquist criterion.
p. 20
"No rotating object in the Universe, that is devoid of a magnetic field, is known".
In the following text clearly the Lundquist parameter is omitted by mistake (some typing glitch).
"Neglecting lightning, planetary atmospheres and hydrospheres are the only domains in the Universe where a non-hydromagnetic treatment of fluid dynamic problems is justified".

1.4 Power Generation and Transmission

On Earth, energy is generated by power stations and then transferred to large distances where it is consumed (dissipated) and becomes "visible". Same is true for space.
"There is a tendency for charged particles to follow magnetic lines of force and this forms the basis of transmission lines in space".
p. 21
Somehow Peratt says that aurora mechanism is unknown - ?.. But anyway he gives it as an example where only the small part of the circuit (aurora itself) is visible.

1.5 Electrical Discharges in Cosmic Plasma

p. 22
"An electrical discharge is a sudden release of electric or magnetic stored energy".
"As such, discharges are local phenomena and are usually accompanied by violent processes".
p. 23
Peratt shows a drawing of the Earth and claims that it is an SDO photo. Granted, it may be a photo of the actual aurora, but superimposed on a drawing.

1.6 Particle Acceleration in Cosmic Plasma

p. 25
Electric field can arise due to motion of charged particles in a magnetic field, charge separation or time varying magnetic fields.
In a collisionless plasma (e.g. magnetosphere) electric fields parallel to magnetic fields can freely accelerate particles.
Possible experimental methods of acceleration.

1.7 Plasma Pinches and Instabilities

p. 26
Pinch effect - abundance of filamentary structures in space plasmas.
Sheared magnetic field - nonpotential field that is caused by shear flows of plasma. It tends to settle in a "force-free" stable configuration. They tend to have a twisted appearance.
p. 27
These are field-aligned currents. Examples: chromospheric fibrils, sunspot penumbra structures.
Constant alpha parameter - lowest magnetic energy, i.e. the most stable configuration.
So in systems where magnetic forces are dominant and there is a possibility of energy dissipation (e.g. through particle acceleration) these configurations are the end result.
Slipping stream (diocotron) instability - disintegration of electron beam into separate vortex-like structures.
It occurs when the local charge-neutrality is no longer maintained.
Same as in the explanation of auroral curtains by Alfven.
p. 28
When a neutral gas moves with respect to plasma with a kinetic energy higher than its ionization energy, it quickly ionizes. This velocity is called critical ionization velocity (Alfven).
p. 30
Important comment in the footnote: the fact that elements tend to naturally separate in cosmic plasmas makes it very difficult to judge what the actual abundances of the elements are in the Universe.

1.8 Diagnosing Cosmic Plasmas

p. 32
E/m radiation. Gammas and X-rays are produced by high energy electrons (e.g. accelerated by double layers).
p. 33
Microwaves are mostly produced by relativistic electrons, though there are various mechanisms.
Density of IR and microwave radiation is the highest in the Universe (density of radio is unknown due to problems with detection of very low frequency waves).
p. 36
Data from space probes.
"Electric fields within the near-Earth plasma were generally not thought possible until space probes measured them directly".
Dangers of assuming behaviour of astrophysical objects without having enough data.

2 Birkeland Currents in Space Plasma

2.1 History of Birkeland Currents

p. 41
Motion of magnetized plasma -> currents (through Lorentz force).
E.g. the auroral circuit.
Discovery of Birkeland currents in 1974.
These currents cause a variety of phenomena in plasma (energy dissipation, separation of elements, structure formation etc.).
p. 42
Birkeland's, Chapman's and Alfven's models of aurora circuit.
p. 45
BC in the aurorae heat the atmosphere up and also cause density depletions.
It seems that the supply of plasma from the solar wind is negligible in comparison to ionosphere-magnetosphere own particles.

2.2 Field-Aligned Currents in Laboratory Plasma

p. 46
Filamentary and helical structures are often formed in lab plasmas.
Vortices as well. These phenomena scale for about 12 orders of magnitude in size.

2.3 Field-Aligned Currents in Astrophysical Plasmas

Filaments everywhere! Of all scales. (List).
p. 47
"Plasmas in relative motion are coupled via currents that they drive through each other. Currents are therefore expected in a Universe of inhomogeneous astrophysical plasmas of all sizes".

2.4 Basic Equations of Magnetohydrodynamics

"Fluid treatment" - through averages and distribution functions.
Boltzmann equation.
p. 48
Two-fluid equations for ions and electrons. Continuity equations etc.
Such average methods ignore the motion of particles as individual entities and therefore cannot describe phenomena like double layers. They're only useful for bulk plasma flow.
p. 49
Changes in magnetic field strength: transport of the field with plasma + diffusion of the field through it.
Their ratio = magnetic Reynolds number.
Lundquist parameter, Alfven speed etc.

2.5 Generalized Bennett Relation

p. 50
Just tons of equations.
p. 53
At uniform current density and temperature one gets a parabolic density distribution in the cross section.
Alfven limiting current - current strength at which the pinch effect is so strong that it shuts the current itself down.
By changing some conditions (e.g. adding external magnetic field) larger currents may still exist.
What is still important is charge neutralization. An unneutralized electron beam would simply form a space charge (negatively charged cloud - a virtual cathode).
p. 54
Electrostatic field produced by beam itself produces a return current.
p. 55
Charge neutralization and plasma instabilities.
p. 56
High current discharges can carry more current if the rotation is introduced.
Carlqvist relation - integrating gravity into plasma equations. That way the relative importance of gravitation and e/m forces can be determined.
p. 57
Analysis of a situation of a hydrogen cloud with current.
p. 59
Analysis of a current sheet pinch situation.

2.6 Application of the Carlqvist Relation

p. 61
Auroral current sheets are basically force-free currents. Currents in the solar atmosphere are as well.
Alfven's heliospheric current model.
p. 62
"Whether or not the polar current is diffuse or filamentary is an important problem for cosmic plasmas".
Estimation of the interstellar currents. They seem to be around 10^(13-14) A.
In heavy cloud the pinch, kinetic and gravitational forces are roughly balanced.
p. 64
Galactic current should be around 10^19 A and the pinch forces mostly balanced by thermokinetic ones.
Intergalactic currents detected by radio emissions. Same magnitude.

2.7 Basic Fluid and Beam Instabilities

p. 65
Gas is unstable to density fluctuations with wavelengths greater than some critical one.
This may lead to gravitational collapse if Lundquist parameter is of the order of 1 or less.
p. 67
Buneman (two-stream) instability.
Negative energy electron waves (they take their energy from kinetic energy of electrons). Bunches of accelerated electrons passing through slower or decelerated electrons. This may produce double layers in BCs and e/m radiation.
p. 68
Sausage instability: magnetic pressure (pinching) reduces the cross-section. This may separate the whole current into a train of plasmoids.
Kink instability - helical mode in the pinch. Often occurs when a strong axial magnetic field is present, i.e. in Birkeland currents.

2.8 Laboratory Simulation of Cosmic Plasma Processes

High voltage pulsed experiments. "Laboratory astrophysics".
Marx bank - huge array of capacitors.
p. 69
"In this way, space and astrophysical magnitude quantities are generated".
Various cameras and detectors etc. Generation of plasmoids.
p. 72
Webster's aurora simulation.

2.9 Particle-in-Cell Simulation of Beams and Birkeland Currents

p. 73
Hollowing instability - cylindrical electron beams may become cylindrical sheet-beams.
p. 74
Birkeland filaments demonstrate: pinching, bulk rotation, release of synchrotron radiation.
Charge neutralized beam propagation. Electrons propagate on top of plasma - the establishment of return current by the plasma electrons in the opposite direction.
Other examples of such propagation - relativistic beams etc.
p. 77
Wake field condition. Production of areas with alternating electric field direction.
p. 78
Large radius beams and large currents -> filamentation instability. Relativism helps too. Strong magnetic fields may inhibit it though.
p. 80
Evolution of a narrow filament.
p. 82
Formation of vortices in thin cylindrical beams. Interaction between separate vortices (long range attraction, short range repulsion).

3 Biot-Savart Law in Cosmic Plasma

3.1 History of Magnetism

p. 94
We would be using Ampere's law (describing magnetic interaction between two loops with current) as a postulate.

3.2 Magnetic Interaction of Steady Line Currents

Biot-Savart law (equation).
"All steady currents must flow around continuous loops or paths since they have a zero divergence".
p. 95
Taken differentially, it contradicts Newton's 3rd law, but the integral over the loop doesn't.

3.3 Magnetic Induction Field

Simplification of the law if B is known - then consideration of the second loop is not needed.
Lorentz force.
Reformulation of the law for conducting volumes instead of thin wires. For conducting surfaces as well.
Ampere's circuital law.
p. 97
Field of an infinitely long wire.
Force between two wires.

3.4 Vector Potential

p. 99
Definition. Finding B through A.
Force between two loops with current.

3.5 Quasi-stationary Magnetic Fields

p. 102
Faraday's law of induction.
"The induced electric field exists in space regardless of whether a conductor exists or not".
This electric field is non-conservative.
Induced field in conductors moving with respect to magnetic field.
Faraday disk.

3.6 Inductance

p. 104
Self-inductance: current carrying loop would induce additional current to negate changes in its own magnetic flux through itself.
Mutual inductance - same but with 2 different loops.
The given expressions are only valid for quasi-stationary magnetic fields, where current and magnetic field have the same phase angle in the whole circuit. For HF processes this is not the case (finite time of signal propagation).

3.7 Storage of Magnetic Energy

p. 105
Expressions for magnetic energy of a system of filaments etc.
Beta - ratio of gas pressure to magnetic pressure.
Photosphere - high beta, corona - low beta.

3.8 Forces as Derivatives of Coefficients of Induction

p. 107
Spatial derivatives of inductances multiplied by currents = force.

3.9 Measurement of Magnetic Fields in Laboratory Plasmas

B-dot probe - measures the time derivative of B. If we add an integrating circuit, we can measure B itself.
p. 109
Rogowski coil - variation of B-dot probe with a toroidal coil.
It can directly measure the current through its center.

3.10 Particle-in-Cell Simulation of Interacting Currents

Two parallel charge neutral and thermalized Birkeland currents. They are driven by external electric field. Description of their interaction through magnetic forced requires numerical simulation.
p. 111
Some approximations -> force between filaments is long range attractive (falls as r^(-1)) and short range repulsive (falls as r^(-3)). Parallel currents cause attraction, and counter-parallel azimuthal currents cause repulsion.
In case of lack of charge neutralization there may also be electrostatic forces.
p. 113
ExB drift causes the distortion (polarization) of the filament cross sections. The net result is a torque.
p. 114
Since we have a constant external field, the currents increase with time. Numerical simulation and laboratory results.
p. 116
Formation of spiral arms from two interacting filaments. Arms thin out, so polarization induced charge separation produces radial electric field across them. This leads to diocotron instability, which appears as a wave motion in the arms, apparent in spiral rotational velocity curves.
p. 118
Components of velocity: linearly increasing one (rigid body rotation), two flat ones (trailing spiral arms). Diocotron instability modulates the latter.
p. 119
Inverse r attraction often leads to filament pairings. E.g. of three filaments, two of which are slightly closer to each other, we'd have a spiraling pair and an isolated third one in the end.

3.11 Magnetic Fields in Cosmic Dimensioned Plasma

p. 121
Indirect measurement of magnetic fields in galaxies:
1) optical polarization (paramagnetic dust grains orient perpendicular to the field);
2) Zeeman splitting of radio lines;
3) Faraday rotation of polarized radio emissions (thermal radio waves are unpolarized, while synchrotron emissions are partly polarized);
4) amount of synchrotron radiation (uses unrealistic equipartition assumption and thus underestimates the field strength).

Interstellar field near the Sun - 0.2 nT. From synchrotron radiation - around 0.6 nT. Maximum field in spiral arms should be around 4.5 nT. This is consistent with fields observed in molecular clouds.
p. 124
Field lines should go along the spiral arms - only a small deviation (up to 6 degrees) is likely.
Possible field reversal in the Sagittarius arm: may indicate a bisymmetric shape of the overall field.
Numerous plasma filaments near galactic center, perpendicular to galactic plane - around 1 ly in diameter and 30-200 ly in length.
"... in the galactic center the magnetic field runs exactly perpendicular to the galactic plane".
The strength is around 0.1 uT.
"Rotation measures show two different large-scale structures of the interstellar fields: axisymmetric-spiral and bisymmetric-spiral patterns".
"The orientation of the field lines is mostly along the optical spiral arms. However, the uniform field is often strongest outside the optical spiral arms".
p. 125
"The tendency for the magnetic field to follow the HI distribution". (HI is neutral atomic hydrogen).
p. 126
"... relative lack of HI in the cores of spiral galaxies but high HI content in the surrounding region".
Simulation and its comparison to observations. Some signs of original pair of currents that produced the galaxy can be seen.
p. 128
Galactic rotation: inferred from Doppler shift of H_alpha line.
Nearly solid-body rotation in the galactic center, nearly constant rotation speed at the spiral arms. Plus distinct structure of the arms themselves on top of it.
Fields of the order of 10 mV/m can produce the necessary currents to create a galaxy. In the geospace DLs have fields of 1-10 mV/m.
Diocotron instability in the arms - seen both in cross-section and velocity profile.
p. 131
Elliptical galaxies are often found near double radio galaxies or radioquasars or in the regions of high density of galaxies. They have weak or absent magnetic fields and demonstrate twisting of outer isophotes.
p. 134
Simulation.
Peratt doesn't explicitly say what should happen for elliptical galaxy to form. He simply mentions "filament interaction". From his words about the beginning of a slight twist it vaguely follows that elliptical galaxy may be a first stage before the formation of a spiral galaxy (with a much larger twist, that is), but who knows.
Intergalactic magnetic fields between Coma cluster and Abell 1367 up to 0.06 nT.

4 Electric Fields in Cosmic Plasma

p. 139
First electric fields in space were thought to be impossible because of vacuum (zero conductivity), and then because of plasma (infinite conductivity).
What an irony.
Then [magnetic] field-aligned electric fields were found above aurorae.
They can hardly be measured directly, and are concluded to exist from probing the characteristics of particle populations.

4.1 Electric Fields

Electric fields may arise from changing magnetic fields or charge separation.
Charge separation happens due to multitude of reasons: plasma instability, gyration in the magnetic field, field and temperature gradient, diffusion, drift, radiation force etc.

4.2 Measurement of Electric Fields

Methods of measurement: quite a few (including ionized barium release and tracking).
V-dot (E-dot) probe: measures the rate of change of voltage.
Electro-optic crystals: use electrically induced (by the measured field) birefrigence (requires strong fields to be detectable).
Spherical double probes: two electrodes separated by tens of meters and spinning with the spacecraft (require careful control of the spacecraft's own electric potential).
Ion detectors: measuring bulk velocities parallel and perpendicular to B.
Electron beams: shoot electrons and then catch them again, probing the fields.

4.3 Magnetic Field Aligned Electric Fields

p. 145
Thermoelectric effect: rapid decrease of friction forces with energy (in a collisional plasma). It is capable of supporting electric potential between plasmas of different temperature without a net current.
Parallel electric fields can also be supported by magnetic mirroring effect - both with and without a current.
Electrostatic shock - jump in potential supported by space charges. In the magnetosphere they produce transverse fields of hundreds of mV/m. Mostly at altitudes of 1000-5000 km and in the 16-22 h longitude. Though they also exist at up to 7 R_E altitudes.
Double layer: tens of Debye lengths thick; field is concentrated between two layers. In space plasmas field strengths of 1 V/m are possible. But such fields would be concentrated in a very thin layer (maybe 100 m thick), which is hard to detect. Instead many weak double layers are observed (hundreds or thousands of them along a BC).

4.4 Magnetospheric Electric Fields

p. 148
Measured electric field in the plasmasphere below 3.3 Earth radii corresponds to the theory well, but above that significant deviations are observed.
During disturbed periods the region of plasmapause also demonstrates anomalous strong electric fields (hundreds of mV/m).
Fields in the plasmasheet are variable as well. In quiet times they are too small (0.1 mV/m or less) to be detected by double probes, though were measured by electron injection.
"During the substorm active phase, the electric fields are both strong and variable. As induction electric fields are important during times of extreme variability, there does not even exist an electric potential on the global scale".
Strong fields (hundreds of mV/m) from 2.5 to 7.5 Earth radii due to electrostatic shocks.
Fields in the neutral sheet: quiet (0.5 mV/m), disturbed (6 mV/m).
Fields in magnetotail are hard to measure due to low particle density. Secondary methods: through anisotropic particle fluxes etc.
"... occurrence of velocity fields with a nonvanishing vorticity".
Magnetopause - violent field fluctuations up to 10 mV/m. They probably override any DC potential there is.
Auroral acceleration region - electrostatic shocks and multiple double layers.
"... extremely strong and irregular electric fields above the auroral oval". They correlate with regions of electron precipitation.
Sharp transition from mV/m fields in subauroral latitudes to hundreds of mV/m at auroral ovals.
p. 153
Reconstructions of the global potential distribution and current systems. Models show a general but not detailed agreement with the observations.

4.5 Outstanding Questions

Still a number of unsolved problems: how plasma enters magnetosphere (from solar wind and ionosphere).

4.6 Phenomena Associated with Electric Fields

Surface discharges in dielectrics, including spacecraft.
p. 158
NB. Neutrons from dense plasma focus (plasma gun). Neutrons are only produced when an inner electrode is an anode.
"In pinch devices, the ions are preferentially heated".
p. 164
Io's volcanoes and their plasma behavior.
"The dominant electric field in the Jovian magnetosphere is one that is associated with the corotational motion of plasma".
Induced voltage across Io is about 400 kV, and the current of 10^6 A was observed flowing out of it.
"It would seem plausible that the current would tend to concentrate in the volcanic plumes".
"Volcanic activity on Io generally occurs within an equatorial band of +/- 30 degrees latitude".
Modeling of Io's volcanoes as plasma gun features. We arrive at the same order of magnitude for ejecta velocity as observed.
p. 167
Radial motion of plasma as a result of ExB forces. Concentration of matter by the filament.
"The cosmic magnetic flux tubes are not directly observable themselves, but the associated filaments of condensed matter can be observed by the radiation they emit and absorb".
Non-ionized components interact through viscosity.
"If the electric field is antiparallel to the current, the drift is outwards".
Marklund: inwards motion of ionized matter, outwards motion of neutral matter -> hollow cylinders of matter with different ionization potentials.
Both the convection process and luminosity increase with external electric field.
p. 170
Electron runaway process: "Electrons with an initial velocity above the threshold velocity gain speed indefinitely (within the limits of relativity), so long as the electric field is present, and "run away", while initially slow electrons come to rest".
Dreicer field.
p. 171
"Thus, electrons in cosmic plasmas are readily accelerated to high energies in the presence of even very small electric fields".
Higher cosmic ray anisotropy for lower energies (0.1), lower - for higher energies (10^(-4) at 10^20 eV).
Supernovae shocks as a source of cosmic rays are inconsistent with such low anisotropy.
"... complete lack of any laboratory evidence that shockwave/charged particle acceleration actually exists".
"... field-aligned electric fields are the most plausible mechanism for producing cosmic rays".

5 Double Layers in Astrophysics

Discovered by Langmuir ("double sheathes"). Alfven: they should exist in space. Later - in situ observations.

5.1 General Description of Double Layers

p. 175
Formation of a DL in current carrying plasma due to instabilities.
Four populations of particles are needed: 1) current-carrying electrons; 2) current-carrying ions; 3) trapped electrons downstream of their flow; 4) trapped ions downstream of their flow.
Because of the acceleration of 1 and 2 by the DL, 3 and 4 are needed to preserve particle density (and charge neutrality).
Field-aligned currents -> there is a component of magnetic field parallel to electric field.
"Thus, the DL is a region where ideal MHD breaks down".
DL accelerates particles.
"The DL acts as an electrical load dissipating energy at a rate I*phi" (I - current through the DL, phi - potential difference). It transforms electrical energy to the directed kinetic energy of accelerated particles.
"Thus, the DL exhibits inertial resistance". Not the same as ohmic and anomalous resistance: their result is thermal or random particle motion.
NB. "Since the DL acts as a load, there has to be an external source maintaining the potential difference phi and driving the current I".
In the lab it's the power supply, in space it's the magnetic energy stored in a larger circuit that produces induced voltage here.

5.2 Time-Independent Double Layer

p. 179
NB. Ion currrent is weaker than the electron current; they are nearly identical only for relativistic double layers.
p. 180
Charge distribution in a DL. Positive spike at anode, negative spike at cathode, uniform distribution in between with slightly higher electron content (negative spike is thinner).
DL may be stationary or moving.
DL are a subset of Bernstein-Greene-Kruskal solutions of Poisson-Vlasov equations. Other such structures include electrostatic shocks, ion-acoustic solitons, nonlinear wave trains.

5.3 Particle-in-Cell Simulation of Double Layers

"... DL are nonuniform in density and produce particle beams with non-Maxwellian velocity distributions".
Two types of simulations: particle codes (trace a large number of individual particles), Vlasov codes (operate with distribution functions). Both have their advantages. This book focuses on the former.
It seems DL may form as a result of two-stream (Buneman) instability in the current - if the drift velocity of electrons is larger than thermal velocity.
Importance of nonlinear effects: 1) deceleration of the electron beam (anomalous resistivity); 2) electron heating; 3) modification of growth rate and frequency; 4) electron trapping.
Two time scales in Buneman nonlinear evolution: termination of the exponential growth and the setting up of electron trapping.
p. 184
"... after electron trapping begins, the electric field energy density oscillates at twice the ion plasma frequency".
Electric field and ions exchange energy. A quasi-standing wave type of situation.
Solar cycle?
"The role of the Buneman instability is to create large amplitude ion density perturbations at a wavelength that corresponds to the most unstable mode".
Simulations of DL: 1d or 2d. Plus purely electrostatic.
Setting up boundary conditions for both fields and particles.
"... periodic particle boundary conditions do not allow the full growth of double layers".

5.4 Double Layers in Current Filaments

p. 187
"... electric currents in cosmic plasmas often tend to flow in thin filaments or sheets ... the current density may reach comparatively high values ... the conditions for double layer formation in filaments are optimal".
DL in a filament cannot be considered as a 1d object, but should be treated as a 2d or 3d structure.
An example system.
NB. Inductance of the circuit is proportional to its length scale and u_0.
Beams of accelerated ions and electrons impose pressure on DL walls, so it can expand (or explode). And it may be a runaway process, since expansion makes potential drop higher.
If the thickness is small compared to width, DL can still be considered in 1d.
Comparison to a capacitor. In thin DL potential drop grows linearly with thickness, at very thick DL it is constant and depends on width.
p. 189
"... maximum potential drop of the relativistic double layer is a function of the total current rather than of the current density".
NB! "... magnetic energy stored in the current filament cannot be released faster than the Alfven travel time ... along the filament".
Again - solar cycles? What is Alfven travel time in terms of the heliosphere?
Hence "there is an upper limit to the power that can be supplied by the circuit". So maximum potential drop can only be reached if this power is enough (which is the case in most situations).

5.5 Basic Properties of Double Layers

Formation of a virtual cathode and virtual anode near the actual cathode and anode - results in DLs.
Same happens at side walls of the plasma chamber: electrons go into walls and ions are located in the plasma nearby, so DL forms with an outwards electric field to ensure ambipolar diffusion (no net charge transfer).
p. 190
Plasma of different composition, density and electron temperature - establishment of DLs to isolate these regions and make them internally homogeneous. E.g. DLs around BCs flowing between the ionosphere and higher magnetosphere.
Voltage over a DL is usually 5-10 times higher than thermal energy. If the DL separates plasmas from different sources, it may be 100-1000 times higher.
DLs exhibit noise due to broadening of electron spectrum. It produces scattering which is much more effective than the thermal one.
DL as a circuit element. Difficulty in space plasmas: circuit elements are not localised, but distributed in space.
"Every circuit that contains an inductance L is intrinsically explosive. The inductive energy ... can be tapped at any point of the circuit. Any interruption of the current I results in the transfer of the inductively stored energy to the point of interruption ... this point is most often a double layer".
Forms of energy release: acceleration of charged particles, generation of noise, localised heating and radiation.
p. 191
Oblique DL - its electric field is not parallel to magnetic field B. Thickness - around 20 Debye lengths.
Such DL will drift at velocities up to ion acoustic speed in the direction of the electron beam.

5.6 Examples of Cosmic Double Layers

DLs in magnetospheric BCs. Trapped electron and ion populations.
Differences of magnetospheric DLs and classic DLs: in the magnetosphere there is magnetic mirroring effect on the ionospheric side of the DL, which helps to trap particles there. Plus there are more particles available due to interaction with the ionosphere itself.
This leads to a significant extension of DL thickness (at least in simulations) and shows that "... the field aligned scale length of a double layer is controlled by the energy of the trapped particle populations". The DL thickness increases together with the trapped particle energy.
Oblique DLs - cause of ion conics and auroral kilometric radiation. Particle trajectories depend on relative strengths of E and B.
Around 1 GW of total power of auroral kilometric emissions. Efficiency of auroral arc energy transformation into radiation is ~ 0.5%.
Solar flare - irreversible release of energy in the form of 10-100 keV particles and heating to 1 eV in the chromosphere and 1000 eV in the corona, plus broad e/m emissions.
Speaking of irreversible - reconnection, if it did exist, should have been reversible, right? It's just a change in field line configuration after all.
Phases of a solar flare. Total energy of 10^22 to 10^25 J.
"Two-ribbon" flares, associated with filament destabilization.
Hyder flares?..
"Currents in the solar atmosphere are inferred from magnetic field measurements".
Vertical currents up to 10^11 A in the vicinity of sunspots.
Current density in the spots of about 10^(-3) A/m^2 -> flare is possible.
Corona and chromosphere: already with a 10^(-3) T field the magnetic pressure is much higher than kinetic pressure -> force-free FAC -> filamentation.
Filaments connecting sunspots through the corona (coronal loops). DL in a coronal loop can lead to a flare.
Calculation of the inductance of coronal loops. Order of magnitude: 1-10 H.
Currents around 10-1000 GA. DL with around 10^10 V potential drop.
During the impulsive phase hard X-rays are emitted from the foot of coronal loop, microwaves - from the top.
Neutron, gamma emissions.
DL is a good candidate to explain particle emissions from flares.
Galactic current of 10^20 A with a 10^17 V DL. If it's a 10 kpc series of DLs, the average field would be 1 mV/m.

6 Synchrotron Radiation

Various mechanisms of radiation in plasmas (tons of them!).
Free electrons moving in a magnetic field - three types of emission depending on energy: cyclotron (non-relativistic), magnetobremsstrahlung (mildly relativistic), synchrotron (highly relativistic).
"In astrophysics, nonthermal (nonequilibrium) cosmic radio emission is, in a majority of cases, synchrotron radiation".
Optical synchrotron radiation also exists.

6.1 Theory of Radiation from an Accelerated Charge

Near-field (induction) and far-field (radiation) zone. Far E and H fields fall off as 1/R, linearly depend on velocity and are orthogonal to radius vector.
p. 209
"... the electromagnetic fields generated by an accelerated electron give rise to a strong near-field which can be identified with the Biot-Savart law as well as weaker, but propagating, radiation fields".
Strong near-fields determine the morphology of the radiating region which is then observed far away through radiation fields. We'll mostly talk about them further.
Nonrelativistic electron - E field lies in the plane of acceleration and radius vector. Dipole approximation.
"For an ensemble of point charges the total radiation field is a linear superposition of the radiated field from each charge emitter".
p. 212
"When properly phased, an array of dipole moments will produce a pencil-like beam of radiation".
In the magnetic field: "If the motion is circular ... and if the electron is ultra-relativistic, the electron will be shown to radiate only in the plane of the orbit. An observer located in the plane of rotation would see pulses of radiation corresponding to those instants when the electron is moving precisely towards the observer".
p. 217
"For an ultrarelativistc electron the radiation is very nearly in the direction of its instantaneous motion".
p. 219
Analogy with an antenna -> definition of gain.
Spectrum of the emissions (it's complicated!).

6.2 Field Polarization

Two modes of propagation: ordinary (E parallel to B) and extraordinary (E perpendicular to B).
Ordinary wave only exists when there is a parallel (to B) component of velocity. It is linearly polarized along B. Extraordinary wave has an elliptical polarization in the plane transverse to B.
Longitudinal plasma waves are also produced.
Polarization at arbitrary angles.

6.3 Radiation from an Ensemble of Electrons

Just a lot of technical stuff.

6.4 Synchrotron Radiation from Z Pinches

"... self-consistent magnetic confinement or compression against the expansion due to thermal pressure".
Particles drift with the current, but also rotate around magnetic field lines -> synchrotron radiation is emitted.
"Manifestations of the pinch effect appear to the laboratory observer as a rapidly occurring phenomena".
Speaking about scaling of time in plasmas.
Lab high-current discharges (10^15 A/m^2) -> wide spectrum of emissions, from microwave to X-ray.
Solar microwave bursts - synchrotron radiation from electrons accelerated in solar flares. Similar emissions are simulated e.g. at PHERMEX facility.
p. 232
Experimental setups with exploding wires. Times of 100 ns, magnetic fields up to kT.
More than one wire or injection of gas between the electrodes -> lots of X-ray emissions.
Three types of emissions from exploding pinches: 1) hot plasma thermal; 2) cool plasma thermal; 3) non-thermal (synchrotron).
Nonthermal X-ray emissions can last longer than the pinch itself.
p. 234
"... intense X-rays originate from hotspots along the plasma".
Exploding wires have the densest X-ray energy production known to man.

6.5 Particle-in-Cell Simulation of Synchrotron Processes

When the current columns approach to a distance where repulsion becomes equal to attraction, a burst of radiation happens.
Interaction of two pinches at higher parallel (rather than perpendicular to B) particle velocity leads to double emission lobes in the direction of B.
Lobes correspond to currents themselves, morphed into C-shaped from the initial circular ones (in cross section). Then they start rotating.
Microwave bursts.
Initially acceleration is highest at the outer segment of the lobes. Then - at the inner. This forms a "butterfly" pattern.

6.6 Synchrotron Radiation from Cosmic Sources

"Most cosmological objects, including galaxies, are emitters of synchrotron radiation, over a relatively wide band encompassing radio frequencies through optical frequencies".
Ratio of radio power of galaxies to their optical emissions ranges from 10^(-6) to 1. The sizes of radio emitting regions vary a lot as well.
p. 243
"The nuclear component of our galaxy ... is a miniature replication of a classic double radio galaxy".
"... what is observed from any radio source is synchrotron radiation that requires only relativistic electrons in the presence of a magnetic field".
Cygnus A - two radio lobes on the opposite sides of an elliptical galaxy. Simulation from two filaments shows decent agreement with the observed parameters. Electric fields in a filament of about 12 mV/m.
Comparison of simulated radio spectrum to Cygnus A spectrum. Good agreement, except after 1 GHz, where neglect of runaway electrons in simulation starts playing a role.
Jets from various objects.
p. 248
NB. Fading of the M87 jet over decades.
p. 249
"Whether or not an observer can see synchrotron radiation depends on his orientation with respect to the polarity of the electric field".
E.g. an observer on the filament axis, but in the opposite direction from electron motion (or out of the gain pattern in general) would only see thermal radiaton.
NB. "Rather than being core ejected material, the simulated "jet" is a sheet electron beam accelerating out of the plane of the page".
"... there is little to distinguish between a double radio galaxy and a radio quasar".
Around 70% of radio quasars and 80% of radio galaxies are interacting objects, with median separations of 20 and 12 kpc correspondingly. Approximately 30% of them have elliptical galaxies between the two lobes (no spiral galaxies though).
All quasars have strong nuclear cores while double radio galaxies have very weak cores.
Time period of quasar variability - around 1 year.
"From the point of view of spectroscopy, quasars cannot be distinguished from Seyfert galaxies".
p. 252
Description of stages of quasar evolution.
p. 255
"Like the aurora and solar flares, X-ray and gamma ray sources are likely to have their radiative energies supplied by electrical currents".

7 Transport of Cosmic Radiation

"... a complication arises when the propagation medium is no longer free space, but instead is plasma".
"... the properties of the radiation are altered".
Modification of the wavelength-frequency relation that now depends on tons of plasma parameters. Plus possible nonlinear effects.

7.1 Energy Transport in Plasma

p. 261
Energy conservation and some equations.
Propagation of e/m waves in plasma.
Group velocity - velocity at which energy propagates.
p. 265
Propagation of whistler waves - frequencies of 300 Hz to 30 kHz. They are generated by lightning and propagate from one hemisphere to another via magnetic field lines.
We get a descending tone due to dependence of group velocity in the ionosphere on frequency.

7.2 Applications of Geometrical Optics

We assume that the medium changes on much larger scale than wavelength and consider e/m waves as linear (noninteracting) rays or bundles. Although in plasma there exist mode conversion processes where the rays do interact.
Spectral flux: both the e/m flux and flux of particles.
p. 270
Bending of light rays in plasma.
In real plasmas the basic assumption of geometric optics is often violated (plasma changes a lot on short scales).
Moreover, refraction index may abruptly change even if density and magnetization remain relatively constant.
NB. There is no Brewster angle in cosmic plasmas.
Collisions of plasma particles may impact wave propagation significantly, yet it is ignored in geometric optics approach.
Limit cases when plasma absorbs nothing or everything.

7.3 Black Body Radiation

Planck's equation (given without derivation), Stefan's law, Wien's law.
Limits for long and short waves.

7.4 Source Function and Kirchoff's Law

Kirchoff's law for anisotropic nonthermal plasma (given without derivation).
"... when the particle distribution is Maxwellian, the source function equals the vacuum black-body intensity".
"... fictitious temperature ... depends on the particle distribution, the frequency of observation, and the direction of propagation".
p. 277
The book focuses on the limit where photon energy is much lower than plasma particle energy.

7.5 Self Absorption by Plasma Filaments

Cosmic currents emit synchrotron radiation. But how much of it they absorb themselves?
It seems the more filaments you get, the less absorption there actually is in total, since they also emit.
"... the radiation intensity increased ... because of each additional current source".
p. 280
Calculated spectrum of the emitted radiation.
Smearing of the lines at higher frequencies due to relativistic effects. Eventually we're approaching a continuous spectrum.
NB. With 10^31 filaments one can get blackbody spectrum.
CMB?

7.6 Large-Scale, Random Magnetic Field Approximation

"... cosmic magnetic fields often present a tangled, almost random appearance on the size scale of interest for synchrotron radiation".
"... a laboratory plasma where current filaments generally flow in a preferred direction but flare, twist, and kink to produce a total magnetic field which, for all practical purposes, is "random".
We assume they're uniform with respect to electron gyroradius but random with respect to the size of a filament.
So much for neat Scott-type filament models.
"In a completely random magnetic field, polarization is absent".

7.7 Anisotropic Distribution of Velocities

One needs to take momentum conservation into account.

8 Critical Ionization Effect in Interstellar Clouds

8.1 Critical Ionization Velocity

When plasma and neutral gas move relative to each other, neutrals would ionize after the relative velocity is higher than some critical one (which depends on the element's mass and ionization potential) - critical ionization velocity (CIV).
Alfven's model of element separation in early Solar System.

8.2 CIV Process in Laboratory Experiments

Experimentally established: the process doesn't come from simple collisions but rather follows from field strength independent plasma instability which transfers energy from fast ions to background electrons. Thus we arrive at non-Maxwellian electron velocity distribution (with an excess of fast electrons), and the faster electrons then ionize the neutrals.
The result sounds like the solar wind!
It follows from the two stream instability which can be created by a longitudinal electric field in a double layer.
So indeed, pretty much a Dreicer effect in a double layer.
CIV is actually a detrimental effect for plasma thrusters.

8.3 CIV Process in Interstellar Space

There is no agreement on whether it naturally occurs in space.
But it might be the case thanks to Marklund convection.
ExB forces produce radial (inward) drift of plasma into the filament, and the equilibrium is established where it is balanced by outward diffusion of recombined neutral particles.
Temperature gradient (e.g. due to radiative losses) -> hollow cylinders of matter are formed, with sorting of the elements according to their ionization potential (the lowest inside, the highest outside).
What if the temperature gradient would be inverted though?
p. 292
"... while the magnetic flux tubes themselves are not directly observable, their existence in the interstellar medium would require both the presence of filamentary structures and a signature of the CIV process".
The first is there. The second is the point of this chapter.
Detailed description of the process where Marklund convection produces fast electrons (through two stream instability, e.g. an axial double layer in the filament) which later participate in ionization.
"... ionization of the neutrals by the fast electrons proceeds effectively by forming a positive feedback loop until thermal saturation ... occurs. It is this thermal signature which manifests itself in HI linewidth spectra".
Bands of elements with characteristic CIV and spectra.
The most ubiquitous are H and He. H has CIV of 51 km/s. This is accessible e.g. in a field-aligned interstellar current with a 25 uV/m longitudinal field.
Unlikely to be seen in neutral hydrogen lines, as it would be ionized.
The CIV thermal signature of He (velocity of 34 km/s) can be seen in HI, on the other hand.
Two other bands with CIV of 13.7 km/s and 6.5 km/s. Their signatures should be seen progressively closer to the axis of the filament.
Third band should be the closest to the axis, where dusty plasma forms.

8.4 Neutral Hydrogen Emission Line Data

Some history and pictures showing filaments.

8.5 Relationship Between Observed HI Emission and CIV Data

Line widths of thermal components (in HI) of CIV signatures of three element bands.
He (first band) component is seen everywhere, second band is seen in filaments, third band is seen inside second band, though sometimes on its own too. And it is associated with dust and molecules (not always).
p. 297
"What the data ... show is that the signature of the CIV phenomenon appears to manifest itself in the motion of HI atoms in interstellar space".

9 Neutral Hydrogen Filaments and Dynamics of Galactic Bennett Pinches

9.1 Interstellar Filaments

p. 299
"... filamentary nature of the diffuse interstellar neutral hydrogen ... validates the hypothesis ... that the existence and stability of galactic filaments is dependent on large-scale cosmic currents".
Not necessarily. Zel'dovich has shown long ago how gravitation can lead to the formation of string-like structures as well.
Wave features observed in filaments.
NB. Verschuur's map shows that all of the HI clouds are associated with filaments and usually appear where the latter change their orientation, as if clouds were defining kinks in the filaments. Therefore, such clouds may be a geometric illusion caused by twisting of the filament towards us. Same happens in lab experiments and simulations - it is called a heteromac.
"Heteromacs, in space, are the coming together of adjacent field aligned currents ... and their subsequent coiling into helices".
"During intense current bursts that may last several centuries, they are visible by the white-light synchrotron light they emit" - at least that's what the modeling shows.
Then the current diminishes and only the dim "cloud" remains. Stronger current may resume again and it may even do so cyclically in a "sawtooth" pattern, as happens in the lab (mentioning of Alfven).
That's the healthy person's version of externally driven cataclysm.
p. 302
"... the brightest features correspond to filament overlap or where the filament twists into the line-of-sight".
Problems with detecting magnetic fields in HI clouds through Zeeman splitting.
"This does not mean that such fields don't exist; only that the technology to detect them does not exist yet".

9.2 Interstellar Filaments as Tracers of Current Flow

Neutral HI is linked to ionized plasma and can therefore be used to see its motion.
p. 306
Estimations of the pressure inside and outside of the filament can help determine its size (and distance).
p. 307
Filament characteristics. For this particular one gravity plays no role in controlling the equilibrium.
Axial current of 10^13 A and toroidal magnetic fields of 0.5 nT.
"... physics of the generalized Bennett pinch applies to gaseous interstellar filaments".
"The role of large-scale currents may be very important in defining interstellar structure".
HI structures demonstrate clear filamentary nature, but it may be overlooked by looking at low resolution maps.

10 Particle-in-Cell Simulation of Cosmic Plasma

10.1 "In Situ" Observation of Cosmic Plasmas via Computer Simulation

No chance for true in situ -> use simulations.

10.2 History of Electromagnetic Particle-in-Cell Simulation

Three-body problem etc. People disliked numerical methods. Only in XX century they really started to become popular.
NB. Hartree built a mechanical calculator machine to compute atomic energy levels.
p. 313
Invention of magnetron and attempts of Hartree's team to explain how it worked (by numerical simulation).
In 1950s more plasma simulations emerged.
"... the general character of plasmas can often be found by studying the collective behavior of collisionless plasmas at wavelengths longer than the Debye length".
Harlow - term "particle-in-cell".

10.3 Laws of Plasma Physics

"We know with certainty the precise and simple laws of nature that govern the particles and fields in plasmas".
What an arrogance!
Yet we can't describe much of anything anyway.
"The message to be presented here is that one might try to let the computer take us all the way from the basic laws to their macroscopic manifestations".
So much for EU hate of modeling.

10.4 Multidimensional Particle-in-Cell Simulation

From 1D through 1.5D etc. to 3D (half dimensions <-> extra velocities).
Trivial difficulty - need more particles. Each new dimension - 2 orders of magnitude more.
But "... relatively few samples can often give very good statistics".
"... in all simulations, time must be discretized". In many of them space should be as well.
Grid should be fine enough to resolve the Debye length.
"Aliassing" - stroboscopic effect of high frequencies masquerading as low frequencies.
Complex field vector combining electric and magnetic ones. Fourier transforms.
Interpolation in the mesh - quadratic and cubic ones are good, but expensive. Thus linear is the one most commonly used.

10.5 Techniques for Solution

Some codes even properly implement relativistic limitations.

10.6 Issues in Simulating Cosmic Phenomena

Fourier methods imply infinite repetition, which is inapplicable to modeling an isolated plasma structure. So as a boundary condition we may choose a certain radius at which particles simply "disappear".
"The most elusive boundary problem for space plasmas is the radiation condition".
Time compression is often necessary. It can be achieved e.g. by artificially lowering the mass of ions, setting a very high temperature (so particles move very fast) or exaggerating the electric field.
Not too many particles -> collisions become much more important. To deal with this, finite-size particle method is used.
NB. Empirical estimation of collisional frequency in 2D systems.
Modeling the collisions with neutrals -> Monte-Carlo methods.

10.7 Gravitation

How to describe a transition between plasma and neutral matter.

10.8 Scaling Laws

Scaling requires evaluation of various parameters. Scaling down reduces the resolution.

10.9 Data Management

A real problem for 3D simulations. We need around 2^24 particles, each having 6 parameters (position and velocity). Plus a ton of field parameters.

11 Further Developments in Plasma Simulation

11.1 Updates in Three-Dimensional, Electromagnetic Particle Simulation Models

Features of the "new" TRISTAN code.

11.2 Astrophysical Plasma and Plasma Cosmology

TRISTAN code was used in studying the formation of galaxies and some other applications.

11.3 Advancement in Particle/Field Methodology

Parallel computation. Local integration of differential equations vs. global procedures like Fourier transform.
Example of the magnetosphere-solar wind simulation.

11.4 Simulation Results

Simulating the difference between oppositely oriented Earth's magnetic field.
Peratt makes the point that some ancient sources are consistent with the opposite polarity (than the current one), which he recognizes as "the North Pole down and the South Pole up". Yet this is exactly the modern configuration. Either he is unaware of that, or maybe I understand him incorrectly, since the phrasing is somewhat ambiguous. The actual picture of his simulation shows the opposite polarity indeed.
Map of currents in this simulation. Ion density etc. Magnetopause corresponds to sudden change in magnetic field strength.
Buneman: "Programming in Fortran is like playing a piano wearing boxing gloves".

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paladin17
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Re: Peratt's "Physics of the Plasma Universe"

Unread post by paladin17 » Mon Feb 15, 2021 12:51 pm

12 Dynamics of Field-Aligned Currents in the Laboratory, Aurorae, and Galactic Space

12.1 Formation and Dynamics of Laboratory Currents

Breaking up of electron beam going parallel to magnetic field into vortex-like structures (diocotron instability). Most pronounced in hollow cylindrical beams. Same happens in proton beams, but not as noticeable due to higher mass.
p. 343
"For plasmas there is a neutral force region where the filaments do not merge but rather start a rotational motion around each other to form a vortex-like geometry".
It is observed in the lab.
Disintegration of a hollow cylindrical beam into separate filaments and then their partial merging.
Twisting and pinching and then untwisting again.
A lot of pictures here.
Example of a helical pinch where closer examination reveals fine structure - it's made of 6 separate filaments.
NB. "... the most common pairing or tripling, as determined from a large collection of observations is 56 (by far the most common)".
But his own graph suggests that the most common one is 28 - ?
The full set of numbers of filaments is: 4, 6, 7, 8, 16, 20, 28, 30, 33, 39, 41, 47, 49, 56, 112, 224.
It would be cool to see a table with data instead of a graph.

12.2 Dense Plasma Focus (DPF)

Powerful discharge through two coaxial electrodes. Plasma sheath accelerates to the ends of electrodes by Ampere's force. After the exit from the tube the inner part of the discharge collapses onto the axis in the form of a columnar pinch (focus). The outer sheath (penumbra) forms a bunch of filaments.
Usually the inner electrode is an anode.
p. 348
"With regard to the DPF, the usual number of filaments formed in the penumbra or "chalice" at the pinch is either 56 or 56-paired filaments".
Some studies "report about 60 filaments".

12.3 Evolution of Plasma Filaments via the Biot-Savart Force

Seems like an overlooked repeat of one of the previous subsections.

12.4 Birkeland's Terrella Experiments

Peratt praises Birkeland for this and that.
Description of the experiment. Earth is made of brass covered with phosphorescent oil. Inside is an electromagnet.
"... his experimental parameters, when scaled, were remarkably close to what is observed and measured around Earth today".
"Altogether, Birkeland constructed 17 terrellas. These ranged in size from 2-70 cm in diameter".
"His largest current generator could deliver 300 mA at 20 kV".
By adjusting the parameters one could make different parts of the circuit visible.
"Densitometer scans across the Bennett-constrained currents in his photographs show approximately 56 filaments, many in pairs".
That might be a confirmation bias. E.g. if you take the actual number and say "it was actually 56, it's just that 40 of them merged in pairs, so we only get 36 in the end".

12.5 Birkeland's Trips to Egypt

He went there in 1910 and then in 1913 settled there for 3 years. He wanted to study zodiacal light.
"Birkeland had spent much effort preparing a treatise that reportedly was nearly as complete as his earlier treatises".
Peratt says that Birkeland must have noticed that Egypt is in the area where the atmospheric currents should flow (comparing Earth to terrella).
Then he decided to return home but he couldn't do it directly due to WWI, so he went through Japan, where he died.
And, of course, his new treatise was lost in the process.

12.6 Macro-Terrella Experiments

"A relevant experiment would be a terrella lowered down-hole with concomitant viewing enclosure and fast diagnostics, subjected to the fluence of a typical nuclear detonation".
RIP, SAFIRE.
"This would show current filaments flowing systematically over the surface ... However, cessation of nuclear testing between the United States and Russia in 1993 now precludes this area of research".

12.7 Properties of a Strong Aurora

Alfven's estimate of current strength: 7 MA. For 56 filaments it would mean 125 kA per each, so they would stay pinched.
If we'd have a GA strong current, its magnetic field would shift the aurora. The plasma would form a "... thin but dense sheath or plasma column".
This column would be pinched and would demonstrate all the Z-pinch instabilities. Plus radiation: X-ray and visible synchrotron.

12.8 Temporal Occurrence and Properties of Intense Auroras

Similar (to the given above) description by Gold.
"According to Gold, a very intense aurora might be expected to occur every several thousand of years or even every 10000 years".
Hello, Davidson.
1000 times increase in auroral strength - 1.25 MA per filament (if there were 56 of them).
"This is what was seen in antiquity, often carved on granite or recorded in other ways".

12.9 Carrington Event

Type A aurora, blood or deep crimson red, so bright one could read under it.
Some descriptions.
"... historically, such accounts are found nearly every few centuries; stronger events every century, and cataclysmic events every several millenia".
Reconstruction of the current pattern with 56 filaments.
p. 357
"Historical accounts suggest that intense aurora differs from concurrent aurora in several aspects".

12.10 THEMIS Mission

Five satellites at 40000 km orbit.
"... discovery of large holes in the Earth's magnetosphere explains an anomaly in the global distribution of petroglyphs on our planet".
Peratt promotes here his own work, stating that petroglyphs are MHD configurations. But he almost makes it seem like it was THEMIS team that made the connection, which is doubtful to me. E.g. "THEMIS researchers have also uncovered what appears to be the earliest records of what was seen in antiquity regarding aurora". Etc.
p. 358
"The symmetry of the two polar currents suggest that full 360 deg. satellite coverage might reveal the existence of six currents".

13 Plasma Astrophysics

(Quote from Alfven)
"... there appears to be no reason why known basic laws, formulated in the laboratory, should not hold just as well at the astrophysical and cosmological scale".

13.1 Cosmic Triple Jump

Alfven's idea of scaling.
"... dimensionless parameters were valid regardless of whether the plasma was measured in microns or gigaparsecs".
Three 10^9 jumps from laboratory sizes to the Hubble distance.
And my double extension of it downwards.

13.2 Near-Earth Plasma Astrophysics

General direction of westward motion of "Earth-current" filaments.
"During intense events, the current flow is true north-south, or for intense synchrotron light emitting relativistic electrons, towards true north from geophysical south".
Geoglyphs in South America. Sudden change in line directions - caused by the current geometry, as seen from the ground and later depicted in a geoglyph.
"These [currents] were seen as white light on the ground, not moving for perhaps centuries".
So a century long intense aurora? That's a strong statement.
The method of optically stimulated luminescence dates Peruvian geoglyphs as 56 kyr old.
Mandalas near Palpa.
"Concentric cairns that number 14, 28, 56, 112 and 224 have been used in their construction".
Similar geometry of Stonehenge.
"The 16 rays are typical of rayed recordings in South America. In comparison, one of the mandalas has 224 (4x56) outer cairns whereas Stonehenge has 56 Aubrey holes on the outer periphery. The former corresponds to an age where the plasma filaments have not yet merged to 56 or lesser numbers".
It would be great to know what kind of numbers are characteristic of plasmoids - possible implications for alternative nuclear physics etc.
"Y and Z rings of Stonehenge, never circular, show the onset of a later time diocotron instability, that is, Buneman's chasing instability".
"Many thousands of man-made objects, while of widely varying sizes, replicate the Stonehenge pattern, all recordings of intense, focused, synchrotron light skyward".

13.3 Cosmic Nebula and Interstellar Clouds

Comparison of a laboratory helical Z-pinch to a helical molecular cloud at the galactic center.
28 filaments seen in supernova 1987A. Plasma sheet hyperboloid with a wheel lemniscoid at the center pinch.

13.4 Galaxies in Plasma Cosmic Space

Double radio galaxies. Sizes up to Mpc, densities around 10^(-3) cm^(-3) and 10 nT magnetic fields.
"The radiation produced by two plasma filaments in proximity replicate both the isophotal and power spectra from double radio galaxies".
The question still remains though: why are the galaxies "flat" if they are born from merging of two linear "wires".
Only the time factor in laboratory simulation should scale accordingly, i.e. microseconds instead of millions of years.
"One now has the ability to forecast what a double radio galaxy will be like millions of years into the future".
"... radio galaxy 3C 315 is starting a rotation that will evolve into a spiral galaxy, i.e. NGC 4151".
Galactic magnetic fields: up to nT.
Comparison of a spiral galaxy to the simulation. Two peaks of neutral hydrogen emission correspond to the original filaments.
What if 3 filaments merge?
"The hydrogen deficient center is the remnant of an older elliptical galaxy formed midway between the filaments, in the magnetic null".

Appendix A. Transmission Lines

A.1 Cosmic Filaments as Transmission Lines

Plasma forms filaments that can transport the energy across large distances.
Transmission line - two or more conducting paths. Not necessarily parallel, but for simplicity we assume they are.
Hypothesis of homogeneity: conductor and dielectric properties are the same everywhere along the line.
We need at least 2 groups of at least 1 conductor each (forward and return conductors), and we assume that the time of signal propagation between them (perpendicular to the line) is negligible. This immediately leads to the conservation of current (forward is the same as return - in strength).
Then we may arrive at a system of partial differential equations with two variables (time and distance along the line).

A.2 Definition of the State of the Line at a Point

Expression of the electric potential at a point on the line.

A.3 Primary Parameters

Resistance and conductance per unit length depend on frequency (due to skin effects, dielectric losses etc.), but we will consider them as constant.
In the same way we introduce self-inductance per unit length and transverse conductance (to account for current flowing perpendicular to the line), as well as capacitance.

A.4 General Equations

Derivation of the telegrapher's equation.
Derivation for a lossless line. Propagation constant and characteristic resistance.

A.5 Heaviside's Operational Calculus (The Laplace Transform)

Calculating the voltage between two conductors and the current in them. Using the Laplace transforms of voltage and current.
Propagation function.

A.6 Characteristic Impedance

The parameter is related to the physical properties of the line (its dimensions and conductive/dielectric properties) and is a function of time.

A.7 Reflection Coefficients

To get a complete solution one needs to set boundary conditions at the end of the line.
"In space plasmas, the end of a transmission line may be a planetary ionosphere or wherever else the conductivity between conducting paths becomes large".
E.g. an arc discharge across a dielectric.

A.8 Time-Domain Reflectometry

Calculating the waveforms in a lossless line by taking an inverse Laplace transform.
Good agreement with observations in the lab.
An example with a planetary ionosphere-magnetosphere transmission line. Calculation with specific parameters (source perturbation of -40 kV, its length 250 ms, source impedance of 2 ohms, line impedance 0.4 ohms, load - ionosphere - impedance of 0.1 ohms, line length 6*10^8 m). Current and voltage readings that the spacecraft will receive in this case. With such readings available "... an accurate determination of the source and ionospheric impedance can be made". Even better - if we have two probes at different locations.
p. 382
NB. "The north and south pole transmission lines need not be symmetric".

Appendix B. Polarization of Electromagnetic Waves in Plasma

Wave equation can be obtained from Maxwell/Hertz/Heaviside.
Matrix elements of the relative dielectric tensor in cold plasma. Only a first-order approximation.
Refractive index - ratio of light to phase velocity.
Plot of phase velocity surfaces of electromagnetic waves.
Left- and right-hand circularly polarized waves (LHCP and RHCP).
Give it away, give it away now!
Extraordinary and ordinary waves. Extraordinary mode is affected by external magnetic field, while the ordinary one is not.
Clemmow-Mullaly-Allis (CMA) diagram.
Faraday rotation of polarized waves.

Appendix C. Dusty and Grain Plasmas

General equation of motion and subdivision of particles into 4 classes depending on their size (very small ones - less than 100 nm - obey electromagnetism only, very large ones - larger than kilometer - obey gravitation only).
p. 392
"The transition of plasma into stars involves the formation of dusty plasma, the sedimentation of the dust into grains, the formation of stellesimals, and then the collapse into a stellar state".

C.1 Dusty Plasma

Plasmas that contain solid matter in the form of very small dust grains. The dust is electrically charged and may have orders of magnitude different temperature than the plasma around it. E.g. 10 K dust + 100 K molecules + 10^3 ions + 10^4 electrons.
"Normally, the potential of a dust grain may be 1-10 V, positive or negative".
But relativistic electron beams may charge it up to kV.

C.2 Grain Plasma

Dust that accreted into larger grains.
Some assumptions and equations derived from them. E.g. one may arrive at the formation of microgram mass grains.

Appendix D. Some Useful Units and Constants

Nothing else here.

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Brigit
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Re: Peratt's "Physics of the Plasma Universe"

Unread post by Brigit » Mon Feb 15, 2021 6:38 pm

There could be an element of truth in the charge that Dr. Anthony Peratt has written a text book on the physics of the plasma universe, and included the mathematical equations used to reflect the relations between physical variables.
“Oh for shame, how these mortals put the blame upon us gods, for they say evils come from us, when it is they rather who by their own recklessness win sorrow beyond what is given…”
~Homer

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JP Michael
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Re: Peratt's "Physics of the Plasma Universe"

Unread post by JP Michael » Tue Feb 16, 2021 9:14 am

Thanks Eugene! Will sift through this over the coming days.

dren
Posts: 36
Joined: Fri Sep 06, 2019 2:25 pm

Re: Peratt's "Physics of the Plasma Universe"

Unread post by dren » Thu Feb 18, 2021 3:51 pm

Thanks! I will be returning to this on occasion.

I also read several of your blog posts and enjoyed them. Russian seems to translate well to English in google translator.

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