Problems With Magnetic Reconnection

[sol invictus]

Is B an infinite vector field or is it not?

yes or no.

I have no idea what you mean by "infinite vector field", that sounds like a term you invented all by yourself.

The magnetic field [latex]$\vec B(x,y,z,t)$[/latex] is a standard real-valued vector field. Zig just gave you an explicit and very simple example of one that reconnects.

 

[Ziggurat]

Fälthammar explains:
http://plasma.colorado.edu/phys7810/articles/Falthammar_MovingFieldLines_2007.pdf

The author argues against using a particular equation when certain conditions required for that equation do not hold. He further points out that "the most interesting plasma physics occurs precisely where and because this equation is not satisfied, such as the auroral acceleration region, magnetic field reconnection, turbulence, shocks, and many wave modes."

Read that sentence carefully. He's saying one cannot use a particular equation to describe magnetic reconnection. But do you know what that means? It means that the author is saying that magnetic reconnection is real. He's saying that if one isn't careful, one can handle it incorrectly, but he's also saying it's a real and interesting phenomenon. Furthermore, he is NOT claiming that everyone who works on magnetic reconnection is doing it wrong. No such claim exists within that paper.

 

[michaelsuede]

I have no idea what you mean by "infinite vector field", that sounds like a term you invented all by yourself.

The magnetic field [latex]$\vec B(x,y,z,t)$[/latex] is a standard real-valued vector field. Zig just gave you an explicit and very simple example of one that reconnects.

I mean a magnetic field is a vector field that has no end and extends for eternity.

Given that this is indeed the case, in order for a null point to exist, it must take form of an infinitely small point.

This is impossible.

 

[Ziggurat]

Is B an infinite vector field or is it not?

yes or no.

I have no idea what you mean by this.

I do know, however, that the magnetic field equation I gave you satisfies Maxwell's equations, it is a rigorously defined vector quantity at every single point in space, and it is therefore a valid magnetic field.

If I am wrong about that, you should be able to demonstrate my error rather simply. Just find a point where the field is not defined, or calculate the divergence to show that it's nonzero.

Do you know how to calculate the divergence of a vector field?

 

[michaelsuede]

The author argues against using a particular equation when certain conditions required for that equation do not hold. He further points out that "the most interesting plasma physics occurs precisely where and because this equation is not satisfied, such as the auroral acceleration region, magnetic field reconnection, turbulence, shocks, and many wave modes."

Read that sentence carefully. He's saying one cannot use a particular equation to describe magnetic reconnection. But do you know what that means? It means that the author is saying that magnetic reconnection is real. He's saying that if one isn't careful, one can handle it incorrectly, but he's also saying it's a real and interesting phenomenon. Furthermore, he is NOT claiming that everyone who works on magnetic reconnection is doing it wrong. No such claim exists within that paper.

ok

How about this one from Fälthammar

http://www.geofisica.unam.mx/divulgacion/geofinternacional/iframes/anteriores/2004/02/Falthamar.pdf

What Fälthammar means by "reconnection" is an exploding double layer.

 

[sol invictus]

I mean a magnetic field is a vector field that has no end and extends for eternity.

Still gibberish. Do you mean you're interested in considering a vector field defined on a spacetime without boundary? If so, that's totally irrelevant to this, but OK.

Given that this is indeed the case, in order for a null point to exist, it must take form of an infinitely small point.

This is impossible.

Wrong again. See e.g. Zig's example.

 

[godless dave]

I shall, in this article, attempt to illuminate the problems with current magnetic reconnection theory. In order to do that, I will first have to try and describe in layman’s terms just what the standard theory says occurs when magnetic reconnection takes place. The scientific press has been rather mute in portraying the problems with this theory.

Generally, when it seems like the scientific establishment is mute on the problems with a theory, it's because those problems either don't exist or aren't very significant.

 

[michaelsuede]

I have no idea what you mean by this.

I do know, however, that the magnetic field equation I gave you satisfies Maxwell's equations, it is a rigorously defined vector quantity at every single point in space, and it is therefore a valid magnetic field.

If I am wrong about that, you should be able to demonstrate my error rather simply. Just find a point where the field is not defined, or calculate the divergence to show that it's nonzero.

Do you know how to calculate the divergence of a vector field?

I know that the B field of any charged object extends for eternity.

If you agree that the B field is an infinitely extending vector field that has no end, then simple logic dictates that magnetic null points are impossible.

 

[Ziggurat]

I mean a magnetic field is a vector field that has no end and extends for eternity.

The equation I gave you does that.

Given that this is indeed the case, in order for a null point to exist, it must take form of an infinitely small point.

Nope. That's not a requirement at all. In this particular case, the volume of the null point is indeed zero, but 1) that's particular to this field, and 2) that's hardly impossible, I just gave you a field which does exactly that and which is a perfectly valid magnetic field. There are plenty of valid magnetic fields with zero-volume null points.

This is impossible.

Indeed. It's impossible to talk about electrodynamics with someone who doesn't understand electrodynamics.

I mean, seriously, have you EVER studied the subject? Ever read a single textbook? Do you know what Maxwell's equations actually mean? Do you even know any vector calculus? Because so far, you don't seem to have a clue about the actual math involved. And that seems to be the sine qua non for physics cranks.

 

[michaelsuede]

The equation I gave you does that.



Nope. That's not a requirement at all. In this particular case, the volume of the null point is indeed zero, but 1) that's particular to this field, and 2) that's hardly impossible, I just gave you a field which does exactly that and which is a perfectly valid magnetic field. There are plenty of valid magnetic fields with zero-volume null points.



Indeed. It's impossible to talk about electrodynamics with someone who doesn't understand electrodynamics.

I mean, seriously, have you EVER studied the subject? Ever read a single textbook? Do you know what Maxwell's equations actually mean? Do you even know any vector calculus? Because so far, you don't seem to have a clue about the actual math involved. And that seems to be the sine qua non for physics cranks.

lines are not vector fields, which encompass 3 dimensions.

If I'm understanding your argument correctly, you are making the claim that there are points in space where the magnetic field is perfectly counter balanced at all points in a sphere leading to a condition where B=0.

All of this taking place right in the middle of a current sheet no less.

That is what you are claiming right?

 

[ben m]

With a peer reviewed paper no less.

You linked to a peer reviewed pedagogical paper which argues the following points:

"The first kind of problem is that the construct of moving field lines is sometimes used to produce the incorrect magnetic field evolution ... "

"The second concern is that the construct of moving field lines is sometimes confused with the concept of moving flux tubes."

and whose overall message is "don't teach your students the equation of motion for field lines without teaching them these caveats."

This does not argue any of your points, which were "field lines are ill defined" (wrong) and "field lines mathematically cannot cross" (wrong). It is, however, a pretty good argument in favor of my point: You, personally, don't know enough plasma physics to conduct a coherent discussion of it. All you have is a pile of Alfven-ite literature that you don't quite understand; you're going to shovel it out randomly and declare intellectual victory after each shovelful.

 

[Ziggurat]

I know that the B field of any charged object extends for eternity.

Then you know something which is not true, because magnetic fields don't come from charges, they come from currents, and one can in fact create closed magnetic field configurations rather easily. A toroidal solenoid is the prototypical example.

If you agree that the B field is an infinitely extending vector field that has no end, then simple logic dictates that magnetic null points are impossible.

Simple logic dictates nothing of the sort. Neither does the actual math. But then, I doubt you'd know anything about the latter.

 

[michaelsuede]

You linked to a peer reviewed pedagogical paper which argues the following points:



and whose overall message is "don't teach your students the equation of motion for field lines without teaching them these caveats."

This does not argue any of your points, which were "field lines are ill defined" (wrong) and "field lines mathematically cannot cross" (wrong). It is, however, a pretty good argument in favor of my point: You, personally, don't know enough plasma physics to conduct a coherent discussion of it. All you have is a pile of Alfven-ite literature that you don't quite understand; you're going to shovel it out randomly and declare intellectual victory after each shovelful.

So you are claiming that two differing plasma fields will not bound themselves by a double layer?

I just want to be sure I'm reading your non-argument correctly here.

Given that you are engaging in ad homs rather than explaining why there is no double layer, I will consider that a victory for my cause.

 

[sol invictus]

What is wrong with this B-field, Michael?

{Bx,By} = {b*y, a*x}

And why don't you illustrate for us that you understand freshman-level electrodynamics by computing its curl and divergence. If you cannot do that in your head or in a few seconds on paper, you have no business whatsoever discussing this topic.

Can you do that?

 

[michaelsuede]

What is wrong with this B-field, Michael?

{Bx,By} = {b*y, a*x}

And why don't you illustrate for us that you understand freshman-level electrodynamics by computing its curl and divergence. If you cannot do that in your head or in a few seconds on paper, you have no business whatsoever discussing this topic.

Can you do that?

I can compute that there is no such thing as a null point singularity in real 3 dimensional space.

Especially in the middle of a current sheet.

 

[sol invictus]

I can compute that there is no such thing as a null point singularity in real 3 dimensional space.

Gibberish.

What are the divergence and curl of that B-field, Michael?

 

[ben m]

Given that you are engaging in ad homs rather than explaining why there is no double layer, I will consider that a victory for my cause.

I am shocked and appalled. Etiquette demands that you blockquote 10kb of text from plasmacosmology.info before declaring victory. A photo of Birkeland's terella would be acceptable if both seconds agree.

 

[Ziggurat]

lines are not vector fields, which encompass 3 dimensions.

I know that. Which is why I started out with an equation for the vector field. That equation gives you a vector quantity at every single point. It was a vector field. Given the vector field (which I specified), one can THEN draw field lines to illustrate that vector field. But the vector field obviously remains, I already defined it, and it's defined everywhere, even where I did not draw the lines.

If I'm understanding your argument correctly, you are making the claim that there are points in space where the magnetic field is perfectly counter balanced at all points in a sphere leading to a condition where B=0.

No, you aren't understanding me at all. The volume over which the field may or may not be zero depends upon the system under consideration. For a toroidal solenoid, the field is completely confined to the solenoid, and is zero everywhere outside the solenoid. If one has a spherical shell of superconductor with nothing inside, then the field will be zero within that sphere. If one has a cylindrical wire with uniform current flowing through, then only the central axis (a zero-volume null point) has zero field. It all depends on the system you're looking at.

All of this taking place right in the middle of a current sheet no less.

I said nothing about current sheets, so this is complete nonsense.

That is what you are claiming right?

Not even close.

 

[dafydd]

Not with me you haven't.

I'm specifically looking for an explanation as to why two differing plasma fields should not have a double layer boundary.

The lack of such a boundary is required for MHD models have any validity at all.

Astrophysicists are basically denying that double layers exist between differing plasmas by ignoring them.

Either circuit theory is wrong and there is no such thing as a double layer, or MHD reconnection is wrong.

One or the other.

Chose which theory to mock.

What makes you so special? All your points have already been answered in other threads. Come back when you win your Nobel prize.

 

[dafydd]

I can compute that there is no such thing as a null point singularity in real 3 dimensional space.

Especially in the middle of a current sheet.

Can you translate that into English? We don't speak gibberish here.