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Old 1st November 2011, 04:31 PM   #4361
W.D.Clinger
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a simple derivation of magnetic reconnection, part 1

So long as Michael Mozina continues to wallow in the pit of denial he's dug for himself, we might as well finish up the derivation of magnetic reconnection in the experiment he's been running away from for most of the past year. By giving up on Michael Mozina, we free ourselves to use freshman-level math and physics that lie far beyond his knowledge and capability.

Simpler demonstrations of magnetic reconnection have already been presented in this or related threads, includingThe purpose of this derivation is to show how we can get from Maxwell's equations to Dungey's figures, the first half of Yamada et al's figure 3, and Wikipedia's animation using no mathematics beyond freshman calculus.

The derivation proceeds along the outline suggested by the five equations I quoted from Jackson's Classical Electrodynamics. Although that is hardly a freshman-level textbook, equivalents of those particular equations appear within Purcell's Electricity and Magnetism and other introductory textbooks.

Equation 1 (Ampère's law with Maxwell's correction)
<br />
\[<br />
\nabla \times \hbox{{\bf H}} - \frac{\partial \hbox{{\bf D}}}{\partial t} = \hbox{{\bf J}}<br />
\]<br />
That's one of the four Maxwell's equations.

By conducting the experiment in a vacuum and changing the magnetic field slowly, we can make Maxwell's correction as small as desired. (Changing the magnetic field more slowly makes magnetic reconnection happen more slowly, so you might be afraid this demonstration will be like watching grass grow. Never fear: We can compensate by using time-lapse animation to view the reconnection.) We can simplify our math by making Maxwell's correction negligible and dropping it from the equation to obtain Ampère's original law:
<br />
\[<br />
\nabla \times \hbox{{\bf H}} = \hbox{{\bf J}}<br />
\]<br />

Equation 2 (relationship between H and B)

Ampère's law is stated using the H-field. For our derivation, we need to use the B-field. In a vacuum, converting from the H-field to the B-field involves a change of units. The conversion factor µ0 is known as the magnetic constant:
<br />
\[<br />
\hbox{{\bf H}} = \frac{\hbox{{\bf B}}}{\mu_0}<br />
\]<br />
Substituting for H in Ampère's original law, we get
<br />
\[<br />
\nabla \times \hbox{{\bf B}} = \mu_0 \hbox{{\bf J}}<br />
\]<br />

Equation 3 (applying the Kelvin-Stokes theorem)

Let S be any smooth compact 2-dimensional surface, and let C (a 1-dimensional curve) be the boundary of S. Applying the Kelvin-Stokes theorem (which is a corollary of the fundamental theorem of calculus in n dimensions) to the equation above, we get
<br />
\[<br />
\oint_C \hbox{{\bf B}} \cdot d \hbox{{\bf l}} =<br />
\int_S \nabla \times \hbox{{\bf B}} \cdot \hbox{{\bf n}} \; da =<br />
\mu_0 \int_S \hbox{{\bf J}} \cdot \hbox{{\bf n}} \; da<br />
\]<br />

Equation 4 (magnetic field around a current-carrying rod)

For our experiment, we can use long rods and perform all of our measurements of the magnetic field in the vicinity of the rods' centers. Under those conditions, the magnetic fields we measure will be the same (to within experimental error) as the magnetic fields around infinitely long rods.

We need to start by calculating the magnetic field around a single current-carrying rod. By symmetry, the magnetic field will look the same in every plane that intersects the rod at a right angle. Taking S to be a disk of radius R in one of those planes with the rod at its center, we find that the integral of B along the boundary of that disk is equal to the total current flux through the disk. By Ampère's law, the magnetic field is tangent to that boundary at every point (with direction determined by the right hand rule). By symmetry, the magnitude of the field is the same at every point on the circle.

Denoting the current through a single rod at time t by I(t), the current flux through S is I(t). Hence
<br />
\[<br />
2 \pi R | \hbox{{\bf B}} | = \mu_0 I(t)<br />
\]<br />
whence
<br />
\[<br />
| \hbox{{\bf B}} | = \frac{\mu_0}{2 \pi} \frac{I(t)}{R}<br />
\]<br />
which is a simplification of Jackson's equation. (His equation illustrated the Biot-Savart law, which we managed to avoid by appealing to symmetry.)

(We have now answered one of Reality Check's critical questions that Michael Mozina was unable to answer.)


Equation 5 (superposition)

Superposition is so simple that many textbooks don't even bother to state it as an equation. Jackson stated superposition as part of the equation that tells how to convert the B-fields through media of different permeability into the composite H-field:
<br />
\[<br />
H_\alpha &= \sum_{\beta} \mu_{\alpha \beta}^\prime B_\beta<br />
\]<br />
By conducting our experiment in a vacuum, transforming from component notation to vector notation, and translating the left-hand side of that equation into the equivalent B-field, we get the unadorned and uncomplicated equation for superposition of magnetic fields:
<br />
\[<br />
\hbox{{\bf B}} = \sum_{\beta} \hbox{{\bf B}}_\beta<br />
\]<br />
(Yes, the Greek letter that confused Michael Mozina has disappeared altogether. Imagine that.)

To be continued...

Last edited by W.D.Clinger; 1st November 2011 at 05:39 PM. Reason: corrected a minor mistake (while leaving a more serious error untouched)
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Old 1st November 2011, 04:32 PM   #4362
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Originally Posted by Michael Mozina View Post
By your logic both of Clinger's books also support God and astrology too because neither author mentions them. Holy cow! Yep, this is *EXACTLY* like arguing with creationists.
Wrong again.
The logic is really simple. Fresh-man level textbooks describe the theory of electromagnetism (Maxwell's equations, etc.). It is the theory of electromagnetism that supports magnetic reconnection.
If you knew or understood EM theory then you would agree but you do not have that knowledge: Michael Mozina's ignorance of high school science (the right hand rule).
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Old 1st November 2011, 04:33 PM   #4363
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Originally Posted by Reality Check View Post
Wrong again.
The logic is really simple. Fresh-man level textbooks describe the theory of electromagnetism (Maxwell's equations, etc.).
Maxwell's equations don't say a DAMN THING about "reconnection".
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Old 1st November 2011, 04:35 PM   #4364
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MM: Can you answer sol invictus's question about magnetic field lines and Gauss' law

Originally Posted by Michael Mozina View Post

Yep, it's *EXACTLY* like arguing with creationists. Denial, denial, dodge, denial.
Wrong: it's *EXACTLY* like arguing with a typical physics cranks: Ignorance, ignorance, dodge, denial, straw man, return to ignorance.

For example, you continue to dodge:
MM: Can you answer sol invictus's question about magnetic field lines and Gauss' law
first asked by sol invictus on 27 October 2011
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Old 1st November 2011, 04:38 PM   #4365
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Originally Posted by W.D.Clinger View Post
By conducting the experiment in a vacuum and changing the magnetic field slowly, we can make Maxwell's correction as small as desired. (Changing the magnetic field more slowly makes magnetic reconnection happen more slowly,....
BS! That permeability factor that you're running like hell from describes *INDUCTANCE* per unit length, not *RECONNECTIONS* per unit length!

http://en.wikipedia.org/wiki/Equivocation

Your entire argument is based on a fallacy. You've simply redefined the term "inductance" to "reconnection"!

Last edited by Michael Mozina; 1st November 2011 at 04:41 PM.
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Old 1st November 2011, 04:41 PM   #4366
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Originally Posted by Michael Mozina View Post
Maxwell's equations don't say a DAMN THING about "reconnection".
Originally Posted by Reality Check View Post
Wrong: it's *EXACTLY* like arguing with a typical physics cranks: Ignorance, ignorance, dodge, denial, straw man, return to ignorance.
How ignorant of you MM.
Maxwell's equations don't say a DAMN THING about magnetic reconnection. They also say nothing about
  • double layers
  • plasma
  • Alfvén waves
  • whistler waves
  • every other EM process in the universe !
EM processes like magnetic reconnection and double layers are based on Maxwell's equations. For MHD we also add fluid mechanics to the mix.
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Old 1st November 2011, 04:45 PM   #4367
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Exclamation Michael Mozina's delusion about "*RECONNECTIONS* per unit length"

Originally Posted by Michael Mozina View Post
BS! That permeability factor that you're running like hell from describes *INDUCTANCE* per unit length, not *RECONNECTIONS* per unit length!
Double BS.
Firstly W.D. Clinger is not running away from permeability. The equations he has cited have permeability in them (one equation is the definition of permeability!).

ETA: The only reason that he has permeability is so that he can use H instead of B for a while. As in his post above, he then transforms back to B and permeability vanishes!

The main idiocy in your post is the delusion that the equations have to have a mythical "*RECONNECTIONS* per unit length" in them.

Last edited by Reality Check; 1st November 2011 at 05:16 PM.
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Old 1st November 2011, 05:04 PM   #4368
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Exclamation Michael Mozina's delusion that permeability is inductance

Originally Posted by Michael Mozina View Post
BS! That permeability factor that you're running like hell from describes *INDUCTANCE* per unit length, not *RECONNECTIONS* per unit length!
The second delusion in this post (see Michael Mozina's delusion about "*RECONNECTIONS* per unit length" for the first one)
is the delusion that permeability is inductance just because permeability has the SI units of henries per meter and inductance has the SI units of henries.

MM: FYI, I could measure permeability in cgs units and inductance in SI units and all of a sudden permeability is not inductance according to your twisted logic !

Perpetual Student's post is the best explanation
Originally Posted by Perpetual Student View Post
Inductance is a property of a circuit element (an object like a coil, an inductor) -- it's a measure of its ability to store energy in a magnetic field, whereas,
Permeability is the ability of a material to support a magnetic field (the degree of magnetization that can be supported) which is why some object's permeability can be seen as inductance per unit length (henry per meter).
A device that is made of a material that has x permeability will have an inductance (henries) based on its size and construction. It only takes a little logic and rudimentary mathematics to understand the difference. Note that inductance is the measure of the property of an object; permeability is the measure of the property of a material.


Last edited by Reality Check; 1st November 2011 at 05:09 PM.
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Old 1st November 2011, 07:08 PM   #4369
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ETA: I might as well make another correction to that equation!

Originally Posted by Michael Mozina View Post
This conversation is *EXACTLY* like arguing with creationists. You guys NEVER actually read or respond to the materials and you make stuff up as you go. No RC, "reconnection" is trivially *IMPOSSIBLE* in basic theory because magnetic lines have no beginning and no ending and no ability to "disconnect" or "reconnect".

Congratulations, Michael Mozina. You have just confirmed (for the umpteenth time) what I wrote here:

Originally Posted by W.D.Clinger View Post
You will have no right to judge anyone until you read and understand the basic concepts of freshman-level electromagnetism.

For example: You have been denying the relevance of
<br />
\[<br />
\lim_{\delta \rightarrow 0}<br />
    \frac{1}{8 r \delta^3} \oint_{S_\delta(r,\theta,z)} \hbox{{\bf B}} \cdot d \hbox{{\bf A}} = 0<br />
\]<br />

What part of that equation do you not understand?

Last edited by W.D.Clinger; 1st November 2011 at 07:17 PM. Reason: added the previously omitted factor of 1/r
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Old 1st November 2011, 07:59 PM   #4370
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Missed this:
Originally Posted by Michael Mozina View Post
No RC, "reconnection" is trivially *IMPOSSIBLE* in basic theory because magnetic lines have no beginning and no ending and no ability to "disconnect" or "reconnect".
...'kinetic energy' gliiberish snipped...
MM, repeating your ignorance about magnetic reconnection is is not wise.

Magnetic reconnection is trivially *POSSIBLE* in basic EM theory.
There are no magnetic field lines beginning and ending in magnetic reconnection. The magnetic fields lines are not cut. No ends of magnetic field lines are glued together.
See MHD reconnection
N.B. The curator of this Scholarpedia article is Eric R Priest.
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Old 2nd November 2011, 12:54 AM   #4371
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Originally Posted by Michael Mozina View Post
IMO you're underestimating the energy conditions inside the pinch during a flare. Something sure is releasing gamma radiation during some types of flare events.
Apparently, like in every paper you read, you have not understood the processes said paper was talking about. This is a paper about curvature radiation, the emitted frequency is specifically given for this process. Try to get that to work in a solar flare, really do the math!

Naturally, there are other mechanisms to create gamma radiation, but those are not in the paper as they were unimportant in the physics of neutron star magnetospheres.
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Old 2nd November 2011, 03:10 AM   #4372
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Originally Posted by Michael Mozina View Post
Yes, I know.
Finally.
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Old 2nd November 2011, 03:11 AM   #4373
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Originally Posted by Michael Mozina View Post
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Old 2nd November 2011, 05:22 AM   #4374
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a simple derivation of magnetic reconnection, part 1 (erratum)

This is the more serious error I didn't correct when editing my post last night. As you can see, it won't affect our derivation in any way.

Originally Posted by W.D.Clinger View Post
Equation 5 (superposition)

Superposition is so simple that many textbooks don't even bother to state it as an equation. Jackson stated superposition as part of the equation that tells how to convert the B-fields through media of different permeability into the composite H-field:
<br />
\[<br />
H_\alpha &= \sum_{\beta} \mu_{\alpha \beta}^\prime B_\beta<br />
\]<br />
No, that equation does not express superposition. It's on page 14 of Jackson's Classical Electrodynamics, third edition, in the section immediately following the section on linear superposition, but I misread the equation. As written, it's the equation for translating from B to H in a medium of non-uniform permeability, and there is no superposition.

It appears that Jackson never bothers to write down the equation for superposition. Since that's the equation we need, however, I'll continue to refer to the following as our equation 5:

Originally Posted by W.D.Clinger View Post
....we get the unadorned and uncomplicated equation for superposition of magnetic fields:
<br />
\[<br />
\hbox{{\bf B}} = \sum_{\beta} \hbox{{\bf B}}_\beta<br />
\]<br />

Last edited by W.D.Clinger; 2nd November 2011 at 05:23 AM. Reason: elided redundant phrase
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Old 2nd November 2011, 07:16 AM   #4375
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Originally Posted by W.D.Clinger View Post
ETA: I might as well make another correction to that equation!
Of course we all know that if *I* had made any of those same mathematical errors, you folks would have been jumping down my throat.

Quote:
Congratulations, Michael Mozina. You have just confirmed (for the umpteenth time) what I wrote here:
Congratulations Clinger, you have just confirmed (for the umpteenth time) what I wrote here:
http://www.internationalskeptics.com...postcount=4303

Quote:
You're totally and completely full of BS. Never have you shown me a published paper or textbook that supports your claim. You're as bad as the worst CREATIONISTS I've ever seen when it comes to HANDWAVING your claims. When can I expect you to provide a published work to support ANYTHING about your so called "experiment" being an example of 'magnetic reconnection"? NEVER! You pulled that ridiculous and FALSE claim right out of your backside.
You have NO INTENTION of EVER providing ANY kind of published support for your *FALSE* claim that your so called "experiment" actually demonstrates "reconnection". You're just going right ahead handwaving away, tossing out a few equations to make it look legit, and your RUNNING away from supporting your actual claim trough ANY published materials. You're EXACTLY like arguing with a creationist that INSISTS "God did it" through some process that has absolutely NOTHING to do with "God".

Quote:
What part of that equation do you not understand?
I don't understand where the million degree plasmas come from at two ZERO points in a couple of magnetic fields.
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Old 2nd November 2011, 07:18 AM   #4376
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Originally Posted by tusenfem View Post
Apparently, like in every paper you read, you have not understood the processes said paper was talking about. This is a paper about curvature radiation, the emitted frequency is specifically given for this process. Try to get that to work in a solar flare, really do the math!

Naturally, there are other mechanisms to create gamma radiation, but those are not in the paper as they were unimportant in the physics of neutron star magnetospheres.
The other important mechanism is a plasma pinch. Somewhere I posted a Chinese paper related to gamma radiation from plasma pinches. I'll see if I can find it later for you.
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Old 2nd November 2011, 07:23 AM   #4377
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Originally Posted by Michael Mozina View Post
I don't understand where the million degree plasmas come from at two ZERO points in a couple of magnetic fields.

To suggest a lack of understanding the current state of solar physics somehow validates an otherwise wholly unsupported conjecture would be an argument from ignorance.
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Old 2nd November 2011, 07:25 AM   #4378
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Originally Posted by Belz... View Post
The "funny" (well "sad") part of your participation in this thread is that you've made absolutely no attempt to check out the validity of the statements RC or anyone else is making *BEFORE* jumping into the conversation. Congrats. You're well on your way to becoming a full fledged EU "hater".

Haters are like creationists. They don't care about the actual science. None of the haters (like RC) ever actually addresses or acknowledges the information presented. The haters also fail to provide any published materials to support their claims too like Clinger refuses to provide any PUBLISHED materials to support his handwaves about his "experiment" being an example of "reconnection". Instead he plows right ahead, ignoring the fact that absolutely NONE of his equations related to "reconnections" per unit length.

If you HAD spend any time checking out Dungey's work or Peratt's work, you'd already know that both Peratt and Dungey describe what they call "electrical discharges" in plasmas. RC is simply in pure denial of scientific fact. In fact he outright lied! Unlike the haters, I actually *HAVE* provided at least two PUBLISHED references to support my claim. When did you intend to read them?

Last edited by Michael Mozina; 2nd November 2011 at 07:35 AM.
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Old 2nd November 2011, 07:27 AM   #4379
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Originally Posted by GeeMack View Post
To suggest a lack of understanding the current state of solar physics somehow validates an otherwise wholly unsupported conjecture would be an argument from ignorance.
Yes, and since you've never bothered to read Cosmic Plasma or Peratt's book in all the YEARS that we've discussed these topics, you've personally made a CAREER out of arguing from pure ignorance.
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Old 2nd November 2011, 07:30 AM   #4380
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Originally Posted by Reality Check View Post
The second delusion in this post (see Michael Mozina's delusion about "*RECONNECTIONS* per unit length" for the first one)
is the delusion that permeability is inductance just because permeability has the SI units of henries per meter and inductance has the SI units of henries.

MM: FYI, I could measure permeability in cgs units and inductance in SI units and all of a sudden permeability is not inductance according to your twisted logic !
Irony overload. You folks are the ones who are DESPERATELY trying to redefine INDUCTANCE as "reconnection". Your entire argument is based on a logical fallacy called equivocation.
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Old 2nd November 2011, 08:00 AM   #4381
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Originally Posted by Michael Mozina View Post
Of course we all know that if *I* had made any of those same mathematical errors, you folks would have been jumping down my throat.
Unlikely. Had anyone been so stupid as to jump down your throat for making exactly the same errors I made, you could have pointed out that all three equations were technically correct as written and follow directly from the definitions and calculations.

You could then explain that the only problem with the first two equations was that they didn't directly contradict your ignorant suggestion that magnetic reconnection is incompatible with Gauss's law for magnetism.

(You could also have pointed out that the second equation implies the third (which does directly contradict your ignorant claims), that the error in the second equation came from forgetting that the surfaces had been defined using cylindrical coordinates instead of Cartesian, and that the second equation would have been correct had a division by r been placed within the definition of those surfaces (which would have been a more natural place for it) instead of leaving that division for the equations. But really, Michael...you don't need to be all that defensive. )

Do you want to know the real reasons so many people are giving you a hard time? It's because you continue to repeat your errors even after you've been corrected, you run away from all relevant questions that could help you to learn something, and when some nice person tries to help you out, you accuse him of lying, hating, and religious bigotry, all the while pretending to be some sort of expert on subjects you actually know nothing about.

For example:

Originally Posted by Michael Mozina View Post
You have NO INTENTION of EVER providing ANY kind of published support for your *FALSE* claim that your so called "experiment" actually demonstrates "reconnection". You're just going right ahead handwaving away, tossing out a few equations to make it look legit, and your RUNNING away from supporting your actual claim trough ANY published materials. You're EXACTLY like arguing with a creationist that INSISTS "God did it" through some process that has absolutely NOTHING to do with "God".
Originally Posted by Michael Mozina View Post
You're well on your way to becoming a full fledged EU "hater".

Haters are like creationists. They don't care about the actual science. None of the haters (like RC) ever actually addresses or acknowledges the information presented. The haters also fail to provide any published materials to support their claims too like Clinger refuses to provide any PUBLISHED materials to support his handwaves about his "experiment" being an example of "reconnection". Instead he plows right ahead, ignoring the fact that absolutely NONE of his equations related to "reconnections" per unit length.
Originally Posted by Michael Mozina View Post
Yes, and since you've never bothered to read Cosmic Plasma or Peratt's book in all the YEARS that we've discussed these topics, you've personally made a CAREER out of arguing from pure ignorance.

That argument isn't working, Michael. Just about everyone has figured out that you don't have a clue about freshman-level math or physics, so you can't possibly have understood whatever legitimate math and physics may be contained within your holy texts.
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Old 2nd November 2011, 08:32 AM   #4382
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Originally Posted by W.D.Clinger View Post
That argument isn't working, Michael. Just about everyone has figured out that you don't have a clue about freshman-level math or physics, so you can't possibly have understood whatever legitimate math and physics may be contained within your holy texts.
Your personal attacks aren't working Clinger, not in any scientific sense anyway. I've learned a LOT from noting the questions that you REFUSE to address.

You REFUSE to provide *ANY* kind of published references for your claim. Even though I provided TWO published references to support the fact that "electrical discharges" occur in plasma, you refuse to embrace that fact. You refuse to really spend any time at all addressing my questions about changing materials and changing *INDUCTANCE* per distance unit. You REFUSE to explain where any of the kinetic energy comes from at a couple "ZERO" points in magnetic field. You've pretty much REFUSED to address ANY of the relevant questions surrounding your so called "reconnection" experiment.

I know you think that attacking the individual has some sort of emotional value to you, but from the standpoint of PHYSICS and KINETIC ENERGY, I know for a fact that you have no idea how to answer any of these questions *WITHOUT* acknowledging CURRENTS that ultimately "reconnect" at that point, particularly in plasma.

Sooner or later other people will ask you for PUBLISHED references to support your handwaving, and they'll want answers about the million degree rise in temperatures. They'll be honestly curious to know those answers. Will you treat them as you've treated me? Will you lie through your teeth in an effort to attack that individual too, and will you run like hell from every relevant question they put before you? Will you NEVER read Alfven and Peratt's work for yourself, and rely upon ignorance and arrogance forever and ever?

Last edited by Michael Mozina; 2nd November 2011 at 08:51 AM.
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Old 2nd November 2011, 11:53 AM   #4383
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Originally Posted by Michael Mozina View Post
The "funny" (well "sad") part of your participation in this thread is that you've made absolutely no attempt to check out the validity of the statements RC or anyone else is making *BEFORE* jumping into the conversation.
The sad part in your response to my participation in this thread is that you think that every participant should do so in order to check out the validity of anyone's statement. My comment was relevant, you just don't like it.
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Old 2nd November 2011, 12:11 PM   #4384
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Originally Posted by Michael Mozina View Post
Your personal attacks aren't working Clinger, not in any scientific sense anyway. I've learned a LOT from noting the questions that you REFUSE to address.
It is not a personal attack: I tis a conclusion dram from your display of ignorance, e.g. Michael Mozina's ignorance of high school science (the right hand rule).

He had given references for his claim (any textbook on electromagnetism) which is that you can demonstrate MR using EM.

You have no references - just delusions about them:
Michael Mozina's fantasy about Anthony Peratt's definition of electrical discharge!
13th January 2011: Dungey's and Peratt's definition of discharge are different
Originally Posted by Michael Mozina View Post
You refuse to really spend any time at all addressing my questions about changing materials and changing *INDUCTANCE* per distance unit.
You are lying: he stated what you should know - the permeability of air is different from the permeability of free space.
And as you see above - there is no permeability in the equations when we get back to B.

There is no *INDUCTANCE* per distance unit: Michael Mozina's delusion that permeability is inductance!
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Old 2nd November 2011, 12:55 PM   #4385
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Exclamation MM: Induction = solar flares take a million years to happen (31st December 2009)

Originally Posted by Michael Mozina View Post
Irony overload. You folks are the ones who are DESPERATELY trying to redefine INDUCTANCE as "reconnection". Your entire argument is based on a logical fallacy called equivocation.
Ignorance overload. We folks are the ones who are FOLLOWING WHAT THE SCIENCE DOES: defining magnetic reconnection as .... magnetic reconnection!

Your entire argument of magnetic reconnection = inductance is based on a logical fallacy called argument from ignorance or maybe a new fallacy which I will call argument from delusion.

You continue to ignore the physics that the energy released from solar flares would take a million years if released through induction !

Magnetic Reconnection Redux V (31st December 2009)
Originally Posted by Tim Thompson View Post
The conversion of magnetic energy into a current always operates on a time-scale characteristic of the system, and that time scale is controlled by the ability of the magnetic field to move through the conductor, in order to create a dB/dt term from which the current is generated. That time-scale in a plasma is rather different than it is for a fixed conductor. Here we find the real deal once again in Priest & Forbes:
"In space physics the distinction between ideal and non-ideal processes is important because simple estimates imply that magnetic dissipation acts on a time-scale which is many orders of magnitude slower than the observed time-scale of dynamic phenomena. For example, solar flares release stored magnetic energy in the corona within a period of 100 s. By comparison, the time-scale for magnetic dissipation based on a global scale length of 105 km is of the order of 106 yrs."
Priest & Forbes, page 6
All of this occurs in the first few pages of the book, but evidently Mozina has not even bothered to look at it. Why bother to suggest books & papers when the evidence suggests that Mozina will never consult them anyway?
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Old 2nd November 2011, 01:23 PM   #4386
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Originally Posted by sol invictus View Post
Specifically, they can evolve as shown in this video http://www.youtube.com/watch?v=oKTyf...74A6AD&index=2 .
That link is a play list of 5 videos. The easiest one to understand in the context of our discussion is Simulation of Magnetic Reconnection in a Dusty Plasma - DENISIS which shows the magnteic field lines curving into the null point at the center of the plasma to form an X and then reconnecting.
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Old 2nd November 2011, 06:08 PM   #4387
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a simple derivation of magnetic reconnection, part 2

In the first part of this derivation and an erratum, we used 5 equations to derive the magnetic field B around a current-carrying rod.

In this part of the derivation, we will express that magnetic field in both cylindrical and Cartesian coordinates.

In part 3, we will show that the magnetic field around four current-carrying rods reproduces both of the figures in Dungey's 1958 paper, figure 3a in the survey paper by Yamada et al, and the still figure in Wikipedia's current article on magnetic reconnection.

In part 4, I will describe a simple variation of the experiment I've been suggesting to Michael Mozina and prove that the topology of the magnetic field changes during that experiment. As Yamada et al explain in their appendix, that change in the topology of the magnetic field is what we mean by magnetic reconnection.

Notation for B

When we write ∇∙B, we're thinking of B as a function of points in 3-space. When we write dB/dt or ∂B/∂t, we're thinking of B as a function of time.

As will become painfully clear if you read Michael Mozina's posts, that contextual overloading of B can confuse people. Let's take a minute to review the notation.

We usually speak of B as the magnetic field, which means it's a function from points in 3-space (which we write as R3) to vectors of magnetic flux density (which we also write as R3). In that kind of context, B is a function from R3 to R3, and it would be correct to write
B ∈ (R3 ➝ R3)
where (R3 ➝ R3) is the set of all functions from R3 to R3.

When we speak of B as a function from time to magnetic fields, it would be correct to write
B ∈ (R ➝ (R3 ➝ R3))
We may also regard B as a function of four variables (x, y, z, and t), so it would be correct to write
B ∈ ((R3 × R) ➝ R3)
Because (R ➝ (R3 ➝ R3)) is isomorphic to ((R3 × R) ➝ R3), these last two meanings for B are consistent.

I'll continue to use the traditional notation (instead of lambda calculus, which would be more precise), but everyone should keep in mind that context determines whether we're thinking of B as a function of space or time.

From part 1, here are the equations we'll need as we move forward:

Equation 3 (integral form of Ampère's law)
<br />
\[<br />
\oint_C \hbox{{\bf B}} \cdot d \hbox{{\bf l}} =<br />
\int_S \nabla \times \hbox{{\bf B}} \cdot \hbox{{\bf n}} \; da =<br />
\mu_0 \int_S \hbox{{\bf J}} \cdot \hbox{{\bf n}} \; da<br />
\]<br />

Equation 4 (magnitude of magnetic field around a current-carrying rod)

In cylindrical coordinates:
<br />
\[<br />
| \hbox{{\bf B}} | = | \hbox{{\bf B}} (r, \theta, z, t) | = | \hbox{{\bf B}} (t) (r, \theta, z) | = \frac{\mu_0}{2 \pi} \frac{I(t)}{r}<br />
\]<br />
where those first two equalities illustrate the context-dependent overloading of B.


Equation 5 (superposition)
<br />
\[<br />
\hbox{{\bf B}} = \sum_{i} \hbox{{\bf B}}_i<br />
\]<br />

Magnetic field around a single rod (cylindrical coordinates)

From equations 3 and 4, the magnetic field around a single current-carrying rod positioned at r=0 is
<br />
\[<br />
\hbox{{\bf B}} = \hbox{{\bf B}} (r, \theta, z, t) = \hbox{{\bf B}} (t) (r, \theta, z) = \frac{\mu_0}{2 \pi} \frac{I(t)}{r} \hbox{{\bf e}}_\theta<br />
\]<br />
where eθ is the unit vector in the θ direction.


Magnetic field around a single rod (Cartesian coordinates)

In part 3, we'll derive the magnetic field for two and then four current-carrying rods. They won't all be positioned at r=0. To derive the magnetic field around rods positioned elsewhere, Cartesian coordinates will be more convenient. From the equation above for cylindrical coordinates, the magnetic field around a single current-carrying rod positioned at the origin of a Cartesian coordinate system is
<br />
\[<br />
\begin{align*}<br />
\hbox{{\bf B}} &= \hbox{{\bf B}} (x, y, z, t) = \hbox{{\bf B}} (t) (x, y, z) \\<br />
&= \frac{\mu_0}{2 \pi} \frac{I(t)}{\sqrt{x^2+y^2}}<br />
\left( - \frac{y}{\sqrt{x^2+y^2}} \, \hbox{{\bf e}}_x + \frac{x}{\sqrt{x^2+y^2}} \, \hbox{{\bf e}}_y \right) \\<br />
&= \frac{\mu_0}{2 \pi} \frac{I(t)}{x^2+y^2}<br />
\left( - y \, \hbox{{\bf e}}_x + x \, \hbox{{\bf e}}_y \right)<br />
\end{align*}<br />
\]<br />
where ex and ey are the unit vectors in the x and y directions.

Everything we've done so far is found within standard textbooks on electromagnetism. In part 3, we'll go beyond freshman-level textbooks by reproducing the magnetic fields shown in Dungey's figures and in Yamada et al's figure 3a.
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Old 2nd November 2011, 06:18 PM   #4388
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Originally Posted by W.D.Clinger View Post
As Yamada et al explain in their appendix, that change in the topology of the magnetic field is what we mean by magnetic reconnection.
The existence of the Yamada et. al. does emphasis a problem that Michael Mozina seems to have: he is so convinced that his fantasies are correct that he ignores the actual science and any citations to the actual science.

Yamada et al were first cited in this thread on 27th January 2011 by tusenfem and there is no sign that MM has even looked at the paper .
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Old 2nd November 2011, 07:16 PM   #4389
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Originally Posted by W.D.Clinger View Post
In the first part of this derivation and an erratum, we used 5 equations to derive the magnetic field B around a current-carrying rod.
In other words, just like any good creationist, you absolutely, positively refuse to provide ANY kind of published work to support your OUTRAGEOUS claims, instead you just keep handwaving away and tossing around formulas related to INDUCTANCE per distance unit, not RECONNECTION. You also refused to answer any of my related questions about kinetic energy at two zero points in a magnetic field. You just keep flailing away, and trying to use completely unrelated work inside of ELECTRICAL DISCHARGE PLASMAS to support your case (Dungey/Yamada). Wow. Evidently you never intend to address those permeability questions or electrical discharge questions (Dungey) in any meaningful way.

Last edited by Michael Mozina; 2nd November 2011 at 07:31 PM.
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Old 2nd November 2011, 07:26 PM   #4390
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Originally Posted by Reality Check View Post
The existence of the Yamada et. al. does emphasis a problem that Michael Mozina seems to have: he is so convinced that his fantasies are correct that he ignores the actual science and any citations to the actual science.
Huh?

Let see. Clinger has name dropped four names now, Purcell, Jackson, Dungey and Yamada in support of his personal "reconnection experiment", two of which NEVER EVEN MENTIONED reconnection. The other two papers he keeps referring to (Dungey/Yamada) occur in PLASMAS, include ELECTRICAL DISCHARGES/Discharge chambers, and have NOTHING whatsoever to do with Clinger's personal 'experiment'. Would Clinger like to throw in Jesus and Einstein too as MR proponents? They never mentioned "magnetic reconnection" either, but that clearly doesn't seem to stop him from trying to use them to support his case.

Last edited by Michael Mozina; 2nd November 2011 at 07:28 PM.
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Old 2nd November 2011, 07:35 PM   #4391
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Originally Posted by Belz... View Post
The sad part in your response to my participation in this thread is that you think that every participant should do so in order to check out the validity of anyone's statement. My comment was relevant, you just don't like it.
http://books.google.com/books?id=e63...dungey&f=false

I think it's reasonable to be asking yourself who's telling you the truth and who isn't. RC is in pure denial of the fact that both Dungey and Peratt described "electrical discharges" in plasmas. In fact Dungey (and Giovanelli before him) specifically linked flares to "electrical discharges" and Dungey specifically links "discharges" to "reconnection" events. The sad part is that you simply don't care to find out who's telling the truth.
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Old 2nd November 2011, 07:38 PM   #4392
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Originally Posted by Reality Check View Post
That link is a play list of 5 videos. The easiest one to understand in the context of our discussion is Simulation of Magnetic Reconnection in a Dusty Plasma - DENISIS which shows the magnteic field lines curving into the null point at the center of the plasma to form an X and then reconnecting.
Oh, science by pretty "looks like a reconnection bunny" pictures. Where does the kinetic energy come from at two ZERO points in two magnetic fields RC? Dungey used ELECTRICAL DISCHARGES.
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Old 2nd November 2011, 07:38 PM   #4393
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Originally Posted by Michael Mozina View Post
In other words, just like any good creationist, ..usual rant....
In other words, just like any honest person, W.D. Clinger is trying (obviously in vain) to educate you about the basic EM theory that the experiment I've been suggesting to Michael Mozina uses.

You continue to lie about his claim:
W.D. Clinger'sclaim is that you can use freshman-level EM to describe magnetic reconnection. His 2 'simple derivation' posts so far have used freshman-level EM to describe the magnetic field around a current carying rod.
FYI: Maxwell's equations are introduced to physics students in their first (freshman) year.

You continue to lie about his references:
W.D. Clinger has cited at least one freshman-level EM textbook, one book on magnetic reconnection and one magnetic reconnection paper (a 2010 review).

He refused to answer your 'kinetic energy at two zero points in a magnetic field' question becuase the question is
  1. Gibberish
  2. Nothing to do with his proposed experiment (no plasma = no particles = no kinetic energy).
Now try reading his posts again:
a simple derivation of magnetic reconnection, part 2
Quote:
In the first part of this derivation and an erratum, we used 5 equations to derive the magnetic field B around a current-carrying rod.

In this part of the derivation, we will express that magnetic field in both cylindrical and Cartesian coordinates.

In part 3, we will show that the magnetic field around four current-carrying rods reproduces both of the figures in Dungey's 1958 paper, figure 3a in the survey paper by Yamada et al, and the still figure in Wikipedia's current article on magnetic reconnection.
So far this is definitely freshman EM: Maxwell's equations plus a bit of calculus.
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Old 2nd November 2011, 07:41 PM   #4394
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Originally Posted by Reality Check View Post
In other words, just like any honest person, W.D. Clinger is trying (obviously in vain) to educate you about the basic EM theory that the experiment I've been suggesting to Michael Mozina uses.
An "honest" man would provide a PUBLISHED REFERENCE that was DIRECTLY RELATED to his actual experiment, he'd explain where the kinetic energy comes from, and he'd answer my questions about permeability and INDUCTANCE per unit length.

Last edited by Michael Mozina; 2nd November 2011 at 07:55 PM.
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Old 2nd November 2011, 07:43 PM   #4395
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Originally Posted by Reality Check View Post
So far this is definitely freshman EM: Maxwell's equations plus a bit of calculus.
You're right, but all of it relates to INDUCTANCE and not a single bit of it relates to "reconnection". Purcell never even mentioned "reconnection", but I'm sure he explained permeability and INDUCTANCE in his book.
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Old 2nd November 2011, 07:47 PM   #4396
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Clingers use of circuit theory is quite ironic, particularly in current carrying plasma (like Yamada and Dungey) where Alfven's double layer paper makes MR theory OBSOLETE.
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Old 2nd November 2011, 07:48 PM   #4397
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Originally Posted by Michael Mozina View Post
Oh, science by pretty "looks like a reconnection bunny" pictures.
Oh, science by plug the laws of physics into a completer simulation and see what we get - pretty pictures that illustrate the science !


This is not your very ignorant 'I see bunnies in the clouds' logic where you ignore the science in favor of your fantasies, e.g.
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Old 2nd November 2011, 07:53 PM   #4398
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Originally Posted by Michael Mozina View Post
An "honest" man would provide a PUBLISHED REFERENCE that was DIRECTLY RELATED to his actual experiment, he'd explain where the kinetic energy comes from, and he'd answer my question about permeability and INDUCTANCE per unit length.
An honest man would not lie about what W.D. Clinger has stated.
He has never stated that the proposed experiment is in a PUBLISHED REFERENCE.
You have been cited many PUBLISHED REFERENCES on magnetic reconnection experiments that are DIRECTLY RELATED to his actual experiment.
He does not have to answer gibberish that is unrelated to his proposed experiment.

He does not have to cater to your delusions: Michael Mozina's delusion that permeability is inductance!
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Old 2nd November 2011, 07:55 PM   #4399
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Originally Posted by Michael Mozina View Post
You're right, but all of it relates to INDUCTANCE and not a single bit of it relates to "reconnection".
None of it relates to INDUCTANCE (and never will) and not a single bit of it relates to magnetic reconnection - yet.

Michael Mozina's delusion that permeability is inductance!
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Old 2nd November 2011, 07:56 PM   #4400
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Originally Posted by Reality Check View Post
None of it relates to INDUCTANCE
Everywhere you see a permeability variable in his equations it's a measure of INDUCTANCE per unit distance, not RECONNECTIONS!
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