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Old 24th March 2011, 11:03 AM   #1
michaelsuede
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Problems With Magnetic Reconnection

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.

For those of you who are totally unfamiliar with the topic, magnetic reconnection is claimed to account for sudden releases of kinetic energy within a field of plasma. Scientists presume these sudden releases of energy are caused by “reconnecting” magnetic field lines. This topic is vitally important in modern cosmology because “reconnection” plays a role in explanations of practically everything we observe in space. Magnetic reconnection is observed to occur on the Sun, in the auroras, in neutron stars, in comets, and practically every other place that matter in a plasma state exists.

Edited by kmortis:  The rest is found here

Last edited by kmortis; 24th March 2011 at 11:59 AM. Reason: Removed to comply with Rule 4
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Old 24th March 2011, 11:13 AM   #2
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Old 24th March 2011, 11:48 AM   #3
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With all due respect, tl;dr.
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Old 24th March 2011, 11:51 AM   #4
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tl; dr. Let's skip the bluffing and go straight to the "tells".

Quote:
In reality, such explanations are totally meaningless. It is meaningless to assert that a field line that was at A is now at B, because there is no way to identify or distinguish one magnetic field line from another in a vector continuum.
Sure there is. Pick a unique point in space. Measure the B field direction. Take a differential step in that direction. Measure the B field direction, take another step. Etc. That traces out a line. This is the definition of a magnetic field line, it's perfectly clear, it ignores E fields by definition.

In any case, it doesn't matter. The "lines" aren't causing anything. Ions and electrons don't care where lines are, they care about local field vectors. If you want to talk about reconnection scenarios purely in terms of the fields, and never mentioning lines, you can do that---the physics is the same, you're just hobbling your ability to describe it to humans.

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Since a magnetic field is an infinite continuum, there can be no splitting and reconnecting of field lines. In order for a field line (which is a mathematical construct used to describe the location of a magnetic field) to “reconnect” it would first have to be spliced in half.
Wrong again. The line "crossing" happens at saddle points, i.e. at places where B=0, where it is perfectly reasonable, indeed necessary, for lines to meet. It does not require a monopole or any Maxwell's Equation violation. Examples are trivial to construct: quadrupole fields like {Bx,By} = {y, x} have "crossing" lines.

Let me give some advice.
  • If you want to make an informed critique of the CIA, don't give in to the urge to blame them for filling the WTC with thermite.
  • If you want to present your ideas for a non-dark-matter cosmology, don't give in to the urge to mention that the Twin Paradox proved Einstein is wrong.
  • If you want to tell the world about your new algorithms for SETI, resist the urge to mention (no matter how excited you are) the inexplicable Face On Mars, the alien-tech Pyramids of Giza, and the Cydonia civilization.
  • If you have a coherent theory of heating in the solar corona, don't append the stupid plasma-cosmology shibboleth that magnetic field lines don't exist and/or cannot cross
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Old 24th March 2011, 12:08 PM   #5
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Originally Posted by ben m View Post
  • If you want to make an informed critique of the CIA, don't give in to the urge to blame them for filling the WTC with thermite.
  • If you want to present your ideas for a non-dark-matter cosmology, don't give in to the urge to mention that the Twin Paradox proved Einstein is wrong.
  • If you want to tell the world about your new algorithms for SETI, resist the urge to mention (no matter how excited you are) the inexplicable Face On Mars, the alien-tech Pyramids of Giza, and the Cydonia civilization.
  • If you have a coherent theory of heating in the solar corona, don't append the stupid plasma-cosmology shibboleth that magnetic field lines don't exist and/or cannot cross
Did you come up with this list before visiting his site? Prescient. However, you forgot the whole global warming is a conspiracy thing.
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Old 24th March 2011, 12:16 PM   #6
michaelsuede
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Originally Posted by ben m View Post
tl; dr. Let's skip the bluffing and go straight to the "tells".



Sure there is. Pick a unique point in space. Measure the B field direction. Take a differential step in that direction. Measure the B field direction, take another step. Etc. That traces out a line. This is the definition of a magnetic field line, it's perfectly clear, it ignores E fields by definition.

In any case, it doesn't matter. The "lines" aren't causing anything. Ions and electrons don't care where lines are, they care about local field vectors. If you want to talk about reconnection scenarios purely in terms of the fields, and never mentioning lines, you can do that---the physics is the same, you're just hobbling your ability to describe it to humans.



Wrong again. The line "crossing" happens at saddle points, i.e. at places where B=0, where it is perfectly reasonable, indeed necessary, for lines to meet. It does not require a monopole or any Maxwell's Equation violation. Examples are trivial to construct: quadrupole fields like {Bx,By} = {y, x} have "crossing" lines.

Let me give some advice.
  • If you want to make an informed critique of the CIA, don't give in to the urge to blame them for filling the WTC with thermite.
  • If you want to present your ideas for a non-dark-matter cosmology, don't give in to the urge to mention that the Twin Paradox proved Einstein is wrong.
  • If you want to tell the world about your new algorithms for SETI, resist the urge to mention (no matter how excited you are) the inexplicable Face On Mars, the alien-tech Pyramids of Giza, and the Cydonia civilization.
  • If you have a coherent theory of heating in the solar corona, don't append the stupid plasma-cosmology shibboleth that magnetic field lines don't exist and/or cannot cross
Throwing out a list of random stuff that has nothing to do with the topic does nothing to diminish the points made in my article.

1. MHD can not describe the double layer condition, which we know must exist between two differing plasma fields.

2. Magnetic reconnection theory does not incorporate a double layer, which we know must exist between two differing plasma fields.

3. Magnetic null points are an artifact of how MHD treats the plasma. As was stated, this treatment is wrong on several levels. Given that an intense electric field is generated along the boundary of two differing plasmas, there is no way that a magnetic null point can form.
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Old 24th March 2011, 12:33 PM   #7
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Haven't we been through all this before?
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Old 24th March 2011, 12:43 PM   #8
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Originally Posted by dafydd View Post
Haven't we been through all this before?
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.

Last edited by michaelsuede; 24th March 2011 at 12:44 PM.
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Old 24th March 2011, 12:47 PM   #9
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Originally Posted by michaelsuede View Post
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.
And you make this point by making points about magnetic reconnection that are wrong... interesting tactic.
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Old 24th March 2011, 12:49 PM   #10
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Originally Posted by Tubbythin View Post
And you make this point by making points about magnetic reconnection that are wrong... interesting tactic.
I didn't say anything wrong.

When a plasma is moving, taking snap shots of the B field and integrating it across time and space while ignoring the parallel electric field, which by necessity is not zero, is meaningless.

Fälthammar explains:
http://plasma.colorado.edu/phys7810/...Lines_2007.pdf

It's a totally pointless exercise used to hide what is really going on.

Last edited by michaelsuede; 24th March 2011 at 12:51 PM.
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Old 24th March 2011, 12:53 PM   #11
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Originally Posted by michaelsuede View Post
I didn't say anything wrong.

When a plasma is moving, taking snap shots of the B field and integrating it across time and space while ignoring the parallel electric field, which by necessity is not zero, is meaningless.

Fälthammar explains:
http://plasma.colorado.edu/phys7810/...Lines_2007.pdf

It's a totally pointless exercise used to hide what is really going on.
Perhaps you should respond to Ben's points then, rather than pretending they're irrelevant.
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Old 24th March 2011, 12:55 PM   #12
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Originally Posted by Tubbythin View Post
Perhaps you should respond to Ben's points then, rather than pretending they're irrelevant.
I thought I just did.

With a peer reviewed paper no less.
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Old 24th March 2011, 12:57 PM   #13
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Originally Posted by ben m View Post
Wrong again. The line "crossing" happens at saddle points, i.e. at places where B=0, where it is perfectly reasonable, indeed necessary, for lines to meet. It does not require a monopole or any Maxwell's Equation violation. Examples are trivial to construct: quadrupole fields like {Bx,By} = {y, x} have "crossing" lines.
Indeed. In fact, we can produce reconnection with only a slight modification. If you use the field

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

then when you change the ratio a/b, you will reconnect points, as shown below:



So the math clearly works. One may dislike the terminology all one wants to, but that's irrelevant. The term is well-defined, and actual magnetic fields which satisfy Maxwell's equations (you can check) fit the description.
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Old 24th March 2011, 12:59 PM   #14
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Originally Posted by Ziggurat View Post
Indeed. In fact, we can produce reconnection with only a slight modification. If you use the field

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

then when you change the ratio a/b, you will reconnect points, as shown below:

http://www.internationalskeptics.com...b6711ad5d6.gif

So the math clearly works. One may dislike the terminology all one wants to, but that's irrelevant. The term is well-defined, and actual magnetic fields which satisfy Maxwell's equations (you can check) fit the description.
B is an infinite vector field.

Therefore for a magnetic null point to exist, the field would have to produce a null point singularity.

Impossible.
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Old 24th March 2011, 12:59 PM   #15
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Originally Posted by michaelsuede View Post
I didn't say anything wrong.
Yes, you did. Your article is wrong.

"In reality, such explanations are totally meaningless. It is meaningless to assert that a field line that was at A is now at B, because there is no way to identify or distinguish one magnetic field line from another in a vector continuum that is moving."

False.

" The only way that the integration even comes close to being valid is when the parallel electric field (the electric field component parallel to the magnetic field line) is zero. This condition is not satisfied in standing theories of magnetic reconnection."

False.

"Since a magnetic field is an infinite continuum, there can be no splitting and reconnecting of field lines."

False.

"In order for a field line (which is a mathematical construct used to describe the location of a magnetic field) to “reconnect” it would first have to be spliced in half. This splicing creates what is tantamount to a magnetic monopole, which we know do not exist."

False.

"It is impossible for a magnetic field line to ever have an end-point. It is no more possible for a field line to have an end point than a contour line on a topographical map to have an end point."

Contour lines on a map of a changing landscape can reconnect for exactly the same reason magnetic field lines can - at a point where the gradient is zero.
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Old 24th March 2011, 01:00 PM   #16
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Originally Posted by sol invictus View Post
Yes, you did. Your article is wrong.

"In reality, such explanations are totally meaningless. It is meaningless to assert that a field line that was at A is now at B, because there is no way to identify or distinguish one magnetic field line from another in a vector continuum that is moving."

False.

" The only way that the integration even comes close to being valid is when the parallel electric field (the electric field component parallel to the magnetic field line) is zero. This condition is not satisfied in standing theories of magnetic reconnection."

False.

"Since a magnetic field is an infinite continuum, there can be no splitting and reconnecting of field lines."

False.

"In order for a field line (which is a mathematical construct used to describe the location of a magnetic field) to “reconnect” it would first have to be spliced in half. This splicing creates what is tantamount to a magnetic monopole, which we know do not exist."

False.

"It is impossible for a magnetic field line to ever have an end-point. It is no more possible for a field line to have an end point than a contour line on a topographical map to have an end point."

Contour lines on a map of a changing landscape can reconnect for exactly the same reason magnetic field lines can - at a point where the gradient is zero.

Great points you made there.

Now tell me why there is no double layer at the boundary of differing plasmas.
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Old 24th March 2011, 01:01 PM   #17
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Originally Posted by michaelsuede View Post
B is an infinite vector field.

Therefore for a magnetic null point to exist, the field would have to produce a null point singularity.
Gibberish. Zig just gave you an example of a B-field that reconnects. It's right there in black and white (or whatever colors you have your display set to).
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Old 24th March 2011, 01:02 PM   #18
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Originally Posted by michaelsuede View Post
Great points you made there.

Now tell me why there is no double layer at the boundary of differing plasmas.
There is no point in discussing advanced topics with you when you do not understand the basics of vector fields.
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Old 24th March 2011, 01:02 PM   #19
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Originally Posted by sol invictus View Post
Gibberish. Zig just gave you an example of a B-field that reconnects. It's right there in black and white (or whatever colors you have your display set to).
Is B an infinite vector field or is it not?

yes or no.
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Old 24th March 2011, 01:03 PM   #20
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Originally Posted by sol invictus View Post
There is no point in discussing advanced topics with you when you do not understand the basics of vector fields.
Good

Looks like I won this round.
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Old 24th March 2011, 01:05 PM   #21
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Originally Posted by michaelsuede View Post
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 $\vec B(x,y,z,t)$ is a standard real-valued vector field. Zig just gave you an explicit and very simple example of one that reconnects.
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Old 24th March 2011, 01:06 PM   #22
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Originally Posted by michaelsuede View Post
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.
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Old 24th March 2011, 01:08 PM   #23
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Originally Posted by sol invictus View Post
I have no idea what you mean by "infinite vector field", that sounds like a term you invented all by yourself.

The magnetic field $\vec B(x,y,z,t)$ 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.
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Old 24th March 2011, 01:10 PM   #24
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Originally Posted by michaelsuede View Post
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?
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Old 24th March 2011, 01:10 PM   #25
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Originally Posted by Ziggurat View Post
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/divulga.../Falthamar.pdf

What Fälthammar means by "reconnection" is an exploding double layer.
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Old 24th March 2011, 01:12 PM   #26
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Originally Posted by michaelsuede View Post
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.

Quote:
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.
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Old 24th March 2011, 01:12 PM   #27
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Originally Posted by michaelsuede View Post
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.
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Old 24th March 2011, 01:14 PM   #28
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Originally Posted by Ziggurat View Post
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.
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Old 24th March 2011, 01:16 PM   #29
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Originally Posted by michaelsuede View Post
I mean a magnetic field is a vector field that has no end and extends for eternity.
The equation I gave you does that.

Quote:
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.

Quote:
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.
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Old 24th March 2011, 01:20 PM   #30
michaelsuede
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Originally Posted by Ziggurat View Post
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?
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Old 24th March 2011, 01:21 PM   #31
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Originally Posted by michaelsuede View Post
With a peer reviewed paper no less.
You linked to a peer reviewed pedagogical paper which argues the following points:

Quote:
"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.
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Old 24th March 2011, 01:22 PM   #32
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Originally Posted by michaelsuede View Post
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.

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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.
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Old 24th March 2011, 01:24 PM   #33
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Originally Posted by ben m View Post
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.
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Old 24th March 2011, 01:24 PM   #34
sol invictus
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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?

Last edited by sol invictus; 24th March 2011 at 01:25 PM.
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Old 24th March 2011, 01:26 PM   #35
michaelsuede
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Originally Posted by sol invictus View Post
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.
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Old 24th March 2011, 01:28 PM   #36
sol invictus
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Originally Posted by michaelsuede View Post
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?
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Old 24th March 2011, 01:29 PM   #37
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Originally Posted by michaelsuede View Post
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.
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Old 24th March 2011, 01:29 PM   #38
Ziggurat
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Originally Posted by michaelsuede View Post
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.

Quote:
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.

Quote:
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.

Quote:
That is what you are claiming right?
Not even close.
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Old 24th March 2011, 01:30 PM   #39
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Originally Posted by michaelsuede View Post
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.
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Old 24th March 2011, 01:31 PM   #40
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Originally Posted by michaelsuede View Post
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.
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