Magnetic Reconnection

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Re: Magnetic Reconnection

Unread postby Zyxzevn » Sat Dec 08, 2018 9:27 am

Experiments at PPPL show remarkable "agreement" with satellite sightings
https://www.pppl.gov/news/2018/12/exper ... -sightings

Experiments at PPPL show..:
"The experiments demonstrated that electron current flows perpendicular, and not parallel as once thought, to the magnetic field." Same with ions.

Plasma physics is 90 degrees off!! That is almost as wrong as you can get it.
Exactly as maxwell and EU predicted.

Can we finally put magnetic reconnection in the trash?
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Re: Magnetic Reconnection

Unread postby seasmith » Sat Dec 08, 2018 3:19 pm

Zyxzevn wrote:Experiments at PPPL show remarkable "agreement" with satellite sightings
https://www.pppl.gov/news/2018/12/exper ... -sightings

Experiments at PPPL show..:
"The experiments demonstrated that electron current flows perpendicular, and not parallel as once thought, to the magnetic field." Same with ions.

Plasma physics is 90 degrees off!! That is almost as wrong as you can get it.
Exactly as maxwell and EU predicted.



Image
[Magnetic Lens]

You know what an electron microscope is.
Is electron flow parallel or perpendicular to magnetic vector lines here ?

It is simply a matter of scale, and if you are looking at micro particle rotation, or macro-scale electric current flow.
btw, so-called "electrons" were posited by J J Thompson, long after Maxwell's "Treatise..."

The article is meant to tease ...
;)
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Re: Magnetic Reconnection

Unread postby Zyxzevn » Sat Dec 08, 2018 4:19 pm

seasmith wrote:You know what an electron microscope is.

Electrons always go from - to +.
(assuming a reasonably static magnetic field)

This is even true for the the electron-microscope.
Or for the magnetic confinement reactor that I described in a post above.

In this specialized instrument, where they made a very strong magnetic
field to focus the electron-beam, the electrons still go from + to -
To focus, the field has to be stronger on the outside,
so the electrons move away from the outside. This can only be accomplished
with artificial objects and has not been observed with astronomical objects.

So this has nothing to do with the astronomy world where there are
no focussing fields.

In the imaginary world of astronomers the electrons can even move without electrical
fields or charges..

That is what magnetic reconnection is all about, imaginary things colliding to
create an imaginary world without electrical fields.
The world of mainstream astronomy.

In the experiments these "scientists" are a full 90 degrees wrong, as they assumed that the electrons
would follow the magnetic field lines.
But instead, the electrons follow electric fields, and are affected by the well known Hall-effect
if there is a magnetic field present.

Back to the sun, this also means that the solar-ropes are not following magnetic field lines.
They are going from - to +, partially bent by magnetic fields.
This again means that the start and end of the ropes are electrically charged.
And this means that the sunspots are electrically charged regions...
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Re: Magnetic Reconnection

Unread postby seasmith » Sat Dec 08, 2018 5:09 pm

Zyxzevin wrote:
"In this specialized instrument, where they made a very strong magnetic
field to focus the electron-beam, the electrons still go from + to -
To focus, the field has to be stronger on the outside,
so the electrons move away from the outside. This can only be accomplished
with artificial objects and has not been observed with astronomical objects.

Now you are conflating direction with parallel & perpendicular. You can go up or down the highway, but your'e still traveling parallel to the road.

So this has nothing to do with the astronomy world where there are
no focussing fields.

Oh really ?

That is what magnetic reconnection is all about, imaginary things colliding to
create an imaginary world without electrical fields.

I pointed out earlier, think it was in this thread, that "reconnection" (like "lines of force") are red herrings for many in the EU camp. Linear and 2D perspectives are being misapplied to 3D-over-T phenomena. It's become almost an EU dogma.

In the experiments these "scientists" are a full 90 degrees wrong, as they assumed that the electrons
would follow the magnetic field lines.
But instead, the electrons follow electric fields, and are affected by the well known Hall-effect
if there is a magnetic field present.

Electrons do not "follow" electric fields, they are Driven by them.
The Hall effect is a micro-scale effect.


Back to the sun, ... "

Some earlier posts invoking a perception of Zeeman and Stark effects were unconvincing at best.
Charge manifestations and dynamics can be present at levels much more fundamental than hot-cold-fast-slow 'electrons', and the whole zoo of named anions.
But no worries mate, just look at how MS science attempts to define "elementary charge", if you want to see a perfect tautology.

;)
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Re: Magnetic Reconnection

Unread postby Zyxzevn » Sat Dec 08, 2018 6:36 pm

seasmith wrote:Zyxzevin wrote:
"In this specialized instrument, where they made a very strong magnetic
field to focus the electron-beam, the electrons still go from + to -
To focus, the field has to be stronger on the outside,
so the electrons move away from the outside. This can only be accomplished
with artificial objects and has not been observed with astronomical objects.

Now you are conflating direction with parallel & perpendicular. You can go up or down the highway, but your'e still traveling parallel to the road.


Only an artificial system can create a magnetic field where the magnetic field
and electric field are parallel.
That is because you need to create two perpendicular electric currents
to create a situation in which electrons follow the magnetic field lines exactly.
Natural systems try to undo any magnetic fields that are created.
In artificial systems we can also use permanent magnets, which must of course
below curie-temperature.

So this has nothing to do with the astronomy world where there are
no focussing fields.

Oh really ?


I think that a focussing field needs a stronger magnetic field on the outside and weaker magnetic
field on the inside.
That is because the spirals will then bend towards the centre.
If the magnetic field is stronger on the inside, like in a natural configuration,
the electrons will spiral outwards.
The electrons will still move from - to +.
The magnetic field just gives a Hall-effect, which is well known
and well tested in laboratories.

That is what magnetic reconnection is all about, imaginary things colliding to
create an imaginary world without electrical fields.

I pointed out earlier, think it was in this thread, that "reconnection" (like "lines of force") are red herrings for many in the EU camp. Linear and 2D perspectives are being misapplied to 3D-over-T phenomena. It's become almost an EU dogma.

I know the 3D version.
It is the hall-effect.
A well tested and well-known phenomenon.

The version that you talk about is related to particle accelerators,
that are driven by strong electric fields.
They use special magnetic fields to focus the particle-bundle.

But if you apply that in normal moving plasma, or plasma currents,
you can see that the magnetic fields cause magnetic breaking and an hall-effect.
That is what all the videos on plasma show.

If "currents" of multiple spiralling electrons come together, they
start interfering with each other.
This is the essence of magnetic breaking, which you also see
when you drop a magnet into a copper pipe.

You can actually see the electrons that are doing the breaking, as they
show as a cloud/puff in the plasma.

In the experiments these "scientists" are a full 90 degrees wrong, as they assumed that the electrons
would follow the magnetic field lines.
But instead, the electrons follow electric fields, and are affected by the well known Hall-effect
if there is a magnetic field present.

Electrons do not "follow" electric fields, they are Driven by them.
The Hall effect is a micro-scale effect.



I've done my electronics study:
Even with magnetic fields, however big, electrons go from - to +.
The Hall effect can be as large as the magnetic field.
Like earth-size or sun-size.
There is no limit to it.

What you are probably thinking of is the Quantum Hall effect.
But even this is still visible on human scales, as the quantized Hall effect
causes magnets to float in air when there is superconductivity.
This is called: quantum locking.
The quantization creates places of stability that can hold the object in place
for a long time.


Back to the sun, ... "

[color=#0000BF]Some earlier posts invoking a perception of Zeeman and Stark effects were unconvincing at best.
Charge manifestations and dynamics can be present at levels much more fundamental than hot-cold-fast-slow 'electrons', and the whole zoo of named anions.
;)


Seriously, I do not think there is much Zeeman effect on the Sun.
I think most of it is Stark effect, with just a bit of Zeeman effect caused by the visible currents.

If there is any other evidence of magnetic fields on the sun and their configuration,
please let me know.

Now what can cause electric fields on the sun's surface?

The charged regions can be caused by nuclear explosions under the surface, as they are similar to EMP bombs.
Or maybe there is some nuclear reaction that causes charge separation, but we do not understand well yet.

The electric separate charged regions float from inside the sun towards the surface, this can cause
strengthening of the electrical voltage like in a vanderwaals apparatus.
When the charged material reach the plasma surface, they start forming electrical
currents towards the other charged material.
These currents form the well-known plasma-ropes that we see on the sun.

The charge material also turns dark due to the free electrons that are released
at the surface. These absorb the light as is visible in electro-chemical experiments (see above).

If the solar ropes encounter each other, it is possible that we get an electrical short-cut,
and a solar flare can happen.
A very strong current can also be expelled due to the rail-gun effect.
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Re: Magnetic Reconnection

Unread postby seasmith » Sat Dec 08, 2018 8:51 pm

Zyxzevin wrote:
I've done my electronics study:
Even with magnetic fields, however big, electrons go from - to +.
The Hall effect can be as large as the magnetic field.
Like earth-size or sun-size.
There is no limit to it.


I think you mean Lorentz
`
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Re: Magnetic Reconnection

Unread postby Zyxzevn » Thu Apr 18, 2019 6:21 pm

From a study of a very complicated time series of dark spots.

Image
click to enlarge


Image
click to enlarge


The red and blue on the graph show the strengths of the electrical fields. These are caused by the charged areas. The charged areas connect with each other via the conducting plasma, and this forms double layers. Double layers can have very strong electrical fields (even 50kV/m). It is similar to diodes in a blocked configuration.

Source falsely claims that the areas are magnetic poles. This requires strong electrical currents. Just try to draw these currents on the map. You have to draw a separate circle around each pole. That is nearly impossible without getting an overly complex picture. More importantly: such currents have never been observed. Strong electrical currents give very bright traces in any plasma. That is how neon-light works for example.

Both magnetic fields and electric fields have very similar effects on light. Both can split lines (Zeeman effect/Stark effect) or affect polarisation (Faraday rotation/ LCD-effect). So this can create confusion for people that do not understand electromagnetism well.

For simplicity, many astronomers assume that electrical fields are impossible in plasma. So they tend to ignore all electrical fields by default. They even ignore electrical currents. In practice plasma is a semi-conductor. We can even create transistors with it. This means that electrical fields in plasma depend very much on the circumstances. And currents in plasma are very normal.

The picture above becomes much clearer when we see these areas as charged regions. And immediately the puzzle is solved. The different charged regions create electrical fields, and in the plasma the regions connect with electrical currents. Currents can flow in plasma, but not very well in gasses or liquids. So that is why the charged regions can be separate inside the sun, but start connecting with each other when they reach the surface.

When the charged regions connect, they form electric currents in plasma. The electrons in these currents go simply from the negative area to the positive area. Also some ions will be flowing, both ways. The electric currents discharge the charged regions. The currents also give off light, as described above. And this is actually what we see on the sun. We see that plasma=ropes form from these charged areas, connecting one area with the opposite other. Just like in a plasma-ball. The brightness varies with the pressure of the plasma, and the strength of the currents. So now we can fully understand how where these ropes on the sun come from.

In the case of an electrical short-cut, they can even cause flares and eruptions. Even this becomes very simple to understand, and is also similar to what we see.

For completeness the source: https://arxiv.org/pdf/1904.08367.pdf
Which is wrong in many of its assertions. If you have read my story above, you can see that it claims something totally different.

One of the worst assumption is the idea that the plasma-ropes automatically follow magnetic field lines. But in experiments and in the basics of Electromagnetism we see that currents in plasma always follow electrical fields. Magnetic fields can only partially modify the path of these currents. Magnetism can cause magnetic breaking, the Hall-effect, and curving/spiralling of the paths of electrical currents. And this can happen all at the same time.

And to create magnetic fields we need electric currents. That is especially true in a conductor like plasma. Any conductor will counter the creation of a magnetic field, by forming a current into the opposite direction. Especially strong fields need strong currents. And the currents that they need are perpendicular to the paths that the currents that we see are taking. These currents would interfere with each other and that creates an impossible situation. Electrical currents that create magnetic fields are also hard to sustain without continuous energy input. So any magnetic fields would disappear soon. The only real visible currents that we see go exactly the wrong way for the theories in the paper.

Some astronomers believe that the magnetic fields can come from nowhere. But they even go so far that magnetic field lines exist and can create explosions when they bump into each other. I think they should go back to school and do some real-world experiments. As proof of their belief, they refer to the sun. Which is stupid circular reasoning.

Changing magnetic fields can also cause electric fields and such currents. But we do not see changing magnetic fields. The fields that we see are reasonable stable and last for days.

So the only conclusion that we can make is that these regions are electrically charged areas. From these areas originate electrical currents. The electrical currents follow electrical fields. And these electrical fields can be very strong due to double layers in plasma. The currents also create magnetic fields exactly perpendicular to what many astronomers believe. The magnetic fields can be derived from the strengths of the electrical current. This all means that the lines in the picture show mainly the direction of the electrical field, not the magnetic field.

And it means that in the sun there are some energetic processes that create charge-separation. This latter is very interesting, as it could mean we might have charge-separations in many places of the universe as well. And this is the basis of an electrical universe.
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Re: Magnetic Reconnection

Unread postby Michael Mozina » Fri Apr 19, 2019 3:11 am

Zyxzevn wrote:When the charged regions connect, they form electric currents in plasma. The electrons in these currents go simply from the negative area to the positive area. Also some ions will be flowing, both ways. The electric currents discharge the charged regions. The currents also give off light, as described above. And this is actually what we see on the sun. We see that plasma=ropes form from these charged areas, connecting one area with the opposite other. Just like in a plasma-ball. The brightness varies with the pressure of the plasma, and the strength of the currents. So now we can fully understand how where these ropes on the sun come from.


Helioviewer movies demonstrate your point visually.

https://thesurfaceofthesun.com/images/s ... 00-131.mp4

The first video is an SDO composite overlay image. It's using a 131A AIA wavelength that shows the location and orientation of coronal loops (magnetic ropes/Birkeland currents) in light blue, and a 1600A AIA image that shows the surface of the photosphere and the location of the sunspots in relationship to the loops. As you'll see, a whole series of coronal loops connect the two sunspots as current through the coronal loops flows from on side to the other, through the surface of the photosphere and through the sunspots. The loops leave bright hot footprints on the 1600A image so some pixels in 1600A around the footprints of loops light up as the current passes through the photosphere.

https://thesurfaceofthesun.com/images/sdo/hmi-171.mp4

This composite overlay shows the same coronal loop process in 171A (yellow) and an SDO HMI image in grey. Again a lot of coronal loops connect the two sunspots, and the lots of loops flow into and out of the sunspots.

https://thesurfaceofthesun.com/images/s ... to-131.mp4

This is a video overlay of an AIA 131A (light blue) showing the coronal loops and a magnetogram image of the surface of the photosphere. The black and white areas in the magnetogram image are aligned along the footprints of the coronal loops/magnetic ropes/Birkeland currents. The orientation of the flow of current through the surface of the photosphere determines the N/S alignments in the magnetogram image.

http://www.thesurfaceofthesun.com/sdo/2 ... Mag-hq.mp4

This is an overlay of 1700A in pink which shows the surface of the photosphere, and a black/white magnetogram image. If you notice the large sunspot on the right looks "murky/milky", whereas the two large ones on the left are darker. That's because the two umbras of the sunspots on the left line up with "black" areas on the magnetogram image, whereas the dark umbra of the sunspot on the right lines up with a white region of the magnetogram image. Sunspots have current carrying filaments running through them, and we can see again from this image that the direction of the current flow through the loops dictates the N/S alignment in magnetogram images. Sunspots are areas of huge coronal loop concentration.
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Re: Magnetic Reconnection

Unread postby Webbman » Fri Apr 19, 2019 4:35 am

at the end of the day you need to remove resistance to cause an explosion. Resistance impedes current flow.

electric current flow causes the explosion not magnetism.

so when these explosions are being looked at you have to wonder how the resistance is being removed to allow all this current to flow.

so the electric fields of a sunspot drive the electrons which drives the plasma in the magnetic field. This concentrates the plasma into a suitable conductor. A conductor proportional to the strength of the field with resistance proportional to the density (and composition!) of the plasma. a sort of semi conductor as someone said where plasma is the resistor until it isnt.

When/if the conductor becomes strong/dense enough resistance is greatly reduced and boom. short circuit.
We shall know them by their works
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Re: Magnetic Reconnection

Unread postby BecomingTesla » Tue Apr 30, 2019 11:48 am

Hey Michael, not sure if you've ever seen this before but I thought it might be interesting for you! I'm happy to see that at least as of '11, some other folks are beginning to question the frozen-in theory as well: https://www.ann-geophys.net/29/1215/201 ... 5-2011.pdf
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Re: Magnetic Reconnection

Unread postby Michael Mozina » Wed May 01, 2019 8:06 am

BecomingTesla wrote:Hey Michael, not sure if you've ever seen this before but I thought it might be interesting for you! I'm happy to see that at least as of '11, some other folks are beginning to question the frozen-in theory as well: https://www.ann-geophys.net/29/1215/201 ... 5-2011.pdf


Thanks for the link. I'll read through it today. I think Alfven regretted ever suggesting such a concept as "frozen-in" magnetic field lines in plasma. He wrote a whole paper warning about it's misuse and the mainstream simply ignored him just like they ignored his double layer paper which was intended to drive the last few nails in the MRx coffin.

https://www.reddit.com/r/plasmacosmolog ... onnection/

FYI, I started a new thread on this topic over at Reddit since apparently the EU/PC hater posse at JREF/ISF *still* have no clue what they're talking about with respect to this topic, almost a full *decade* after I did my very best to explain their *numerous* errors. I'll try again at Reddit if the haters want to give it a whirl.

After my various conversations about this topic around the internet, I can better appreciate why Alfven just called the whole concept "pseudoscience". It's "pseudo' correct in the sense that magnetic field energy can indeed be converted into particle acceleration as a result of changing magnetic fields, but the proper scientific term from that process is induction. To date, *nobody* has ever been able to produce a real laboratory experiment that clearly distinguishes the physical difference between ordinary induction in a plasma conductor due to changing magnetic fields, and "magnetic reconnection". That's because there is no physical difference between them.

http://adsabs.harvard.edu/abs/1992A%26A...258..535D

Even Priest clearly links electrical current through the z axis to his so called "magnetic charges" in equations 16 and 17. I'd be fine if they called the process "circuit reconnection", or "particle reconnection", but the term "magnetic reconnection' is unnecessarily misleading and it doesn't include the whole circuit when looking at the total energy available at the point of 'reconnection". I'm pretty sure that is why Alfven flat out rejected the whole concept.
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Re: Magnetic Reconnection

Unread postby BecomingTesla » Wed May 01, 2019 9:48 am

Michael Mozina wrote:I think Alfven regretted ever suggesting such a concept as "frozen-in" magnetic field lines in plasma. He wrote a whole paper warning about it's misuse and the mainstream simply ignored him just like they ignored his double layer paper which was intended to drive the last few nails in the MRx coffin.


I've seen him quoted as saying as much, but haven't been able to find a source to the quote. Do you have a link to this paper? I'd like to read it if you don't mind sharing it.
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Re: Magnetic Reconnection

Unread postby Michael Mozina » Wed May 01, 2019 7:41 pm

BecomingTesla wrote:
Michael Mozina wrote:I think Alfven regretted ever suggesting such a concept as "frozen-in" magnetic field lines in plasma. He wrote a whole paper warning about it's misuse and the mainstream simply ignored him just like they ignored his double layer paper which was intended to drive the last few nails in the MRx coffin.


I've seen him quoted as saying as much, but haven't been able to find a source to the quote. Do you have a link to this paper? I'd like to read it if you don't mind sharing it.


I'd imagine his most scathing critism comes from this paper, but unfortunately I don't have a PDF copy of that particular paper.

https://agupubs.onlinelibrary.wiley.com ... i022p04019

He also talks about it in his book Cosmic Plasma (page 12):

The concept of `frozen-in magnetic field lines' has played a central role in plasma physics due to the fact that in several situations, but far from all, it is legitimate to use it . The restrictions on its use are clarified in CE(5 .4) . Further, it has a quasi-pedagogical appeal. An impression is developed that you understand a situation even if in reality you have misunderstood it.


He then goes on to list a whole set of criteria where the concept of "frozen in" does *not* apply which ends in the following comment:

As the aforementioned effects are common in low density cosmic plasmas (especially in `collisionless plasmas'), the `frozen-in' concept is very often invalidated. In particular, when combined with the `magnetic field-line reconnection' concept (`magnetic merging'), it has led to a serious misunderstanding of many important phenomena (II .33, II.5 .3 and CE 5 .4).


Essentially he rejects the "frozen-in" concept in all current carrying environments, almost all low density plasma environments, and anything to do with "magnetic reconnection/merging".

FYI, here's a directory full of Alfven's papers that I've collected over the years.

http://www.thesurfaceofthesun.com/Alfven/
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Re: Magnetic Reconnection

Unread postby BecomingTesla » Thu May 02, 2019 1:02 pm

I found that first paper you referenced by searching for Alfven thru a few databases, was pretty disappointed to find that a fifty-year old paper is pay-walled for ~$40...It feels pretty obvious that the majority of people can't just drop that kinda cash easily on a digital copy of a paper. When people talk about the academy being responsible for gate-keeping, this is the kind of thing that makes that critique feel legitimate to me. But, I'll just have to save for it.

I was able to find a pretty good, albeit short, critique of magnetic reconnection from Alfven in his paper "Double Layers & Circuits" (https://ntrs.nasa.gov/archive/nasa/casi ... 005703.pdf), Section III. Double Layers and Frozen-In Magnetic Field Lines. Worth a read, especially in combination with the paper of Lui's from '11. Bridges the chronological gap nicely.

I can't read "Cosmic Plasma," it's another textbook that's unfortunately pay-walled for over $100, so it'll have to wait too...
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Re: Magnetic Reconnection

Unread postby BecomingTesla » Thu May 23, 2019 10:17 am

Found this in my regular round of weekly research, figured it'd be worth sharing here for folks to read. The watermark on the left-hand side says it's from '14, but the post date in the title says it's from '18, so not really sure there. But at the very least, as recently as five years ago, these folks have leveled a really heavy critique of the frozen-in theory and the concept of frozen-in magnetic field lines: https://arxiv.org/pdf/1208.2961.pdf

We discuss this topic and find that in the study of the frozen-in field lines concept, the
effects of inductive and capacitive reactance have been omitted...Because the frozen-in concept is of prime importance to plasma physics, it is widely mentioned in the literature and is presented in almost all textbooks of plasma physics. Although the applicability of this concept has long been contested, and Alfven, the concept’s founder, also criticized its use and stated that it is often misleading it still plays an important role in astrophysics...Here we present experimental and analytical evidence to support a conclusion that the concept of frozen-in field lines should not be used in the dynamics study of plasma.

When our analysis is applied, the origin of the magnetic field of sunspots can be interpreted easily. In addition, we also present experimental results to support our analysis...The magnetic field of sunspots can be simply explained as follows: 1) It is the sun’s rotation that results in plasma crossing the non-rotating general magnetic field along the isomagnetic surface; 2) It is the field-line crossing motion that results in polarization charges appearing in the photosphere; 3) It is the eddy current of the polarization charges that results in the magnetic field of the sunspots.


Emphasis mine. And if I understand correctly, by "polarization charges" they're simply referring to double layers: "In fact, the interaction between the fluid and the magnetic field can destroy the electrical neutrality and result in the appearance of surplus positive or negative charges inside the fluid." Altho, don't quote me on that, because I'm not positive that they're synonymous, or that the authors intended such.

From what I understand reading Aflven, Falthammar, and now Liang, this is really the whole root of issue in mainstream (read: US) astrophysics: the broad misapplication of the assumption that because the plasma is infinitely conducting, that no electric fields parallel to the magnetic will be present, hence, the field lines can be considered as 'frozen-in'.

The equation v = E x B/(B^2) (Belcher, 2005) describes the velocity of the magnetic field line [1], but as noted in by both Alfven and Falthammar, [1] is only satisfied when [2] B x curl [B(E-B/B^2)] = 0 (Falthammar, 2007), i.e. when E|| = 0 - when there is no electric field parallel to the magnetic field. It is broadly assumed that this is the case in space plasma, because the plasma is considered infinitely conductive and it is generally assumed that E|| = 0 in an infinitely conductive plasma. But that isn't the case.

There is an opinion in some textbooks: When an ideal conducting fluid traverses magnetic field lines, it must induce an electric field. However, because the conductivity is infinite and an infinite current is impossible,
so the induced electric field and the perpendicular velocity component must be infinitesimally small and the field-line crossing motion is therefore prohibited.

In fact, this opinion is wrong. From electrical engineering we know that in a non-steady circuit system, beside resistance, inductive and capacitive reactance can also restrain the current growth. In other words, it is the complex impedance (not only the resistance) that controls the current growth. This law is also valid in MHD field because the electric field, current, and magnetic field are generally time-variant. It is similar that in the DC circuit, only resistance is considered, but for the AC circuit, the reactance also needs to be considered. Below, we show how the inductive reactance and capacitive reactance restrain the current growth and why the fluid can traverse magnetic field lines.


So despite the conductivity being infinite, it cannot be assumed that E|| = 0. Parallel electric fields can exist, and what's more confusing is that they've been detected in-situ in Earth plasma for the last fifty-something years now...

I'm happy that these authors included textbooks, because it should be really easy (once I've fully learned the maths and spent some time playing with plasma) to read the literature and determine whether Aflven/Falthammar/Liang's critiques have been taken into consider or not. But so far, it does seem correct that the frozen-in theorum is (a) incorrect, and (b) has been broadly applied in astrophysics the wrong way.
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