MH's ideal coil and voltage question

[minnie]

   The old tinman's dug himself into such a deep hole I'm
   expecting him to emerge in the U.K.
         John.

[verpies]

The electric field is a force,,

Strictly speaking it is not a force.
Electric field is a region of space where an electric charge experiences a parallel force.

However in a mechanical analogy the voltage can be symbolized by an unbalanced force, or torque, or pressure...

voltage is a differential within that field, current responds to that differential.

It would be more correct to write that electric charges respond to that differential.
Electric current is not electric charges. It is the motion of these charges ...not necessarily electrons.

The magnetic field is a force,

Again, strictly speaking it is not a force.
Magnetic field is a region of space where a moving electric charge experiences a perpendicular force.
A "field" is an abbreviation for a "force filed" ...or in other words: "field of forces".

is a reaction to current being excited by voltage.

It would be more correct to write, that magnetic flux is proportional to electric current.

It is possible to create electric current in an inductor without inserting a voltage source into it. 
For example as in your example cited below:

If I place an open superconductor next to a source of controllable magnetic field,, I turn up that field as to envelope the superconductor,, then I close the super conductor and try to turn down the source of the magnetic field.

Then you will create an electric current in the superconducting coil without inserting a voltage source into it.

The moment you close that superconducting coil, the level of magnetic flux penetrating that coil will became frozen. It will not change no matter what you do with the external "source of controllable magnetic field".  If you remove that source altogether, the closed superconducting coil will maintain the level of flux, which existed at the moment the coil was closed. 

This means that the closed S.C. coil will become a sort of a "permanent magnet" ...which will attract iron chunks and repel or attract other permanent magnets (depending whether their N or S poles are facing the closed S.C. coil).

So if I supply the differential and the current responds but it does so with no resistance except to build the magnetic field,

...which is called the inductive reactance.

and at some point that field stalls in growth,

Why would it stall?

[verpies]

Bad choice of words,, is there not a curve to the change in flux density?

Coils do not care about the flux density (B) but they do care about the magnitude of flux (Φ).

There is no limit to the flux magnitude in an ideal inductor energized by an ideal voltage source inserted in it.
However, for resistive coils there is a flux limit. Namely Φ_MAX=LV/R
For resistive coils there is also a current limit. Namely i_MAX=V/R

I am assuming that the differential will have some cost,, so choosing the better bang for the buck on the curve is what I was getting at.

Choosing the best point on the i vs. t curve makes a lot of sense with resistive coils. However with ideal or S.C. coils it does not make much sense below the superconductor's breakdown limit.

I would think that "if" the S.C. could be opened across a low resistance device and then if it were a coil that created the magnetic field,

Do you mean that the "low resistance device" is a 2^nd coil that is resistive and in series with the previously energized S.C. coil?

If "yes", then you have one coil transferring electric current to a second coil.  This is known as one of the most inefficient energy transfers in existence, because the energized S.C. coil behaves as an almost ideal current source, feeding a 2^nd coil whose reactance is opposing a current change. 
A coil is the worst device to receive current from another coil (while a capacitor is the best).

The result of a coil-to-coil transfer is a huge voltage spike at the beginning and a lot of the energy radiated away as EM wave. This is very, very bad for the efficiency of the energy transfer.

I also refer to the local area effect,, as in turning off the local area field effect,  not meaning turning off the field but just the effect,, the gradient is changed.

Coils don't care about the gradients of magnetic flux nor about the flux density.  They care only about the total flux magnitude that penetrates them.  Really!

However the force exerted on a magnet or another coil is very dependent on the magnetic flux density gradient.
But because a higher gradient also means a shorter distance, then the integral of force over distance (which is work or energy) is the same as with a lower gradient but over a larger distance, thus it is a no-win scenario.

But don't despair. There might be a light in the tunnel if you consider the closed coil in your example that attracts a soft iron chunk or better yet: a nonconductive soft ferrite.

[verpies]

So the ideal source does not "need" to have a closed short.

The ideal voltage source cannot have a short. If it did, an infinite current would flow through it.
The ideal current source cannot have an open. If it did, an infinite voltage would develop across it.

A voltage source can be directly connected to a current source in parallel, without bad consequences (infinities).

An energized capacitor behaves like a voltage source.
An energized inductor behaves like a current source.

[verpies]

I thought that coils cared abut the change in flux density,,

They don't.

so that would be the flux and the rate of change of that flux.

That's correct.  Coils "care" about the total flux very much.
It is important to distinguish the flux (measured in Webers) from the flux density (measured in Webers/m² or Teslas or Gauss).

I used that understanding to build my dual voltage generator.  It provided 2 different voltages at the same time from the same coil,, just by using a different rate of change,, 

It is not surprising.
It must have been a different rate of change of flux (dΦ/dt), not a different rate of change of flux density (dB/dt)

I look at voltage like pressure...

So do I.