I've read that stars are so highly conductive that "the electric field goes to zero in a frame of reference co-moving with the magnetic field."

I get electricity and magnetism, but I don't understand what that means exactly. I don't understand how a magnetic field can exist without a permanent magnet or some voltage/current.

Also, can anyone give a dumbed-downed explanation of "magnetic recombination," which is a concept that I think may be related to the set-in magnetic field line idea, that two of the lines combine or collide or something, not really sure. They both seem to treat magnetic field lines as physically real somehow.

Needless to say I don't have a clue, can anyone help?

Well, you ain't asking the difficult questions, are you?

Secondly, if this is just a question, I would like this moved to Q&A or general physics, because I certainly am not going to give ATM answers on this topic.

Let's see what we can do here. Magnetic fields and plasmas and current go all together. Now, you have to be a little versed in electrodynamics and stuff to work on the topics that you mention here.

Naturally, magnetic fields are either created by a solid magnet or by currents, there is no other way. So for plasmas, stars etc. we have currents that take care of the generation of magnetic fields. Note, however, that it need not be local currents that generate the magnetic field, like the magnetic field of the Earth, which is generated in the core of the Earth, but extends many Earth radii outside of it.

Now, Hannes Alfvén, while developing the theory of MagnetoHydroDynamics (MHD the theory of the dynamics or magnetic fluids) came up with an interesting phenomenon. Generally you find that for a plasma there is an Ohm's law, just like in electric circuit theory, but there are some more terms in this law, when dealing with a plasma. Therefore, they call it the generalized Ohm's law. I will only write a little bit of it down here which is important for your question about frozen in fields:

E + v x B = η J

This says that the current density J is dependent on the electric field E and the velocity of the plasma and the magnetic field in the plasma. A moving or changing magnetic field generates an electric field, this is how the dynamo on your bicycle works. Here η is the resistivity of the plasma. You see that, if the plasma is very conducting then the value of η is very very small and the right hand term of the equation is negligible and we end up with:

E + v x B = 0

This is the "frozen in condition" as found by Alfvén. If the above holds, then you have to do some math here which I will only describe here in words. Take a surface that consists of magnetic field lines, and so that all the field lines lie in that surface. Then you move this surface with the flow and because of the flow the surface can have changed. However, because of the condition above, you will find that still all field lines are in that surface, non of them has suddenly obtained a direction perpendicular to that surface. This means that the magnetic field moves along with the flow of the plasma and thus can be said to be frozen in.

One thing you will have to keep in mind, though, is that this is an approximation. Although the resistivity of the plasma is very small, it will never truly be zero. Thus, the frozen in condition does not hold indefinitely. There is something called the diffusion time scale, at what rate a magnetic field can diffuse through a conductor, which is dependent on η. The smaller η the longer the diffusion time. So, one can only assume frozen in fields on timescales shorter than that diffusion time (something which sometimes gets forgotten, also by scientists).

A dumbed down version of reconnection?
Two oppositely directed magnetic field lines touch somewhere in the middle and reconnect themselves into two new field lines. (is that dumb enough?)

Naturally I do not know what you know, but I will give you the basics of the Petchek mechanism. Here you have a magnetic field with one direction at z < 0 and another at z > 0

Now, imagine that something presses the fields together in the middle. The you will get something like this

Now in the flat region in the middle the total magnetic field will be zero in this simple but realistic model, and actually there is no field exactly in the centre. Thus there is a possibility that the field lines re-arrange themselves. Now, the exact micro physics of this re-arranging/re-connecting is not know. Note, that field lines are not real objects, they only give the direction of the magnetic field. However, one can find from Maxwell's equations that field lines cannot be cut. But then you have to take into account that we are dealing with a region where the total field disappears, and thus talking about field lines does not make sense anymore.

However, in the end you end up with the following situation:

and you see that the topology has changed.

This is in a nutshell magnetic reconnection.

__________________
************************************************** *************************
Optimism does not change the laws of physics. (T'Pol)
A good scientist has freed himself of concepts and keeps his mind open to what is. (Dao De Jing 27)
************************************************** *************************
Martin ( http://www.geocities.com/DrMartinV )

Tusenfem,

Thank you very much for your well written and informative answer. You cut right to the heart of what was confusing me. I mean, really, this was just fantastic.

I have follow up questions if you're bored and feel me worth of further enlightenment.

Thanks for bringing up the general form of Ohm's law. I'd seen that before but I was under the mistaken impression that the set-in assumption was based on the idea of current density going to zero, which is actually not even a variable in the equation! D'oh.

I'd like to know if resistivity is the method by which a mechanical/fluid dynamic analysis of a plasma combines and interacts with an EM analysis. I've read that the set-in assumption holds better in the case of cooler and denser plasmas and from what you told me I think I can make sense of why the assumption would work in that case. I'm curious about ordinary situations. Would a rigorous analysis take the general form of Ohm's law, put the proper d's in to make it into the differential form - Jdn/dt+ndJ/dt = d(E + v x B)/dt (I'm no math whiz and then integrate up? The real fun part there would be looking at physical qualities like density and temperature to determine dn/dt (change in resistivity), which will probably end up being a non-linear function of basically every variable in the system. Of course by "fun" I mean setting up a bank of high powered computers to crunch through numerical methods calculations.

About the magnetic recombination. I'm still a bit confused. The graphics you drew looked a lot like a plasma z-pinch, where two birkland currents twist together. If the lines in your graphs were current lines and there was mass in the system I think that's what a z-pinch would look like. Are z-pinches and magnetic recombination related in any way?

Also, I'm confused as to how or why changing magnetic forces in empty space can release energy. I thought that the magnetic force didn't really exist unless there was a particle in the field for it to act upon, like how the electric force doesn't really exist in a system with just one electron. If the "set-in lines" of a plasma were "combining" I could see how that might release energy, because the materials are coliding, but I'm confused as to what would be going on in empty space.

One thing Tusenfem forgot to mention in his reconnection part is that there is a cross current a z=0.

I dont think that z-pinch and reconnection are all that related. A reconnection is more a reconfiguration of field lines than anything else.

As for how magnetic fields can release energy, there is an inherent energy contained in every magnetic field. Should this field be changed, then there can be an energy release. What seems to be confusing you is the difference between energy and force. Without another particle, a field does not exert a force, but it still can contain some energy.

If you have 'set-in lines' of a plasma that are recombining, then the space isnt empty. You have to have some currents to make the changes.

Lastly, unless you are going to start in with an ATM theory, you should ask to have this thread moved to Q&A. So far it is completely mainstream.

In reply to the location of this post, I apologize if I'm rocking the boat. I was reading EU/Plasma cosmology sites that brought up the set-in lines and recombination ideas. I figured since I read about them there discussions belonged on this thread. I got the impression that this forum takes the with/against the mainstream split very seriously and I did not want to anger anyone by putting an EU idea in an improper subject heading.

I think that I'm ready to make an "against the mainstream point" though. From what I now know about the set-in field assumption, I can't imagine it actually holds for the Sun. Hydrogen atoms are not very conductive, the overall density is just a little above that of water, and the overall ionization is low. Also, the internal flow dynamics of the fusion model seem to contradict the notion of the constant and very small resistivity, all that churning would have to create local eddys of density or something, I just don't get how the inside of the sun can have all kinds of highly energetic collisions and interactions happening but still maintain the uniform and very small resistivity the set-in line assumption requires.

The plasma theory explanations for the surface phenomena seem much more rigorous and verifiable. The explanation of sun spots as a break-down in a dual layer does a fine job of explaining the observed magnetic fields that result. The notion of the dual layer at the surface makes good sense out of the light coming from the surface. It makes good sense of the magnetic field dynamics at the surface. It makes good sense of the cause of flares and CME's. Perhaps it's not against the mainstream, but I think what's going on with the conventional solar models is they've made a simplyfying assumption that doesn't actually hold for the system they're evaluating. To properly model the sun probably requires calculating internal voltages and dynamically modeling the whole thing with non-linear differential equations and numerical methods.

I can't imagine how the very small resistivity assumption would be checked against experiments in the sun. In basic equilbrium chemistry you always end up with dx/(x-dx) as one part of the equation. The simplifying assumption is to say dx<<<x, and that the equation can be rewritten as dx/x, which is much simper math. To check the result, you take the dx from the new equation and compare it to x, if dx is calculated by this method to be very small then you're good, but if it's like 5% of x or anything then you have to go back and do the problem completely right. How do the solar model makers check the set-in line assumption? I can't really think of a way how.

About the magnetic recombination, I'm very skeptical of the idea that "there is an inherent energy contained in every magnetic field line." Without something for the force to act upon the force does not exist. One electron by itself does not exert an electric force on anything. Also, since a magnetic field cannot do any work, how does a line contain a potential energy?

I'm willing to believe that the internal dynamics that create the two magnetic fieilds whose lines are being considered can affect each other at a distance, and if this "recombination" energy is released in the matter where the current is flowing and making the magnetic field then I'm fine with the theory. But if the theory says that energy will suddenly appear in empty space because theoretical abstractions of potential forces that aren't actually occuring go to zero, then I'm going to need some experimental proof before I buy into it. As far as I know there have never been actual experiments, just computer simulations that only fully describe the hypothesis and can't test anything.

There isnt any anger, it is just that ATM has different rules than Q&A.
Both statements are irrelevant. The overall density may be low, but the local density at any depth rises rapidly. Temp and ionization also increase with depth also. While the photosphere may be very low pressure and ionization, the interior is very ionized and high pressure.
Again, the interior is ionized and high pressure. You cant avoid the energetic collisions.

Also, the Sun's global dipole field is not a frozen in field. It is a generated field, so all the restrictions to keep a frozen in field dont apply. The dipole field is generated due to turbulence at the base of the convection zone.
Even if this paragraph were correct, it still dosent cange the fact that the current model also explains the surface dynamics of the sun quite well also.

What simplifying assumption do you think has been made to the solar model?

Again you dont seem to understand the internal structure of the sun. The interior is ionized gas at relatively high density. It dosent have an internal voltage or an internal voltage gradient, and the whole this is modeled by non-linear differential equations and numerical methods. Where do you think the current models come from, fortune cookies?
First, the sun isnt chemistry, it is physics. Second, the solar model is based on having a ball of gas a temp K, surface density p, total mass M, luminosity L, magnetic field g, rotation rate ln, composition H,He,Z, then they take the laws of physics and start numerically solving these laws for the shell just inside the current shell. They continue the process from surface to core.
Be as skeptical as you want, but read a physics book. Any field has an inherent energy involved with its creaton. For magnetic fields, look at the energy required to create the magnetic field in an inductor when a voltage is applied. The energy in a magnetic field is a well known quantity. Again, there is a difference between a force and an energy. You can have energy without force and force without energy.
And you would be wrong. Reconnection is an active field of study in physics. It isnt a magic energy from nothing, it is generally and energy release from a magnetic field that is reconfiguring itself into a lower energy state.

One of my current fields of study is plasma detachment in the magnetic nozzle of the VASIMR. Basically, this involves the plasma exhaust of the rocket causing a reconnection to get off of the confinement field lines so it can flow away from the rocket.

My understanding of magnetic reconnection, is that the "reconnection" does not necessarily imply that fields lines "break" resulting in two open field lines (which I think would violate Gauss's Law). There appears to be no doubt that field lines appear to re-configure, and if you blink, you might think (mistakenly) that the field lines broke, and reconnected.

It was Hannes Alfvén (last week was the 100th anniversary of his birth) who came up with the concept of "frozen-in" magnetic field lines, but only under certain circumstances (in infinitely conductive magnetized fluid). Alfvén wrote:

Alfvén continues:
You can read Alfvén thoughts on the matter in his Keynote Address of the Double Layers in Astrophysics symposium, Proceedings, NASA Huntsville, Alabama March 17-19, 1986 (see section III. Double Layers and Frozen-in Magnetic Fields Lines) (Record | Full text (PDF)).

__________________
Ian Tresman
plasma-universe.com

As an additional side note on the frozen-in condition: In real plasmas, the magnetic field will eventually decay away. In that respect, frozen-in is a misnomer. If actual useage, frozen-in is a handy way of looking at different time scales.

Say you have a highly conductive plasma with a set field in it. For purpose A, we are looking at what happens when the field is turned off. In this case, the field is not frozen in. It decays away very quickly. For purpose B, we are looking at a high frequency wave in the plasma. In this case, looking at any one wave, the field is frozen in. The reason it is treated as frozen in it that in the time period of any one wave, the change in the field is very small. What is interesting is that it is possible to do both purpose A and purpose B at the same time in the same plasma. The only real change is that you would be looking at a set of high frequencies for purpose B, each of which is treated as a different frozen in field as the field decays away. Eventually the period of the wave will get too long, and the assumption that the change in the field is small over the period of the wave will no longer apply, and you will have to treat your waves differently.

Thanks to iantresman for the alfven link, I'll give it a read.

And Korjik, at the end you wrote:

"One of my current fields of study is plasma detachment in the magnetic nozzle of the VASIMR. Basically, this involves the plasma exhaust of the rocket causing a reconnection to get off of the confinement field lines so it can flow away from the rocket."

First, that's totally awesome. I wish I were working on the VASIMR engine. Second, the notion of magnetic recombination suddenly makes sense - I think Could I think of magnetic field lines as a kind of inertial crevace for a charged particle? In that an electron or proton moving on a magnetic feild line will tend to continue on the path of that line, rather than in a straight line (same direction as the velocity vector) which is the path delineated by more conventional inertia for a neutral particle. That engine uses dueterium right? So you have the proton/neutron pair of the dueterium nucleus moving along one magnetic field line inside the acceleration chamber, but it won't propel the rocket forward if it goes in a circle, it has to move straight back and away from the rocket for that to happen. So that saddle-point shape that magnetic recombination describes, if one of those forms at the exhaust nozel, then the dueterium nucleus can kind of "slide" (maybe?) from one magnetic field line to another and then continue to move straight away from the engine instead of in a loop around the chamber that's generating the magnetic field.

Am I on the right track? In my mind I'm trying not to think of a magnetic field line as a potential force, but rather as an inertial characteristic of space. The magnetic recombination theory then says that when two sources of magnetic force are competing to create inertial characteristics of space, the forces do not cancel out. Rather one's dominance controls the inertial characteristic, and when they equal each other a stress of independant energy and effect arises (perhaps they never really equal each other, but rather churn on some quantum level). This stress would then allow for observations that look like "broken magnetic field lines." While the theoretical plot shows circular paths for particles where one would nudge right up against the region and then do basically a U-turn, a particle could enter the area one one magnetic feild line and leave on another because it can slide between inertial crevaces where they intersect. The second and third pictures from the first reply from tusenfem is what I'm looking at when I talk about paths and u-turns and slides.

I'm probably about to sound like a fool, but could the tendency of the ion to leave the nozzle be different if you used regular hydrogen instead of deuterium? I'm thinking that the neutron in the deuterium nucleus should have standard traditionial inertia as it's about to get near the nozzle, could it be that the inertia of the neutron helps slide the nucleus onto an outflow path? Or is the energy of the recombination event what pulls the ion outside the engine?

I think I should also probably concede this post properly belongs in Q&A. Clearly I'm not the one with any theory to speak of I really appreciate all the answers to my questions though. This is very interesting.

Thanks for finding that omission, dear friend. Indeed, I should have mentioned that in this simpified model there is a current coming out of the screen, which makes it possible for the to oppositely directed magnetic fields to exist.

Ah, you may have misunderstood my drawing here, the arrows are the direction of the magnetic field, not the direction of currents. So, there are no Birkeland currents (field aligned currents) there is only a current coming out of the screen.

A z-pinch is much different, there we have the following situation:
1. A bunch of magnetic field lines (say for simplicity a pencil) pointing in one direction.
2. For some reason or other there is a field aligned current (you might want to call it Birkeland current, but I am a purist, and Birkeland currents are only a special current system in the (Earth's) magnetosphere for me). There is a battery working that drives the aligned currents. Dashed lines are magnetic fields, dotted lines are current:
3. The currents that are flowing create their own magnetic field which is circular around the magnetic field lines that are drawn in the figure above.
4. Now if the current gets strong enough the magnetic tension of the new field can start to "pinch" the original magnetic field and plasma. This is given by the Bennett relation, which says that 2 N k (Te + Ti) = mu I² / 4 pi mu0 (look e.g. at the wiki page on [ulr=http://en.wikipedia.org/wiki/Bennett_Relation]pinches[/url]).
5. Then we get the following (if I can draw it)
where there should be more dashed lines in the compressed centre here.
6. Note that all field lines are in the same direction. Note also that I am unable here to show that the field is not straight but twisted like a rope (magnetic fields add up vectorially)
7. So no reconnection can happen, because there is no oppositely directed field.

Basically the magnetic fields are stretched because the foot points remain at one location (e.g. the Earth) an get drawn along with the plasma "in the middle" (e.g. in the Earth's magnetotail by the solar wind). This means that like a rubber band there is energy stored in the field (magnetic tension) and when, like in the first drawing very much above, the reconnection takes place, the part on the side of the Earth shoots back, relaxing the tension. and thereby pulls along the plasma on the field lines, and that is how magnetic energy is converted to bulk motion of plasma.

Resistivity is a characteristic of ANY CONDUCTING MEDIUM and has to do with the collisions that the current carriers (most of the time electrons) make with the surroundings (to keep it simple). In plasma physics, to obtain e.g. the wave modes that are possible, one needs to calculate the eigen functions of the dielectric tensor, and the plasma conductivity comes in in some way (this is way to complicated to put here on the board, you need to read an introductory book on plasma physics).

The generalized Ohm's law has many many more terms, if you are really interested, here it is (from Cravens, Physics of solar system plasmas, 1997):

E = - u_e × B - (n_e e)^-1 grad(p_e) + m_e g/e + m_e/e Σ_t≠eν[sup]et[/sub](u_e=u_t) - m_e/e (du_e/dt + u__e·grad(u__e)

And this is the starting point, basically, of all plasma physics. The term you see with the summation basically describes an effective resisitivity through collisions with other particles (the nu is the "collision frequency").

So, no you cannot just "derivative" the short equation that I wrote down.

I noticed, at a quick glance in your solar model thread in Q&A several misconceptions about plasma physics. I will see if I have the time today to answer you further. Don't forget that there is a (now inactive) thread called plasma physics for dummies.

__________________
************************************************** *************************
Optimism does not change the laws of physics. (T'Pol)
A good scientist has freed himself of concepts and keeps his mind open to what is. (Dao De Jing 27)
************************************************** *************************
Martin ( http://www.geocities.com/DrMartinV )

Thanks for finding that omission, dear friend. Indeed, I should have mentioned that in this simpified model there is a current coming out of the screen, which makes it possible for the to oppositely directed magnetic fields to exist.

Ah, you may have misunderstood my drawing here, the arrows are the direction of the magnetic field, not the direction of currents. So, there are no Birkeland currents (field aligned currents) there is only a current coming out of the screen.

A z-pinch is much different, there we have the following situation:
1. A bunch of magnetic field lines (say for simplicity a pencil) pointing in one direction.
2. For some reason or other there is a field aligned current (you might want to call it Birkeland current, but I am a purist, and Birkeland currents are only a special current system in the (Earth's) magnetosphere for me). There is a battery working that drives the aligned currents. Dashed lines are magnetic fields, dotted lines are current:
3. The currents that are flowing create their own magnetic field which is circular around the magnetic field lines that are drawn in the figure above.
4. Now if the current gets strong enough the magnetic tension of the new field can start to "pinch" the original magnetic field and plasma. This is given by the Bennett relation, which says that 2 N k (Te + Ti) = mu I² / 4 pi mu0 (look e.g. at the wiki page on [ulr=http://en.wikipedia.org/wiki/Bennett_Relation]pinches[/url]).
5. Then we get the following (if I can draw it)
where there should be more dashed lines in the compressed centre here.
6. Note that all field lines are in the same direction. Note also that I am unable here to show that the field is not straight but twisted like a rope (magnetic fields add up vectorially)
7. So no reconnection can happen, because there is no oppositely directed field.

Basically the magnetic fields are stretched because the foot points remain at one location (e.g. the Earth) an get drawn along with the plasma "in the middle" (e.g. in the Earth's magnetotail by the solar wind). This means that like a rubber band there is energy stored in the field (magnetic tension) and when, like in the first drawing very much above, the reconnection takes place, the part on the side of the Earth shoots back, relaxing the tension. and thereby pulls along the plasma on the field lines, and that is how magnetic energy is converted to bulk motion of plasma.

Resistivity is a characteristic of ANY CONDUCTING MEDIUM and has to do with the collisions that the current carriers (most of the time electrons) make with the surroundings (to keep it simple). In plasma physics, to obtain e.g. the wave modes that are possible, one needs to calculate the eigen functions of the dielectric tensor, and the plasma conductivity comes in in some way (this is way to complicated to put here on the board, you need to read an introductory book on plasma physics).

The generalized Ohm's law has many many more terms, if you are really interested, here it is (from Cravens, Physics of solar system plasmas, 1997):

E = - u_e × B - (n_e e)^-1 grad(p_e) + m_e g/e + m_e/e Σ_t≠eν[sup]et[/sub](u_e-u_t) - m_e/e (du_e/dt + u__e·grad(u__e)

And this is the starting point, basically, of all plasma physics. The term you see with the summation basically describes an effective resisitivity through collisions with other particles (the nu is the "collision frequency").

So, no you cannot just "derivative" the short equation that I wrote down.

I noticed, at a quick glance in your solar model thread in Q&A several misconceptions about plasma physics. I will see if I have the time today to answer you further. Don't forget that there is a (now inactive) thread called plasma physics for dummies.

By the way it is "frozen-in" field, not "set-in".

__________________
************************************************** *************************
Optimism does not change the laws of physics. (T'Pol)
A good scientist has freed himself of concepts and keeps his mind open to what is. (Dao De Jing 27)
************************************************** *************************
Martin ( http://www.geocities.com/DrMartinV )

It is magnetic reconnection! please keep the terms correct.