Magnetic reconnection and physical processes

[brantc]

Quote:
Originally Posted by Tim Thompson
"This is the basic equation of magnetic behavior in MHD, and it determines B once v is known. In the electromagnetic theory of fixed conductors, the electric field and electric current are primary variables with the current driven by electric fields. in such a fixed system the magnetic field is a secondary variable derived from the currents. However, in MHD the basic physics is quite different, since the plasma velocity (v) and magnetic field (B) are the primary variables, determined by the induction equation and the equation of motion, while the resulting current density (j) and electric field (E) are secondary and may be deduced from equations (1.8) and (1.10a) if required (Parker, 1996)."
Priest & Forbes, page 14.

What they have done with MHD is turn the basic physics around. They are expecting that reality will match their equations when in fact their math has to match reality.
Plasma(bulk velocity) is different than particle velocity. I dont think bulk velocity will show you a Maxwellian distribution.
MHD works off of turbulence(top down) vs EM works on instabilities(particle up).

 

[Michael Mozina]

You claimed, with confidence, to be able to explain something that you appear unable to explain.

http://www.aanda.org/index.php?opti...29&url=/articles/aa/pdf/2008/37/aa9086-07.pdf

Do you even know how to use a search engine? Try "ohmic resistance coronal loop heating". I think even your MR theories depend on resistance to current flow to heat the loops if I'm not mistaken.

Holy cow dude, get a grip. Absolutely *NO* scientific theory rises and falls on a single individual's personal math skills. You're in total and complete denial on this point. Evidently you think that if your math skills exceed those of another poster, that automatically makes you right on any and every topic under the sun by default. I'm afraid "knowledge' is not limited to a mathematical expression alone. Your math skills are irrelevant Mr. "Flying stuff? What flying stuff?" Get over it. Your observation skills stink to high heaven, and your pathetic attempt at bullying the individual is just boring at this point.

 

[brantc]

Originally Posted by brantc View Post
It will not happen without the involvement of current or electron flow.

The magnetic field needs a source, currents, but the source need not be local, that is what you are forgetting here.

You will find that the source of the magnetic field will start at the same place as the start of the flux tube which is the same starting place as the electric field that drives the plasma through the flux rope tube thingy.

That may not be local but that does not matter. It still goes back to electrons are the source of the magnetic field local or not.

If the flux tube is a million bizillion miles long, it still starts at some place where there are electrons that create the magnetic field. This field is continuous from the starting point to the ending point and is supported by the current flow through the tube.

Shut off the electron flow to the tube and the tube collapses.

That does not make any sense, if the magnetic field does not move around, then it cannot generate an electric field. About the generation of a flux tube, see above.

Well thats just some circular logic. You are assuming that the only way to generate a current flow through the loops is by the shear of the footprint so since there is a loop then the footprints must be shearing.

Thats what this is all about. I'm saying there is another mechanism that is generating the current flow through the loops.

There is no doubt about the opposite polarity measurements at the base of the loops. This polarity difference is responsible for the loops.

Of course we KNOW that currents are flowing along the magnetic loops, because we see the shearing motion of the foot points and we observe the effects of such currents.

I will show you some movies of loops that have no appear apparent shearing motion but are still growing. All it take is one to disprove that theory.
There definitely is no buoyancy happening unless you say the Lorentz force is buoyancy..

 

[Reality Check]

Please present your "long" response proving Birkeland currents = flux tubes

Before I get into the "long" response, please explain to us how you think an ordinary filament in a plasma ball forms, and how you believe your "flux tube" is physically different from such a "structure" in plasma.

Lets see how your knowledge of simple facts has progressed:

• An ordinary filament in a plasma ball is an electrical discharge driven by an AC added by the manufacturers to make a pretty display.
• A magnetic flux tube is not an electrical discharge.

First asked 18 Ferbruary 2010
Michael Mozina,
Please present your "long" response.
Will this prove Birkeland currents = flux tubes?

 

[Michael Mozina]

What they have done with MHD is turn the basic physics around. They are expecting that reality will match their equations when in fact their math has to match reality.
Plasma(bulk velocity) is different than particle velocity. I dont think bulk velocity will show you a Maxwellian distribution.
MHD works off of turbulence(top down) vs EM works on instabilities(particle up).

Note that Alfven's orientation inside current carrying plasma was almost always skewed toward the E orientation, what he called a "particle' orientation of MHD theory, rather than the B (field) orientation alone. Whereas Alfven was fluent in both the E and B orientations, today's astronomers are fluent in only the B orientation, thus everything is "magnetic yada yada yada', rather than "electromagnetic yada yada yada". They seem to be in complete denial of the ability to look at MHD from a particle/circuit orientation. Even when presented with papers that clearly do exactly that, they bury their heads in the sand and ignore it. I guess they figure if they never acknowledge it, it never happened.

The bottom line is that these same 'magnetic ropes" can be explained in terms of "macroscopic circuits" of energy. The tubes come "collapsing back" to the photosphere because the circuit is broken, the loop cools off, and the heavier materials inside the loop have nowhere to do go but down. That electromagnetic behavior seemed to be quite the revelation to the 'magnetic flux tube' crowd.

Alfven spent the first couple of chapters in Cosmic Plasma working on boundary issues and application preferences related to conditions in the plasma. In some instances (like kink instabilities for example) he used the B field to do many of his calculations mainly because it was easier. When it came to 'flux tubes' however, he clearly understood they could be treated as "circuits". The mainstream has lost that understanding somewhere along the way.

 

[tusenfem]

Before I get into the "long" response, please explain to us how you think an ordinary filament in a plasma ball forms, and how you believe your "flux tube" is physically different from such a "structure" in plasma.

I have already explained this to you, but as you don't pick up anything that anyone tells you and as it is easier to ask peeps to do something than do something yourself (which you NEVER do), I guess I will have to go through it again.

A plasma ball has a cathode in the middle on a plastic pedestal. The glass globe around it is an anode, the space inside the ball is filled with a pretty lightening gas. Now, between the cathode and the anode there will be an electric field and as soon as the electric field reaches a critical level that the break down level gets crossed, and a narrow ionization trail gets formed between cathode and anode (similar to what happens in the Earth's atmosphere during "dark" lightning). Then there is a conducting path and there can be a discharge between cathode and anode can take place which in the atmosphere would be the real lightning, hitting and exciting the atoms, which fall back and emit the pretty pink light.

Now, naturally this would give one burst and not the nice continual lightning that you see in a plasma ball. Therefore, instead of having a constant cathode-anode, there is an oscillator put onto both 'odes and when the voltage difference, the gas pressure and the oscillation frequency are correct, the lightning does not stop.

Now, naturally, these lightnings consist of short bursts of electric currents and thus around every channel you see there will be a slight toroidal field, i.e. circles around the channel, but not along the channel.

So, you may define the current channel as a current tube, however, it is NOT a magnetic flux tube as it has NO field along its axis.

Now "my" flux tube is defined, just like Alfven does it as a bundle of field lines, nothing more, nothing less. And thus this flux tube is totally different from the current channel in a plasma ball, as that channel is determined by the break down channel and the field is toroidal around it.

So, now a flux tube in a plasma, like I said in the discussion below the Alfven text, in principle there is NO reason why the straight bundle of field lines, as drawn by Alfven, cannot exist. And to repeat the discussion if I describe the field by B = B z, then along the field there is NO current as j_z = dBy/dx - dBx/dy = 0, simple Maxwell. And then, if indeed the flux tube as drawn by Alfven is limited in its radial extent, then there will be a surface current driven by the jump in B and it will be circling around the tube in a toroidal fashion, just like the magnetic field of the plasma ball was toroidal around the current channel.

Now, naturally, this is an idealization, and in nature such a tube will be very rare. In the lab, they can easily be defined.

When we do something to the field, twist it at one side, then a EMF is generated through vxΒ and currents will start to flow along the field lines of the flux tube in order to create the twisting of the tube (and then we will forget for now the launching of an Alfven wave along the tube, initiating the twisting of the field).

Field aligned currents are ubiquitous, probably half my papers are dealing with field aligned currents. But let's look at the Intrator experiment, where they have two flux tubes defined from two anodes to two cathodes, but naturally the whole volume is with magnetic field. These flux tubes don't do much. Should they get together nothing happens as the field is jn the same direction. Now, they turn on the voltage between the cathodes and through the two defined flux tubes current starts flowing, as there is a plasma around. Now we have the two flux tubes (with same directed field) with current flowing along them (parallel currents) and superposed the toroidal magnetic field of the current. This twists the flux tube into a flux rope. The paralel currents attract eachother, and when the the two ropes get together, then, because they twist in the same direction, we get oppositely directed field brought together. Then a reconnection can happen, such that a field line that was wrapped around the first tube in the beginning, suddenly finds itself wrapping around one, until the touching place and then wrapping around the other. This is a true topological change, which cannot be described by simple "induction," and then I have not even addressed the relaxation of the magnetic tension of the field, which accelerate the plasma and magnetic energy is transformed into bulk plasma energy (i.e. not currents, but electrons and ions accelerated in the same direction)

So, I have I think explained a lot rather clearly, now I would like to see a similar clear explanation of "circuit/particle reconnection" or anything else that you think would be interesting to post here.

 

[tusenfem]

Thats what this is all about. I'm saying there is another mechanism that is generating the current flow through the loops.

Prithee, what would be this other source, either it is the Lorentz force or you put a battery into the plasma.

I will show you some movies of loops that have no appear apparent shearing motion but are still growing. All it take is one to disprove that theory.
There definitely is no buoyancy happening unless you say the Lorentz force is buoyancy..

I never said that the current is letting the loops grow, that I your idea.
When the loops are above the photosphere there is basically no buoyancy anymore, and no the Lorentz force is not buoyancy.

 

[GeeMack]

http://www.aanda.org/index.php?opti...29&url=/articles/aa/pdf/2008/37/aa9086-07.pdf

Do you even know how to use a search engine? Try "ohmic resistance coronal loop heating". I think even your MR theories depend on resistance to current flow to heat the loops if I'm not mistaken.

Holy cow dude, get a grip. Absolutely *NO* scientific theory rises and falls on a single individual's personal math skills. You're in total and complete denial on this point. Evidently you think that if your math skills exceed those of another poster, that automatically makes you right on any and every topic under the sun by default. I'm afraid "knowledge' is not limited to a mathematical expression alone. Your math skills are irrelevant Mr. "Flying stuff? What flying stuff?" Get over it. Your observation skills stink to high heaven, and your pathetic attempt at bullying the individual is just boring at this point.

Standard response. Another argument by tantrum.

Why is it that no professional physicist on Earth agrees with your position on this, Michael?

 

[tusenfem]

What they have done with MHD is turn the basic physics around. They are expecting that reality will match their equations when in fact their math has to match reality.
Plasma(bulk velocity) is different than particle velocity. I dont think bulk velocity will show you a Maxwellian distribution.
MHD works off of turbulence(top down) vs EM works on instabilities(particle up).

What does that even mean, that last sentence. I do hope you realize that MDH does not have any particles, it is a fluid description of the plasma, which fails when you want to look at spatial scales smaller than the ion gyro radius or at temporal scales shorter than the ion gyration time. Any idea you might have a "particle up" EM process in MHD is ludicrous. I guess that Alfven had it all wrong when he developed his theories, he'd better give back his Nobel prize.

 

[Michael Mozina]

What does that even mean, that last sentence. I do hope you realize that MDH does not have any particles, it is a fluid description of the plasma, which fails when you want to look at spatial scales smaller than the ion gyro radius or at temporal scales shorter than the ion gyration time. Any idea you might have a "particle up" EM process in MHD is ludicrous. I guess that Alfven had it all wrong when he developed his theories, he'd better give back his Nobel prize.

What?

Chapter 1 of Cosmic Plasma:

Exploration of those plasma properties which can be described by the magnetic fields CHAPTER I concept have in general been successful . However, this is not the case for those phenomena which cannot be understood by this approach . The present monograph shall concentrate on the latter, and try to give a survey of cosmic plasmas based on the particle (electric current) aspect.

Perhaps you could explain then what Chapters 1.3 - 1.5 are all about?

 

[tusenfem]

try to give a survey of cosmic plasmas based on the particle (electric current) aspect.

Perhaps you could explain then what Chapters 1.3 - 1.5 are all about?

Of course you can mix full plasma physics easily with the approximation MHD. But that is not what is meant by Alfven, when he says "particle" aspect, note the "electric current" which basically means he wants to discuss things from a current point of view, which is okay. And then he wants to discuss, e.g. double layers.

Question 1: Please give us the definition of MHD.
Question 2: Can double layers exist in MHD?

 

[brantc]

Originally Posted by brantc View Post
What they have done with MHD is turn the basic physics around. They are expecting that reality will match their equations when in fact their math has to match reality.
Plasma(bulk velocity) is different than particle velocity. I dont think bulk velocity will show you a Maxwellian distribution.
MHD works off of turbulence(top down) vs EM works on instabilities(particle up).

What does that even mean, that last sentence. I do hope you realize that MDH does not have any particles, it is a fluid description of the plasma, which fails when you want to look at spatial scales smaller than the ion gyro radius or at temporal scales shorter than the ion gyration time. Any idea you might have a "particle up" EM process in MHD is ludicrous. I guess that Alfven had it all wrong when he developed his theories, he'd better give back his Nobel prize.

The last sentence means that MHD, when they describe turbulence effects, the cause is from the outside in, like a fluid. The environment is causing the perturbations. Its because they dont consider the particle to provide the energy for the reconnection that they use MHD. Thats why when you look at a MHD simulation it looks like water turbulence.
It does not look like plasma instabilities which form from the particles up.

It is the interactions between the particles that cause the large scale instabilities as experimentally show by Peratt.
http://www.scribd.com/doc/14145750/...urrent-ZPinch-Aurora-as-Recorded-in-Antiquity

That is the problem with MHD. It works good for easy calculations on bulk flows but tells you nothing about the energetics. And your computer wont explode from too many calculations......

PIC starts with the particles being the source of the energy for the current channels and the curl field. The parallel field can be either induced or external.

We know that the particles provide the energy in the LAPD experiments.

So if we know that MHD fails at a limit or is an approximation, then why do we put so much weight on MHD simulations??????
Look into MHD fluid pumps. They are amazingly inefficient.

When you use MHD there is no room for particle simulations so you automatically use your MHD hammer on the flux tube screw.....
It confines you to the idea that the energy is supplied from an external magnetic field.

Here in wiki they say Structures in MHD systems. There is no such thing as a MHD system. You can characterize a system using MHD formulations but the system itself is a plasma particle based system.
http://en.wikipedia.org/wiki/Magnetohydrodynamics#Structures_in_MHD_systems

Instability is different from turbulence.

 

[brantc]

Now, naturally, these lightnings consist of short bursts of electric currents and thus around every channel you see there will be a slight toroidal field, i.e. circles around the channel, but not along the channel.

So, you may define the current channel as a current tube, however, it is NOT a magnetic flux tube as it has NO field along its axis.

Yes that may be true by your definition but you have just confirmed the point to this discussion, that there are current carrying plasma discharges that follow the right hand rule. And they dont need field aligned currents.
Plasma filled flux tubes are just another manifestation of plasma currents.

Now "my" flux tube is defined, just like Alfven does it as a bundle of field lines, nothing more, nothing less. And thus this flux tube is totally different from the current channel in a plasma ball, as that channel is determined by the break down channel and the field is toroidal around it.

So, now a flux tube in a plasma, like I said in the discussion below the Alfven text, in principle there is NO reason why the straight bundle of field lines, as drawn by Alfven, cannot exist. And to repeat the discussion if I describe the field by B = B z, then along the field there is NO current as j_z = dBy/dx - dBx/dy = 0, simple Maxwell. And then, if indeed the flux tube as drawn by Alfven is limited in its radial extent, then there will be a surface current driven by the jump in B and it will be circling around the tube in a toroidal fashion, just like the magnetic field of the plasma ball was toroidal around the current channel.

Now, naturally, this is an idealization, and in nature such a tube will be very rare. In the lab, they can easily be defined.

When we do something to the field, twist it at one side, then a EMF is generated through vxΒ and currents will start to flow along the field lines of the flux tube in order to create the twisting of the tube (and then we will forget for now the launching of an Alfven wave along the tube, initiating the twisting of the field).

Field aligned currents are ubiquitous, probably half my papers are dealing with field aligned currents. But let's look at the Intrator experiment, where they have two flux tubes defined from two anodes to two cathodes, but naturally the whole volume is with magnetic field. These flux tubes don't do much. Should they get together nothing happens as the field is jn the same direction. Now, they turn on the voltage between the cathodes and through the two defined flux tubes current starts flowing, as there is a plasma around. Now we have the two flux tubes (with same directed field) with current flowing along them (parallel currents) and superposed the toroidal magnetic field of the current. This twists the flux tube into a flux rope. The paralel currents attract eachother, and when the the two ropes get together, then, because they twist in the same direction, we get oppositely directed field brought together. Then a reconnection can happen, such that a field line that was wrapped around the first tube in the beginning, suddenly finds itself wrapping around one, until the touching place and then wrapping around the other. This is a true topological change, which cannot be described by simple "induction," and then I have not even addressed the relaxation of the magnetic tension of the field, which accelerate the plasma and magnetic energy is transformed into bulk plasma energy (i.e. not currents, but electrons and ions accelerated in the same direction)

So, I have I think explained a lot rather clearly, now I would like to see a similar clear explanation of "circuit/particle reconnection" or anything else that you think would be interesting to post here.

That is one of the most amazing things I have heard. This mathematical entity called flux tubes can get together.
There is nothing there. Nothing extends from any electrode to any other electrode except a continuous field..
I might as well define a flux tube that goes from the center of the galaxy to our sun......

How can something that you have defined, that is not real, not physical have properties?? The flux tubes as you have defined them are part of the background parallel field.
They have no independent life or function of their own. The background field is unchanging and smooth. The flux tube could never change or do anything unless you change some parameter in your equation since they are defined by your equation.

And then when you turn the current on, your prediction is not going to match. All the flux tube work is empirical. So you cant even say you flux tube definition is a prediction except in the broadest sense of there will be 2 current channels with a twist..

Do you see? The flux tubes have no relation to any physical parameter...
You cant just say they might touch. The only way that the "flux tubes" might touch is from a sausage or kink instability and that has nothing to do with the parallel field. That is a result of the right hand rule or curl. And this would only happen with plasma.

They do not exist except in math. I would even venture to say that they are just wrong as defined.

It would be better to say the "area enclosed by the plasma column is the ~area to be considered in calculating the effect of a parallel field on the plasma column".

Cause and effect, causality.

 

[Ziggurat]

It confines you to the idea that the energy is supplied from an external magnetic field.

Nonsense.

First off, whether you take a particle view or an MHD view, the magnetic and electric fields contain energy, and it's the same energy in either case.

Second, the only other form of energy available is kinetic energy (since we're not talking about fusion right now). In the particle view, we can calculate this by looking at kinetic energy of individual particles and adding them up. But we can ALSO get that energy by calculating a center-of-mass kinetic energy plus a kinetic energy of each particle relative to this center of mass. Both methods are mathematically identical.

But guess what: MHD will contain this exact same energy. The first quantity is the kinetic energy of the fluid, the second quantity is the thermal energy of the fluid. The energy is exactly the same.

 

[brantc]

Of course you can mix full plasma physics easily with the approximation MHD. But that is not what is meant by Alfven, when he says "particle" aspect, note the "electric current" which basically means he wants to discuss things from a current point of view, which is okay. And then he wants to discuss, e.g. double layers.

Question 1: Please give us the definition of MHD.
Question 2: Can double layers exist in MHD?

From wiki.

The importance of kinetic effects

Another limitation of MHD (and fluid theories in general) is that they depend on the assumption that the plasma is strongly collisional (this is the first criterion listed above), so that the time scale of collisions is shorter than the other characteristic times in the system, and the particle distributions are Maxwellian. This is usually not the case in fusion, space and astrophysical plasmas. When this is not the case, or we are interested in smaller spatial scales, it may be necessary to use a kinetic model which properly accounts for the non-Maxwellian shape of the distribution function. However, because MHD is relatively simple and captures many of the important properties of plasma dynamics it is often qualitatively accurate and is almost invariably the first model tried.

Effects which are essentially kinetic and not captured by fluid models include double layers, Landau damping, a wide range of instabilities, chemical separation in space plasmas and electron runaway.

 

[brantc]

Nonsense.

First off, whether you take a particle view or an MHD view, the magnetic and electric fields contain energy, and it's the same energy in either case.

Second, the only other form of energy available is kinetic energy (since we're not talking about fusion right now). In the particle view, we can calculate this by looking at kinetic energy of individual particles and adding them up. But we can ALSO get that energy by calculating a center-of-mass kinetic energy plus a kinetic energy of each particle relative to this center of mass. Both methods are mathematically identical.

But guess what: MHD will contain this exact same energy. The first quantity is the kinetic energy of the fluid, the second quantity is the thermal energy of the fluid. The energy is exactly the same.

But where does that energy come from??? Does it come from the particles that have picked up EMF at the beginning of the "tube" from an electric field or does it come from the external magnetic field that imparts the emf to the particles?
MHD says it comes from the external magnetic field. PIC says it comes from kinetic particles.

When you use MHD you cannot differentiate because you cannot see below macroscopic.
You say things like frozen in fields, twisting (of the tube) is caused by rotating of the attached body of mass, etc. because you are confined to using an approximation.

All of these effects can be attributed to current flow-right hand rule which can only be shown by PIC.

 

[Ziggurat]

But where does that energy come from???

What energy are you referring to? The kinetic energy of the particles?

MHD says it comes from the external magnetic field. PIC says it comes from kinetic particles.

"kinetic particles" makes no sense. Particles have kinetic energy, but they are not "kinetic particles". That energy is included in MHD in both the kinetic energy of fluid flow and thermal energy of the fluid. In both pictures, energy can be transfered from fields to kinetic energy of particles, and vice versa. In both pictures, different particles can exchange kinetic energy with each other. Energy isn't what makes MHD and a particle picture different.

All of these effects can be attributed to current flow-right hand rule which can only be shown by PIC.

What the hell are you talking about? The right hand rule is a basic part of Maxwell's equations (in fact, of any equation which uses a vector cross product), and MHD incorporates Maxwell's equations entirely, so MHD rather obviously includes the right hand rule.

 

[tusenfem]

The last sentence means that MHD, when they describe turbulence effects, the cause is from the outside in, like a fluid. The environment is causing the perturbations. Its because they dont consider the particle to provide the energy for the reconnection that they use MHD. Thats why when you look at a MHD simulation it looks like water turbulence.
It does not look like plasma instabilities which form from the particles up.

And that is why reconnection cannot happen in MDH, as I already claimed pages ago.

However, there can be normal cascading and inverse cascading of energy in MHD, so it can easily go in both directions (actually I just co-authored a paper on that).

It is the interactions between the particles that cause the large scale instabilities as experimentally show by Peratt.
http://www.scribd.com/doc/14145750/...urrent-ZPinch-Aurora-as-Recorded-in-Antiquity

Oh dear Peratt and his antique Z-pinches ...

That is the problem with MHD. It works good for easy calculations on bulk flows but tells you nothing about the energetics. And your computer wont explode from too many calculations......

PIC starts with the particles being the source of the energy for the current channels and the curl field. The parallel field can be either induced or external.

We know that the particles provide the energy in the LAPD experiments.

So if we know that MHD fails at a limit or is an approximation, then why do we put so much weight on MHD simulations??????
Look into MHD fluid pumps. They are amazingly inefficient.

When you use MHD there is no room for particle simulations so you automatically use your MHD hammer on the flux tube screw.....
It confines you to the idea that the energy is supplied from an external magnetic field.

Here in wiki they say Structures in MHD systems. There is no such thing as a MHD system. You can characterize a system using MHD formulations but the system itself is a plasma particle based system.
http://en.wikipedia.org/wiki/Magnetohydrodynamics#Structures_in_MHD_systems

Instability is different from turbulence.

First of all, MHD is a wonderful tool that can be used throughout most of astrophysical and space plasmas. Even the "frozen in field" that results from MDH is observed to be a very good approximation for the observations and people have a hard time finding observations that show that the froze in condition is violated (somewhere there is a Lui et al. paper in this thread that discusses this, if I am not mistaken).

Secondly, all numerical research was done in MHD because that was the only thing that people were even reasonably able to model on a computer. Basically, one has to merge MDH codes (to get a look at the global pattern) and PIC codes to get the details that are happening in the Rx region. It was, and still is impossible to model, e.g. the whole magnetotail of the Earth in a PIC simulation, however, computers are getting faster, memory is getting bigger, but still the enormous amounts of particles that you have to follow is mind boggeling, and therefore a merging technique will have to be used, and various groups are working on that.

Basically, the Earth's magnetosphere can be well described with MHD so, one could say it is an "MHD system" not that I like the term, but then that's WIKI for you.

 

[tusenfem]

Yes that may be true by your definition but you have just confirmed the point to this discussion, that there are current carrying plasma discharges that follow the right hand rule. And they dont need field aligned currents.
Plasma filled flux tubes are just another manifestation of plasma currents.

Have I EVER said that a current (e.g. flowing along a field line) does not generate a toroidal magnetic field? NO NEVER. Don't try twisting my words into something that I never said. This toroidal field is WHY we get the flux rope structure.

And no, these currents don't need a field to flow along, and I have never claimed that currents need that. However, when MM comes with his Birkeland currents again, these per definition are flowing along field lines.

In the case of a discharge/lightning, the current just follows the path along which the break down has taken place. That is a small channel of ionized gas bounded on all sides by neutral gas, so the only way the current can flow is along that ionization channel.

That is one of the most amazing things I have heard. This mathematical entity called flux tubes can get together.
There is nothing there. Nothing extends from any electrode to any other electrode except a continuous field..
I might as well define a flux tube that goes from the center of the galaxy to our sun......

Well, I am sorry if my explanation is too difficult for you imagination.

How can something that you have defined, that is not real, not physical have properties?? The flux tubes as you have defined them are part of the background parallel field.
They have no independent life or function of their own. The background field is unchanging and smooth. The flux tube could never change or do anything unless you change some parameter in your equation since they are defined by your equation.

A bit of creative thinking trying to envision where I am going with this "gedanken experiment" would not hurt you.

And then when you turn the current on, your prediction is not going to match. All the flux tube work is empirical. So you cant even say you flux tube definition is a prediction except in the broadest sense of there will be 2 current channels with a twist..

Oh for goodness sake, read Intrator et al. 2009, where there are two flux ropes interaction, note that I say flux ropes, meaning that current is flowing.

Do you see? The flux tubes have no relation to any physical parameter...
You cant just say they might touch. The only way that the "flux tubes" might touch is from a sausage or kink instability and that has nothing to do with the parallel field. That is a result of the right hand rule or curl. And this would only happen with plasma.

Like I say a little creative thinking for educational purposes goes a long way.

They do not exist except in math. I would even venture to say that they are just wrong as defined.

It would be better to say the "area enclosed by the plasma column is the ~area to be considered in calculating the effect of a parallel field on the plasma column".

Cause and effect, causality.

Well, maybe you should rewrite all the plasma physics books.

 

[tusenfem]

From wiki.

Wow, this is getting convoluted.

Here, I ask brantc what he means by what he writes.

Then here MM answers for brantc

And then I ask MM a question

and then brantc tries to answer for MM, but only quotes what limitations there may be on MDH.

Is there a symbiosis going on here, or is this Jackyll & Hyde?

However, it is rather clear that brantc has no idea what MHD is and how it works or which equations it uses, as is clear from his discussion with zuggurat (and me). Apparently the right hand rule rules the world.