Is magnetic flux quantified only near superconductors?

[jarek]

Quantization of magnetic flux going through superconducting ring is explained that along this loop, quantum phase (order parameter in this case) has to return to the initial phase, so it makes integer number of full rotations - this number determines the total magnetic flux going through this loop, like on this picture:

There appears natural question - why we couldn't take this argument into just a loop in vacuum?
In static picture, we should be able to decrease such abstract loop down to having single flux quant going through it and so they seem to be physical lines in space.
These natural consequences of quantum mechanics are called 'vortex lines' by prof. Bialynicki-Birula (well known in Poland).

Very similar concepts are popular in considerations of corona plasma of our Sun.
There is generally a problem for standard MHD models to explain that while the surface has thousands of kelvins, for corona it exceeds million kelvins ('coronal heating problem'). The hope could be the observed magnetic flux ropes (some paper with such explanation, or different Physorg news, sometimes called nanoflares) - charged particles instead of just repelling each other, gathers in nearly one-dimensional objects along magnetic lines, which carries very large energy released mainly while magnetic reconnections.

Such lines should have large energy density per length, so in low temperatures we could expect them rather only in microscopic scales. Quantum rotation operator suggests that such lines should go through fermions along their spin axis - it could explain their tendency to couple (electrons in orbitals, Cooper pairs, nucleons in nuclei), but also suggests how optical photons looks like: topology says that to destroy such couple for e.g. deexcitation, we should twist one of them 180 deg - changing its spin by 1: like from 1/2 to -1/2.
Such twist is angular acceleration then deceleration - angular momentum conservation suggests that there should be created kind of EM wave 'carrying this 180deg rotation' ('have spin 1'), it could also help destabilizing other excited couples (stimulated emission) - we get optical photon candidate:

Accepting such 1D structures also allows for other particle-like constructs, for example if on such vortex line there would be additional 'rotation toward the center of line', it would get charge and it would change it into opposite vortex line (became magnetic dipole) - we would get lepton-like construct (pictures).

Could (some?) magnetic flux lines be physical objects?
Is something like corona's magnetic flux ropes observed also in plasma experiments like polywell - that against Coulomb repulsion, charged particles have tendency to gather on lines along magnetic field?
Would it affect its stability?

[Joseph Chikva]

Could (some?) magnetic flux lines be physical objects?

No, they could not (are not) as magnetic flux lines are abstraction for better understanding how real magnetic field acts.

Is something like corona's magnetic flux ropes observed also in plasma experiments like polywell - that against Coulomb repulsion, charged particles have tendency to gather on lines along magnetic field?
Would it affect its stability?

Stronger magnetic field - better confinement. There is no any novelty.
Conventionally conducting magnets limit is about a few Tesla, superconducting - up to 10 Tesla and may be a little more.
One difficulty is that neutron flux can destroy superconductivity.

[jarek]

Do you also disagree that magnetic flux going through superconducting ring is quantified?
Look at pictures of corona (like here) - why there are bright lines on them?
Why corona has millions of kelvins, while the surface only thousands?
Why in magnetic reconnection article there is written "This process is not well understood: once started, it proceeds many orders of magnitude faster than predicted by standard models."?
Do you have a more concrete explanation of e.g. electron coupling on orbitals than abstract Pauli's principle just describing observations?
We know that optical photon is EM wave - what is its exact structure?
...?

[Joseph Chikva]

Do you also disagree that magnetic flux going through superconducting ring is quantified?

I do not understand what you mean under "quantified"
All things may be "quantified". And what?

Look at pictures of corona (like here) - why there are bright lines on them?
Why corona has millions of kelvins, while the surface only thousands?

As I understand you are asking why temperature in center is more than at surface?
It can be easily explained. Via radiation.

Magnetic_reconnection]magnetic reconnection article[/url] there is written "This process is not well understood: once started, it proceeds many orders of magnitude faster than predicted by standard models."?

As I understand there are different kinds of instabilities. They can accelerate some particles with the help of various plasma waves.

We know that optical photon is EM wave - what is its exact structure?

Why? Because

[jarek]

Quantization of flux going through superconducting ring literally means that it is some integer multiplicity of magnetic flux quantum: 2.067 833 667(52)×10^-15Wb ... it's strongly related to Aharonov-Bohm effect ...

As I understand you are asking why temperature in center is more than at surface?

Sun's corona isn't in its center, but its the plasma field around.

As I understand there are different kinds of instabilities. They can accelerate some particles with the help of various plasma waves.

They intensively work on MHD for many decades and still get orders of magnitude smaller values ...

Why? Because Smile

Maybe you are satisfied with such explanations, but I'm not.

ps. Here is some paper explaining coronal heating problem using magnetic flux ropes.

[Joseph Chikva]

Why? Because Smile

Maybe you are satisfied with such explanations, but I'm not.

Ok, I am not satisfied too but that is axiom. With the help of which many phenomena can be explained.
And before the uniform field theory won't be created nobody can offer you better explanation.
So,

And why the temperature in corona of higher than at surface?
Because of radiation.

[jarek]

You are not satisfied with current 'explanations', but you don't even want to look at explanations I'm asking about ... Because.
Coronal heating problem is far nontrivial - energy is generated in the center of Sun, its surface is 'warm', while when you go away it becomes hotter and hotter up to 200 times the temperature of surface ... seems against 2nd law of thermodynamics - what radiation transfers energy from cold to hot?
There are dozens of approaches to this very important questions and it seems there is no satisfactory one - please read something about it before replying.

[Joseph Chikva]

You are not satisfied with current 'explanations', but you don't even want to look at explanations I'm asking about ... Because.
Coronal heating problem is far nontrivial - energy is generated in the center of Sun, its surface is 'warm', while when you go away it becomes hotter and hotter up to 200 times the temperature of surface ... seems against 2nd law of thermodynamics - what radiation transfers energy from cold to hot?
There are dozens of approaches to this very important questions and it seems there is no satisfactory one - please read something about it before replying.

I saw football (or soccer) now Barcelona vs. Man U
Regarding corona I think that is plasma instability. What are you waiting for here? Analytical solution? As I understand people who really are engaged with that issue could not solve that.

[Joseph Chikva]

Jarek:

One hypothesis

...energy is generated in the center of Sun,...

Why are you so sure?
May be an instability throws out from the Sun’s depth the very dense clots of plasma in which the number density is much more. Fusion power density is proportional to square of number density. If it’s so this is very similar to Dense Focus Fusion where very hot dense plasma clot (up to 10^26 m^-3) is in comparatively cold and rare remain plasma environment.

Coronal heating problem is far nontrivial - energy is generated in the center of Sun, its surface is 'warm', while when you go away it becomes hotter and hotter up to 200 times the temperature of surface ... seems against 2nd law of thermodynamics - what radiation transfers energy from cold to hot?

If my hypothesis correct there simply fusion goes more vigorously than in the center and so no any contradictions with any law.

PS:
I have found something: http://adsabs.harvard.edu/abs/1999JGR...104.9709F
The number density in Corona has an order of magnitude 10^13-10^14 m^-3.
I do not know that's enough for considering effect or no.

And here is the description of layers of the Sun: http://fusedweb.pppl.gov/cpep/chart_pag ... ayers.html

The corona is hotter than some of the inner layers. Its average temperature is 1 million K (2 million degrees F) but in some places it can reach 3 million K (5 million degrees F).

Temperatures steadily decrease as we move farther away from the core, but after the photosphere they begin to rise again. There are several theories that explain this, but none have been proven.

[jarek]

Your hypothesis seems to be related with 'spikules', but the Wikipedia article says that it has been discounted.
According to this articles there are two mainstreams of trying to explain this fundamental MHD problem:
- by magneto-acoustic waves from the sun, or
- the magnetic reconnections I'm talking about.

Ps. Oh your are implying that there is fusion happening in corona?
I haven't met with such hypothesis, it could sound reasonable ... but the density is very low and they measure temperature by presence of highly ionized ironium - fusion would produce single gammas, it's difficult to use them to highly ionize in such sparse environment (?) IMHO

[chrismb]

jarek, you might be interested to read Thomas Smid's ideas; http://www.plasmaphysics.org.uk/research/sun.htm . Notwithstanding the conclusion, I have to say that I find his rationale convicing (partly because it is a simple, straight-forward description of the system that ends up at 'the right number'. I'm not into hieroglyphics explanations, or hand-wavy that no numbers can be put into, nor gotten out of. This is how I like to see an idea expressed!!).

I've also speculated, then heard other such speculations, of fusion in the corona. The problem is the issue of density, thus total fusion rate, which is still low. I would not invest too much credit into that idea, but one might presume it must happen to some degree.

[Joseph Chikva]

Ps. Oh your are implying that there is fusion happening in corona?

May be fusion and may be mass transfer from the depth of Sun.
Both as result of instabilities.

[D Tibbets]

Hydrogen fusion in the corona? Of course this occurs, but the quantity is extremely, extremely, extremely, extremely,..., extremely trivial compared to core fusion. Before you advocate for coronal fusion being significant, you need to consider how this would change the properties of a star.

Physical reasons hydrogen fusion does not occur to any significant extent in the corona of Sun like main sequence stars is straight forward.*
The corona is generally ~ 1-2 million K, even hot spots may only reach temperatures of ~ 2-4 million K. This is ~ 1/5th the temperature of the Sun's core. P-P fusion scales at ~ temp^4 . That translates to a P-P fusion rate of ~ 1/ 25th of the core based on temperature alone. When density is added, the fusion rate would be decreased by ~ 10^15 squared or ~ 10^30
Final fusion rate would be ~ 1/10^31 per cubic meter. The volume of the corona may reclaim several orders of magnitude, but this would still leave the relative fusion rate in the corona compared to the core at ~ 1 billionth of 1 billionth of 1 billionth (~10^-27) lower (assuming a generous 10,000x increased volume of the inner corona compared to the core).

When you consider the CNO hydrogen fusion chain the difference would be even worse. In the Sun's core CNO fusion (at ~ 15,000,000 million degrees K) is about 1% of the fusion rate from P-P fusion. The CNO fusion rate scales as the temperature ^16 or 18th . So at a temperature of ~ 1/5th, the CNO fusion rate would be ~ 1/ 5^18.
Deuterium fusion would be higher by a ratio of ~ 10^20th, but any surviving deuterium in the corona would not be any higher than that in the original solar nebula (less than ~ 1/ 6000th of hydrogen). There is deuterium produced in the Solar core from the first step of P-P fusion, but this is quickly consumed by subsequent reactions in the P-P chain. Also, in Sun sized stars there is little mixing of the gasses in the core with outer layers.

This is fortunate as any D-D or P-P fusion occurring in the corona would produce neutrons and / or gammas which would fry us here on Earth if the flux was more than extremely tiny compared to the rates in the core.

If there was significant tritium , or even deuterium in the corona the relatively low temperatures might lead to significant fusion, but these are fortunately rare. Hydrogen fusion at these temperatures are extremely trivial, partly due to the lower temperatures, but mostly due to the tremendous density ^2 difference.


*There can be significant fusion on the surface of a star under special conditions. Examples of this are certain Nova and Supernova explosions.

Dan Tibbets

[Joseph Chikva]

Hydrogen fusion in the corona? Of course this occurs, but the quantity is extremely, extremely, extremely, extremely,..., extremely trivial compared to core fusion. Before you advocate for coronal fusion being significant, you need to consider how this would change the properties of a star.

Physical reasons hydrogen fusion does not occur to any significant extent in the corona of Sun like main sequence stars is straight forward.*
The corona is generally ~ 1-2 million K, even hot spots may only reach temperatures of ~ 2-4 million K. This is ~ 1/5th the temperature of the Sun's core. P-P fusion scales at ~ temp^4 . That translates to a P-P fusion rate of ~ 1/ 25th of the core based on temperature alone. When density is added, the fusion rate would be decreased by ~ 10^15 squared or ~ 10^30
Final fusion rate would be ~ 1/10^31 per cubic meter. The volume of the corona may reclaim several orders of magnitude, but this would still leave the relative fusion rate in the corona compared to the core at ~ 1 billionth of 1 billionth of 1 billionth (~10^-27) lower (assuming a generous 10,000x increased volume of the inner corona compared to the core).

When you consider the CNO hydrogen fusion chain the difference would be even worse. In the Sun's core CNO fusion (at ~ 15,000,000 million degrees K) is about 1% of the fusion rate from P-P fusion. The CNO fusion rate scales as the temperature ^16 or 18th . So at a temperature of ~ 1/5th, the CNO fusion rate would be ~ 1/ 5^18.
Deuterium fusion would be higher by a ratio of ~ 10^20th, but any surviving deuterium in the corona would not be any higher than that in the original solar nebula (less than ~ 1/ 6000th of hydrogen). There is deuterium produced in the Solar core from the first step of P-P fusion, but this is quickly consumed by subsequent reactions in the P-P chain. Also, in Sun sized stars there is little mixing of the gasses in the core with outer layers.

This is fortunate as any D-D or P-P fusion occurring in the corona would produce neutrons and / or gammas which would fry us here on Earth if the flux was more than extremely tiny compared to the rates in the core.

If there was significant tritium , or even deuterium in the corona the relatively low temperatures might lead to significant fusion, but these are fortunately rare. Hydrogen fusion at these temperatures are extremely trivial, partly due to the lower temperatures, but mostly due to the tremendous density ^2 difference.


*There can be significant fusion on the surface of a star under special conditions. Examples of this are certain Nova and Supernova explosions.

Dan Tibbets

First
I am not advocate but only assume.
As jarek spoke about infringement of the second law of thermodynamics, I have assumed more rational version.
I would ask you from another side: number density 10^13-10^14, temperature 2-3 million K, is it possible or no occurring self-supporting fusion?
I don't know, can you calculate? Consider please so often repeated by you scaling factor.
But you told about scaling between 1 and 3 meters. And at the Sun you have order of magnitude thousands kilometers. I think that even reactions having a very low cross section are possible at significant amounts.

My second version was simply the carrying out of matter from depth of the Sun (mass transfer).

[jarek]

jarek, you might be interested to read Thomas Smid's ideas; http://www.plasmaphysics.org.uk/research/sun.htm

crismb, using virial sounds interesting ... but it's completely not this case - it's used for simple situations of stable gravitational systems.
Here we would need some concrete source of such e.g. gravitational energy - sun throws matter away with high energy (definitely not sufficient to explain the problem) and gravity only decreases this energy.
To obtain some energy from absolute gravitational potential like in virial theorem, something would have to fall on Sun - like part of matter it throw away ... but it's still orders of magnitude smaller than required in coronal heating problem ...

About coronal fusion possibility - additional argument against its importance could be that electrons might be important to screen Coulomb barrier for fusion - it could be more difficult in such ionized environment IMHO
Joseph, "carrying out of matter from depth of the Sun" seems like spicules, but as I've written, Wikipedia article says that such explanation has been discounted.

What do you think about magnetic flux ropes, magnetic reconnections?
There are observed clear bright lines in corona ... such view for coronal plasma seems to became well established ... ?