Message from the Dawn of time...

[RealityCheck01]

...snipped insane emphasis on MR in plasma when we are taking about MR in vacuum...

The repeated ignorance of citing a Wikipedia article on magnetic reconnection in plasma to refute a textbook section on magnetic reconnection in vacuum !

The ignorance of citing a Wikipedia article on magnetic reconnection in plasma to refute papers mentioning magnetic reconnection in vacuum (6 November 2014)

 

[RealityCheck01]

..rand snipped...

What has a fact less rant have to with the easily understood science to anyone who has studied electromagnetism or English about MR in vacuum, Michael?

 

[Michael]

Repeat of the delusion that Somov's MR in vacuum example contains plasma.

It contains two parallel currents, both of which are composed of moving charged particles, AKA *plasma*. His whole book is on the topic of *plasma* physics.

Repeat of the delusion that "magnetic attraction" means "magnetic reconnection".

That's your own delusion apparently. You can't even keep your own strawmen straight, because you can't accept that wires, unlike *plasma* wouldn't move, therefore there wouldn't be any "reconnection" going on.

A new delusion - that a current in plasma forms

Birkeland current

A Bennett Pinch is one of many kinds of plasma or solid or liquid pinches.

Any ordinary plasma ball with demonstrate the "shape" of the current stream. It's a twister like filament in (drum roll) *plasma*.

Nothing in that rant is the answer to the question:
5 November 2014 Michael: Where does magnetic reconnection happen in Somov's example?

http://www.christianforums.com/t7810720-38/#post66607488

You're apparently in denial of my answer so let me quote you again:

I've answered that question a bunch of times for you. You simply ignore what I say and repeat the same question. The magnetic attraction takes place *all around* the current streams, not in tiny little "lines" as you seem to imagine in your *toy* understanding of physics. The attraction occurs within and between *entire fields* which are *created by*, and connected to the moving plasma. The "reconnection" (transfer of stored energy) occurs *at the particles* as they *move* as a result of that *attraction*.

It's the *transfer* of energy from field to particle movement that defines the difference between your *toy/pretend* understanding of plasma physics and the real deal RC. Priest explained it clearly and you ignored him, so I'm sure you'll ignore me too *yet again*.

It's the *movement/displacement* of the current that is called "magnetic reconnection", not just the magnetic field topology changes that result from that movement.

Somov's example included both A) plasma in the form of "current" in the so called "vacuum", and B) plasma movement in the form of current displacement! WIKI's definition is consistent with Priest's distinction between a *toy* process involving no plasma, and the "real" process that *requires* plasma! Your own *published* references, as well as WIKI all refute your own claims:

Magnetic reconnection - Wikipedia, the free encyclopedia

Magnetic reconnection is a physical process in highly conducting plasmas in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration.

unless I interpret it as total ignorance about magnetic reconnection and where it happens, Michael .

It happens in plasma and results in *plasma displacement*! You're ignoring my answer, WIKI's answer, Priest's answer and Somov's *inclusion* of current. Somov's vacuum isn't A) devoid of moving charged particles, or B) devoid of charged particle acceleration like Clinger's *toy*!

There are no "wires" in Somov's examples about *plasma physics*. You made up those wires in your head because you refuse to read an actual textbook on the topic of plasma physics. When are you going to stop arguing this topic from ignorance RC? Even if they were "wires", the magnetic attraction wouldn't result in movement of the wire, so no 'reconnection" would take place! Oy Vey. When are you going to visit a real library?

 

[Michael]

Your entire argument about "reconnection" comes down to a pure oversimplification fallacy on your part. The "real" process of reconnection is defined by WIKI as:

Magnetic reconnection is a physical process in highly conducting plasmas in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration.

You're trying desperately to "dumb down" the process to read:

"(Process X) is a physical process in which the magnetic topology is rearranged"

Process X in a vacuum is simply *magnetic flux* in a vacuum which results in a *zero* rate of "reconnection" regardless of how much *flux* you introduce into the vacuum. It's a *toy*.

The *real* version of "reconnection" happens A) in plasma and B) to plasma!

 

[RealityCheck01]

...usual rant snipped...

*AKA* total ignorance about plasma and that it is an ionized gas that expands to fill a vacuum unless constrained somehow, Michael .

Denying that you know basic English again: magnetic attraction" does not mean "magnetic reconnection".

Drumroll - a delusion about plasma !
They are filled with a neutral gas, not plasma. There are the electrical discharges (lightning!) in that neutral gas from the central electrode to the outer sphere.
The Wikipedia plasma globe article confusingly calls these plasma filaments which is not quite correct - they are electrical discharges surrounded by plasma. Plasma filaments are filaments of plasma without any cores of electrical discharges.

Drumroll - ignoring scientific definitions: Birkeland current, Bennett Pinch

I write

Nothing in that rant is the answer to the question:
5 November 2014 Michael: Where does magnetic reconnection happen in Somov's example?

And you quote a "magnetic attraction"/"current streams" rant that does not state where the magnetic reconnection happens in Somov's example

If you just cannot spell magnetic reconnection then the 'all around the currents' bit is wrong.
Maybe the question
5 November 2014 Michael: Where does magnetic reconnection happen in Somov's example?
is too hard for you, Michael !
So I will give you a hint: Magnetic reconnection involves magnetic field lines breaking. Somov states where this happens. Somov labels where this happens in his diagram.

You should not rant about imaginary "Somov's examples" (plural) when we are talking about the single example of Somov's example of magnetic reconnection in vacuum. That rant did not answer:
Michael (30 October 2013): If we have electrical wires producing the current in the vacuum of Somov's example then would you claim that magnetic reconnection happens in the electrical wires? without any display of ignorance about the wires not producing the same magnetic fields.

 

[RealityCheck01]

Your entire argument ...snipped ignorance...

My entire argument is based on science, Michael

• Citation of a scientific textbook.
• Citations of scientific papers.
• A easily understood tutorial on MR without any plasma.

I am smart enough to read an article on MR in plasma and know that it is not an article on MR in vacuum
The repeated ignorance of citing a Wikipedia article on magnetic reconnection in plasma to refute a textbook section on magnetic reconnection in vacuum (30 October 2014) !

The ignorance of citing a Wikipedia article on magnetic reconnection in plasma to refute papers mentioning magnetic reconnection in vacuum (6 November 2014)

But I wonder just how long you have had the delusion that that article is about MR in vacuum. I will check...
In this forum the delusion appears on 23rd October 2013 in an ignorant rant about the Tutorial Derivation of Magnetic Reconnection by W.D. Clinger
To show how ignorant that rant was, I asked you to show the mistakes in part 3 of that Tutorial Derivation of Magnetic Reconnection by W.D. Clinger on 25th November 2011

And he did show that "The magnetic reconnection described in Dungey's paper can be reproduced without plasma." in a simple derivation of magnetic reconnection, part 3.

You reply with a rant about kludging and incoherent gibberish. Either put up or shut up:

No putting up unless you count rants about plasma in an example of MR in vacuum and definitely no shutting up!

At the JREF forum it is harder to see when this delusion started given the number of posts about magnetic reconnection you wrote.
20th March 2012 quotes the article
24th March 2012: Cites the article but is basically gibberish.

 

[RealityCheck01]

My entire argument is based on science, Michael

• Citation of a scientific textbook.
• Citations of scientific papers.
• A easily understood tutorial on MR without any plasma.

More science:
4th March 2012, a working astrophysicist, tusenfem, cites Birn & Priest, Reconnection of magnetic fields, Section 4.1.1 which starts with a discussion of vacuum superposition models.

 

[Michael]

*AKA* total ignorance about plasma...[\quote]

Your total ignorance of plasma is directly related to the fact that you refues to read a textbook on MHD theory. When did you intend to rectify your self imposed ignorance?

Most of your rant isn't even coherent, so I'll simply ignore it.

And you quote a "magnetic attraction"/"current streams" rant that does not state where the magnetic reconnection happens in Somov's example

You simply cannot handle my answer so you make me repeat myself.

It *happens* where the *current/moving plasma* takes place. That is the physical location where a *conversion of field energy* results in *plasma acceleration*. I predict you'll ignore my *very clear* answer yet again.

Somov's example has no 'wires'. You invented them in your head. His example wouldn't even work with wires because the magnetic attraction between *solid* wires doesn't result in the movement of the wire. You are grasping at straws because you refuse to visit a library and pick up a book on MHD theory. When did you intend to do that RC? It's been nearly 3 years and counting at this point.....

 

[Michael]

My entire argument is based on science, Michael

Nope. Priest clearly differentiated between a "toy" process from the 'real' process called "magnetic reconnection'. You keep pathetically trying to equate the "toy" to the real thing.

• Citation of a scientific textbook.

Bzzzt. Somov's textbook *included* A) plasma, and B) plasma displacement. Your textbook citation disproved your claims!

Citations of scientific papers.

Double Bzzt! Priest even specifically explained the difference between what he called a 'toy' and what he called the 'real' process, and the difference was *plasma*! Double epic fail!

• A easily understood tutorial on MR without any plasma.

It's an *unplublished* pile of horse manure that describes nothing more than magnetic flux in a vacuum. The really *sad* part is that even the magnetic flux that occurs *actually* occurs everywhere *except* his stupid *NULL*! The NULL has a *zero* magnetic field, so it's incapable of inducing currents in plasmas anyway! Oy Vey! I might as well be talking QM with my cat.

I am smart enough to read an article on MR in plasma and know that it is not an article on MR in vacuum

Apparently "education" just isnt your "thing". You rather fancy yourself as an "expert" on plasma physics based on a few things you heard on a some *random* website in cyberpsace. Wow! Simply amazing. You've cited your ignorant self endlessly, and some *random* unpublished website, but every actualy *published* reference that you've sited actually *falsifies* your claims. Even Priest clearly and methodically described the difference between your *toy* understanding of physics and the 'real' process in *plasma*. You're simply stuck on your own personal denial-go-round and some references to some unpublished random website in cyberspace. Pathetic.

 

[Michael]

I am smart enough to read.....

.......anything *other than* a real textbook on MHD theory.
When are you going to visit a library RC?

 

[RealityCheck01]

...snipped rant...It *happens* where the *current/moving plasma* takes place...

Oh dear, Michael, your ignorance just keeps on going !
There is no "moving plasma" in Somov's example. A "moving plasma" is a flow of ions and electrons which is overall neutral - not a current which is a net flow of charge.

There is no magnetic reconnection at the place that the currents are. Somov's example is two parallel equal currents in vacuum. The magnetic field is caused by the currents and is thus outside of the currents.

Maybe the question
5 November 2014 Michael: Where does magnetic reconnection happen in Somov's example?
is too hard for you, Michael !
So I will give you a hint: Magnetic reconnection involves magnetic field lines breaking. Somov states where this happens. Somov labels where this happens in his diagram.

Another hint: What is outside of the currents or even your imaginary "moving plasma", Michael?

 

[RealityCheck01]

Michael (30 October 2013): If we have electrical wires producing the current in the vacuum of Somov's example then would you claim that magnetic reconnection happens in the electrical wires? without any display of ignorance about the wires not producing the same magnetic fields?

 

[Michael]

Oh dear, Michael, your ignorance just keeps on going !
There is no "moving plasma" in Somov's example.

Irony overload. The ignorance is all yours, and it's entirely self imposed. Are you *ever* going to read a textbook on MHD theory RC, or did you intend to argue the topic of plasma physics from pure ignorance for the rest of your life?

A "moving plasma" is a flow of ions and electrons which is overall neutral - not a current which is a net flow of charge.

Bzzt! Even a cathode ray is a type of "plasma".

Plasma (physics) - Wikipedia, the free encyclopedia

Your ignorance of this topic is just over the top, much like your "tude". Most folks in your shoes would have cowered away in pure embarrassment by now. Really RC, are you *ever* going to pick up a textbook on plasma?

There is no magnetic reconnection at the place that the currents are.

False again. Strike two. I have explained to you (like WIKI and Somov and everyone else) that a *transfer* of field energy *into particle movement* is what makes it "reconnection". Without particles, and particle acceleration, there is no "reconnection'.

Somov's example is two parallel equal currents in vacuum. The magnetic field is caused by the currents and is thus outside of the currents.

You're half right. They "surround' the currents. They aren't little tiny lines the way you *imagine* them to be however, they are *entire fields*, the the gravity fields around the Earth. It's a *continuum*, not a bunch of tiny lines as you imagine them in your simplified world. Much like gravity pulling two *objects together*, the *magnetic fields* pull the two *plasma streams* together over time. The *movement of the objects* is what is called *reconnection* RC, not tiny little lines that make and break in your ignorant and imaginary world.

Another hint: What is outside of the currents or even your imaginary "moving plasma", Michael?

The fields that are *created by* those moving currents is *transferred* into particle kinetic energy! When are you going to stop pretending that your *oversimplified fallacy* isn't reality RC? The WIKI article, along with Somov's *diagram* require a *transfer of energy* to *particles*! Get it?

 

[Michael]

Michael (30 October 2013): If we have electrical wires producing the current in the vacuum of Somov's example then would you claim that magnetic reconnection happens in the electrical wires? without any display of ignorance about the wires not producing the same magnetic fields?

There are no 'wires' in Somov's example, and wires would not work. Solids would not move, therefore solids would not 'reconnect". Get it?

Oy Vey RC. This really is akin to arguing about QM with my cat. We aren't even speaking the same language, because you don't even have the first clue about the language of MHD theory because you refuse to pickup and *read* a textbook on the topic. When are you going to rectify that problem RC?

 

[RealityCheck01]

There are no 'wires' in Somov's example,...

There is no plasma in Somov's example but you seem to think you have the power to introduce plasma which has no magnetic fields around it , Michael !

And wires will work. They produce the same magnetic field as a current. They can be moved as in the example. Get it, Michael?

Solids would not move, therefore solids would not 'reconnect".

Magnetic (not current or plasmas or wire or solid ) reconnection . Get it, Michael?

Michael (30 October 2013): If we have electrical wires producing the current in the vacuum of Somov's example then would you claim that magnetic reconnection happens in the electrical wires? without any display of ignorance about the wires not producing the same magnetic fields?

 

[RealityCheck01]

..snipped insults, ignorance and rant...

An obvious hint in

There is no "moving plasma" in Somov's example. A "moving plasma" is a flow of ions and electrons which is overall neutral - not a current which is a net flow of charge.

There is no magnetic reconnection at the place that the currents are. Somov's example is two parallel equal currents in vacuum. The magnetic field is caused by the currents and is thus outside of the currents.

Another hint: What is outside of the currents or even your imaginary "moving plasma", Michael?

and the previous hint: "Magnetic reconnection involves magnetic field lines breaking. Somov states where this happens. Somov labels where this happens in his diagram."

And you still have no idea what Somov is describing after several years, Michael .

So I will give you the answer: X marks the spot !

This is simple:

1. Somov's example is two parallel equal currents in vacuum.
2. The magnetic fields are caused by the currents and are thus outside of the currents.
3. Magnetic field lines are a continuum of lines - there are an infinite number of them. No one would be idiotic enough to draw every magnetic field line in a diagram. Somov is not an idiot - he draws a few examples.
4. Magnetic field lines do not exist where there is no magnetic field - which should be obvious .
5. Somov marks the spot where there is no magnetic field with an X.
6. Somov displaces the currents by an unspecified driven displacement dl.
7. This moves magnetic field lines across the point X where magnetic field lines do not exist.
8. The magnetic field lines that cross X break and reconnect.
9. This is magnetic reconnection in the vacuum at point X.

 

[Michael]

There is no plasma in Somov's example

You're in pure denial of fact. He has two parallel *currents* running through the vacuum RC. That means there are two streams of charged particles flowing through the vacuum. They *move* too as a result of "reconnection". There are two defined streams of charged particle traversing his vacuum. For crying out loud RC, he even *drew* you a *diagram* and showed you how the charged particle *currents* moved closer to each other!

but you seem to think you have the power to introduce plasma which has no magnetic fields around it , Michael !

You are utterly unqualified to be discussing plasma physics RC. All moving charged particles have a magnetic field around them. There is no way to introduce moving "currents" and not introduce a moving magnetic field. The term "plasma" can be applied to *neutral* batches of charged particles, or *non* neutral batches of charged particles. You're changing terms to suit yourself, from the term 'reconnection' (involving moving charged particle acceleration), to the term "discharge" (which doesn't require a breakdown of a dielectric in Dungey's model), to the term 'plasma' (which can apply to non neutral plasmas). You're simply "making up terms" to suit yourself that have *nothing* to do with MHD theory or plasma physics. Are you *ever* going to read a real textbook on this topic, or just continue to argue the topic from ignorance for the rest of your life?

And wires will work.

Bzzt! They would *not* work because the "attraction" from the magnetic fields would *not* move the "wires". The need for plasma is *absolute*. Your wire example is another prefect example of you *changing* the terms Somov used to suit yourself, and a perfect example of taking is *plasma physics* example from a book on MHD theory *completely out of it's physical context*!

They produce the same magnetic field as a current. They can be moved as in the example. Get it, Michael?

I "get" that you have changed Somov's plasma "currents" into "wires" to suit yourself, Dungey's "discharges" into something other than an "actual" discharges to suit yourself, and you've dumbed down the entire reconnection process to ignore the whole need for plasma and plasma particle acceleration. I might as well be having a conversation about QM with my cat.

Magnetic (not current or plasmas or wire or solid ) reconnection . Get it, Michael?

Bzzt! The solid wires wouldn't move. Get it? You're changing the whole example Somov gave. You're *intentionally* taking it *out of context*! It won't even work in the context that you've taken it, because solid wires would not move as a result of the magnetic attraction between the two currents. You've messed it up at every level RC.

The definition of magnetic reconnection is the very same definition of an electrical discharge given by Peratt. EM field energy is *converted into* particle acceleration. You've in pure denial of every published author on all these topics. There are no "wires" in Somov's example about the behaviors of *plasmas*. There are "actual" electrical discharges in plasma in Dungey's paper on solar flares. There are *actual* transfers of magnetic field energy required in 'magnetic reconnection".

You left out the plasma particles, so the *rate of magnetic reconnection* is always and eternally *zero* in your messed up example of "flux" in a vacuum, regardless of how much *flux* you and poor ignorant Clinger introduce into your pathetic "vacuum" that is devoid of charged particles and charged particle acceleration.

You don't even have plasma particle to your name, so it's impossible to *convert* any magnetic field energy *into* particle acceleration in Clingers sorry example of his own personal ignorance of plasma physics. It's impossible to describe a rate of 'reconnection' that is greater than zero in Clingers nonsense, therefore *zero* reconnection happens in his 'vacuum'.

Your entire argument is based upon an *oversimplification fallacy*. The definition of reconnection is a *transfer of energy* in *plasma*. You've tried to remove both the plasma and the transfer of energy and still claim it's the same thing. It's not the same thing. More false advertising from someone who in this case is simply *clueless* about the topic by choice.

Are you *ever* going to read a real textbook on MHD theory, or are you just going to argue this topic from ignorance forever?

I've met lazy and ignorant "skeptics" before, but you simply take the cake.

 

[Michael]

An obvious hint in

and the previous hint: "Magnetic reconnection involves magnetic field lines breaking.

But magnetic field changes are *not* the *only* thing it "involves". There's your error in a nutshell!

Somov states where this happens. Somov labels where this happens in his diagram."

Yes he does. He shows you that the *currents move* during the 'reconnection' process. Their *movement* is what makes it "reconnection". You have no "movement" of charged particles in Clinger's pathetic empty vacuum, and no *transfer* of energy taking place! It's just simple magnetic flux in a vacuum! You can't even tell the difference between solid state physics and plasma physics, and you don't even understand *solid state* physics, or you wouldn't be referring to ordinary magnetic flux in a vacuum as 'magnetic reconnection".

When are you going to read a textbook on this topic RC?

And you still have no idea what Somov is describing after several years, Michael .

I know exactly what he's describing, namely a transfer of magnetic field energy into *particle acceleration*, just like the WIKI definition. You're clueless about MHD theory by choice.

So I will give you the answer: X marks the spot !

X is meaningless. Unlike Clinger's pathetic *empty* vacuum, where there is no transfer of energy taking place, Somov's example is A) inclusive of plasma, and B) inclusive of plasma particle movement.

This is simple:

1. Somov's example is two parallel equal currents in vacuum.

Yep. He included plasma whereas Clinger did not.

The magnetic fields are caused by the currents and are thus outside of the currents.

Duh! That's why they are able to "attract" the two currents, and *move* them!

Magnetic field lines are a continuum of lines

That's like claiming that gravity is a continuum of lines. It's meaningless to talk about magnetic *lines* to begin with. They are magnetic *fields* that can transfer their *energy* into particle acceleration (or not). Somov can and does transfer field energy into charged particle movement. Clinger cannot and did not.

- there are an infinite number of them. No one would be idiotic enough to draw every magnetic field line in a diagram. Somov is not an idiot - he draws a few examples.

It's idiotic of you to be talking about where X marks the spot and not be talking about the X in the middle of the current stream. That particle *movement* is what makes it "reconnection", not simply magnetic field changes.


You've dumbed down the process to suit yourself like always.
Magnetic reconnection - Wikipedia, the free encyclopedia

Magnetic reconnection is a physical process in highly conducting plasmas in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration.

You're erroneously trying to dumb the whole thing down to magnetic field changes alone!

 

[RealityCheck01]

...snipped usual delusion about plasma in Somov's example...
...snipped usual insults...
..snipped usual delusion about Dungey's "model"
Bzzt! They would *not* work because the "attraction" from the magnetic fields would *not* move the "wires".

Bzzt! A new bit of ignorance from you Michael!.
The currents in Somov's example move because he says they do. He says that some unspecific driver displaces the current.
If a charged plasma (not a general plasma which is quasi-neutral and does not generate outside magnetic fields) moving in a tube were to replace each of the currents then the tubes would have to be displaced by an external force.
If a wire were to replace each of the currents then the wires would have to be displaced by an external force.

But magnetic reconnection in a plasma is different. There we have current sheets whose separation is basically controlled by the magnetic field. A variation in the magnetic field changes the separation of the current sheets which causes magnetic reconnection as the magnetic field lines break and reconnect when they pass across the null point.

...snipped more plasma fantasies and insults...

Which only leaves:

Michael (30 October 2013): If we have electrical wires producing the current in the vacuum of Somov's example then would you claim that magnetic reconnection happens in the electrical wires? without any display of ignorance about the wires not producing the same magnetic fields?

 

[RealityCheck01]

But ...

But you cannot understand English, Michael - There's your error in a nutshell !
I gave you two hints:

• Magnetic reconnection involves magnetic field lines breaking. Somov states where this happens. Somov labels where this happens in his diagram.
• What is outside of the currents or even your imaginary "moving plasma", Michael?

The answers are

• Somov marks the point with an X that is in vacuum.
• There is vacuum outside of the current - even with your imaginary "moving plasma"

Yes he does.
..snipped irrelevant rant...

Yes Somov states where this happens - in vacuum
Yes Somov labels where this happens in his diagram with an X in vacuum.

Then there is t repeated ignorance, e.g. that a Wikipedia article on magnetic reconnection in plasma is about magnetic reconnection in vacuum

X is meaningless.

You really are determined to show how ignorant you are about Somov's example of magnetic reconnection in vacuum, Michael.
X is the most important place in the diagram -X marks the spot where the magnetic reconnection is happening !
X is the most important place in the section -X is where Somov states that the magnetic reconnection is happening !
No X point = no magnetic reconnection !
23rd November 2011 Michael Mozina's delusions about Somov's 'Reconnection in a Vacuum' section II has the text for that section:

Chapter 4. Motion of a Particle in a Field
4.4.2 Reconnection in a Vacuum.
X-type points consist a topological peculiarity of a magnetic field. They are places where where redistribution of magnetic fluxes occurs, which changes the connectivity of field lines. Let us illustrate such a process by the simplest example of 2 parallel electric currents of equal magnitude I in vacuum as shown in Figure 4.17. The magnetic field of these currents forms three different fluxes in the plane (x,y). Two of them belong to the upper and the lower currents, respectively, and are situated inside the separatrix field line A, which forms the figure of the eight-like curve with zeroth X-point. The third flux belongs to both currents and is situated outside of the separatrix.

If the currents are displaced in the direction of each other, then the following magnetic flux redistribution will take place. The currents proper fluxes will diminish by the quantity dA, while their common flux will increase by the same quantity. So the field line A2 will be the separatrix of the final state.

This process is realized as follows: Two field lines approach the X-point, merge there, forming a separatrix, and then they reconnect forming a field line which encloses both currents. Such a process us termed reconnection of field lines or magnetic reconenction. A2 is that last reconnect field line.

Magnetic reconnection is of fundamental importance for the nature of many non-stationary phenomena in cosmic plasma. We shall discuss the physics of this process more fully in chapters 16 to 22. Suffice it to say that reconnection is inevitable associated with electric field generation. The field is the inductive one, since
[equation 4.65]
where A is the vector potential of magnetic field,
[equation 4.66]
In the above example, the electric field is directed along the z axis. It is clear if that if dt is the characteristic time of the reconnection process shown in Figure 4.17 then according to (4.65)
[equation 4.67]
the last equality will be justified n Section 9.2

Reconnection in vacuum is a real physical process: magnetic field lines move to the X-type neutral point and reconnect in it as well as
| the electric field is induced and can accelerate a charge particle or
| particles in the vicinity of the neutral point.