According to BAC, you apparently think you can violate Gauss's law with refrigerator magnets. Start with this:
...........................
...........................
...........................
.....NS.......NS.......
...........................
...........................
...........................
Draw the field lines in the middle. Introduce two more magnets, slowly, until you have this:
.............N...........
.............S............
...........................
.....NS.......NS.......
...........................
.............N.............
.............S.............
And withdraw the original magnets:
.............N...........
.............S............
...........................
............................
...........................
.............N.............
.............S.............
And draw the field lines. Seriously, take four magnets off of your fridge and try it. Good heavens! You must have violated Gauss's law! Quick, call the Monopole Response Unit and get scrubbed down!
What are you talking about? How does a standard example of a neutral point between four magnets show magnetic reconnection?
Do the experiment I showed you with the four magnets. Did the experiment "actually occur"? Good. You have just shown that reconnection can actually occur.
Yes, I did it, and oddly enough there was no explosive release of energy as the lines reconnected. The field lines did exactly what they should do, cancelled out in the necessary places, and due to this the topology of the abstract lines changed. The lines certainly appear to 'reconnect' or cross, but there is a good reason for that, they cancel out and form a neutral points. No energy release involved.
What this has to do withmagnetic reconnection is beyond me, and i really think you need to check upon what is thought to happen in magnetic reconnection, becasue this is certainly not it.
That equation is satisfied for the field Zig and I have posted. Do you or do you not dispute that?
1) Yes or no?
Yes. I was referring to the idea of open magnetic fields and how they cant exist according to Maxwell, and your field is not an open configuration. Helps if you read my posts, or the links i have provided you with. Since you seem unable to, i'll just have to copy some of the necissary material.
Do you agree that given a magnetic field, we can unambiguously draw the field lines and use them to answer the question of whether two points are or are not connected by a field line? And do you further agree that the plot I posted above is correct for that field, and that it shows that as we vary the values of a and b over time, some pairs of points go from being connected by a field line to not connected by a field line (and some other pairs the opposite)?
2) Yes or no?
Yes. Although instead of saying "we can unambiguously draw the field lines and use them to answer the question of whether two points
are or are not connected by a field line?" It may be better terminology to just make sure that someone reading this is aware that there is nothing actually physically connecting these two points, as you wording certainly implies.
The statement we are discussing is whether the magnetic field lines for a magnetic field which satisfies ∇ · B = 0 can reconnect. There is nothing ill-defined or "erroneous" about that question. It doesn't make any difference if the lines physically exist - the field exists, and given a field we can draw field lines and see what they do. We have given you an example of such a field. Do you or do you not dispute that the lines of the field Zig and I posted reconnect? (This is the same question as 2).)
3) Yes or no?
Yes, the lines appear to reconnect, just as they do in any model of a standard neutral point. Given the definition of what field lines are representing, it would not make any sense for them to not. A simple interaction between solenoid fields can easily demonstrate this.
The field in question is not a mathematical model - it is a physical field configuration which satisfies Maxwell's equations, and which we could create in a lab (and has been, many many times). Do you agree that magnetic reconnection - which means that the MAGNETIC FIELD LINES associated with a physical magnetic field RECONNECT - can occur? If you have answered "yes" to the other three questions, the answer to this one must also be yes - but consistency is not your strong suit, so...
4) Yes or no?
In your example, the topology of the lines describing the vector field do appear to reconnect, Yes. And there is a simple reason for that: cancelling opposite and equal magnitudes of a vector field. And as far as i am aware, this process releases no energy.
Well, now you've demonstrated once again you completely fail to grasp what is actually claimed to occur in magnetic reconnection, and the difference between this process and the simple act of cancelling out lines that represent a vector field.
In this magnetic reconnection configuration, the field lines are bent tightly like the elastic strings of a catapult. When the field lines suddenly straighten, they supposedly fling out plasma in opposite directions. The reason that they suddenly straighten is assumed to be the second term in the MHD pressure equation, i.e,
∇(p + B2/2μo) − (B∇)B/μ0 = 0.
For a start off, Alfvén addressed this point by noting that the second term in this relationship is equivalent to the pinch effect that is caused by electric currents.
Heres a basic configuration thought to cause energy release in a magnetic reconnection process;
The standard explanation of reconnection (above picture) is that magnetic field lines 1 and 2 move in from the left and from the right, and eventually come together (short circuit) at the central point. There they change their structure: The two top halves join (reconnect) and move up, ultimately reaching the position of line 3, while the two bottom halves join and form the line that later moves to position 4.
Although the proposed reconnection mechanism changes the topology of the magnetic field, it does not explicitly reduce the strength of any part of the magnetic field. Thus, it cannot liberate magnetic energy that is stored in that field.
Lines 1, 2, 3, and 4 are magnetic field lines and, as such, cannot move or “reach the neutral line.” An additional error is made in assuming that plasma is “attached” to those lines and will be bulk transported (which is shown by the dashed paths in the above picture) by this movement of the magnetic lines.
One source explains reconnection as being caused by the breaking of magnetic field lines. “
Magnetic reconnection is a fundamental physical process occurring in a magnetized plasma, whereby magnetic field lines are effectively broken and reconnected, resulting in a change of magnetic topology, conversion of magnetic field energy into bulk kinetic energy and particle heating”
Proposing that magnetic field lines move around, break, merge, reconnect, or recombine is an error based on the false assumption that the lines are real entities in the first place.
This is an example of reifying an abstract theoretical concept. Field lines are not real-world 3-D entities and thus cannot do anything. Like mathematical singularities, field lines are pure abstractions and cannot be reified into being real 3-D material objects.
The central point in the above picture from which energy is (supposedly) released by magnetic reconnection is a neutral point, one at which the magnetic field strength is zero valued. I've said this before, so Lets break this down a bit.
At the neutral point (or line), the current on the right produces a magnetic field strength vector that is vertically upward. Similarly, the current on the left produces a magnetic field vector that is vertically downward at that point. Therefore, these two field strength vectors sum to zero at the center of the figure, and the strength of the B field at such a neutral point is identically zero.
The energy that is stored at any point in a magnetic field is proportional to the square of the magnitude of the magnetic flux density at that point, i.e.,
[latex]W_{B}=\frac{1}{2\mu_{0}}\int{B^2_{I}}dv[/latex]
where B
I is the magnitude of the magnetic field, and dv is a small volume element. Thus, if BI = 0 at any given point, then the stored energy there would be W
B = 0. No energy is stored at a neutral point; this is why it is called a neutral or null point.
No energy release can occur from any point at which no energy is stored.
This is what it comes down to, either magnetic fields have some new mysterious property that enables them to release energy when the topology of the lines describing the field changes (note that the actual field itself does not change, just the topology of the lines describing the field), or there is a more rational explanation than this using well known plamsa effects.
http://members.cox.net/dascott3/IEEE-TransPlasmaSci-Scott-Aug2007.pdf
However, a large amount of energy can be stored in and released from the surrounding field structure but only if either or both currents, I, take on lower values. This is easily demonstrated in the example in Fig. 2, which is given in the following. The total energy that has been delivered to an electrical element, by time T0 is given by:
[latex]W(t_{0})=\int_{-\infty }^{t_{0}}v(t)i(t)dt.[/latex] ..............(6)
For the case of the flux-linked conductors in the example, i(t) = 2I, and v(t) is the voltage drop across a unit length of the conductor in the direction of i(t). Faraday’s law indicates that;
[latex]v(t)=\frac{d\phi(t)}{dt}[/latex] .................(7)
where Phi ([latex]\phi[/latex] is the total magnetic flux that links the conductors. Thus, the energy that is stored in the magnetic field that surrounds the conductors at time t0 is given by;
[latex]W(t_{0})=\int_{-\infty}^{t_{0}}\frac{d\phi}{dt}i(t)dt=\int_{\phi(-\infty)}^{\phi(t_{v})}id\phi[/latex] ..............(8)
Where the total magnetic flux depends on the current’s amplitude, i.e.,
[latex]\phi(t)=Li(t)[/latex] ..................(9)
The constant of proportionality L is called the inductance, which may be a constant or a function of φ. When a current flows in large regions, this single inductance element L should be replaced by a transmission line, and the situation is then more accurately (but less intuitively) described by partial differential equations [1]. Equations (6)–(9) demonstrate the basic principle that the total energy that is stored magnetically in the infinite volume surrounding the conductors completely depends on the current. That is, using (9), (8) may be written as an integral in terms of only the current. The total energy that will be released from this volume over any time interval is thus clearly a function of the change in current amplitude over that interval.
If these twin currents are disrupted (e.g., by an exploding DL in their path), the field will quickly collapse and liberate all of the stored magnetic energy that is given by (8).
Investigators who prefer to avoid explicit mention of electric current as a primary cause of cosmic energy releases fall back on magnetic reconnection as an explanation.
In certain situations, magnetic reconnection supposedly directly converts magnetic energy into kinetic energy in the form of bidirectional plasma jets. The process is initiated in a narrow source region that is called the “diffusion region.” According to the theory, both resistive and collisionless processes can initiate reconnection. One of the key predicted signatures of collisionless reconnection is the separation between ions and electrons (plasma) in the diffusion region. This separation is said to create a quadrupolar system of Hall currents and, thus, an associated set of Hall magnetic fields. Even here however, it is understood that any released energy comes not from neutral points, lines, or surfaces, where no energy is stored, or bulk movement of plasma but from the surrounding magnetic field structure that depends on those Hall currents for its existence.
The crucial difference between the two explanations is the question of which quantity (time-varying electric current or moving magnetic “lines”) causes energy release from the magnetized plasma.
Alfvén was explicit in his condemnation of the reconnecting concept: “Of course there can be no magnetic merging energy transfer. The most important criticism of the merging mechanism is that by Heikkila, who, with increasing strength, has demonstrated that it is wrong. In spite of all this, we have witnessed, at the same time, an enormously voluminous formalism building up based on this obviously erroneous concept."
So Sol, make your choice now. Either the motion of field lines themselves causes energy release, or like Alfvens interpretation of this phenomenon, a time varying electric field causes it. (And If you choose magnetic field lines, I will expect a quantitive derivation of how a magnetic field line in the process of reconnecting can do something physical like release energy)
