News, Reviews & Discussion of EEStor Inc.
It is worth reviewing the old killer flux arguments. Another motivation is that peterP has discovered a new electrostatic principle why they don't work which he will share with us:
I have made enough mistakes in my life to cope with valid disagreement. The problem is you don't understand electrostatics. This is proven by your "killer flux" invention. If you apply the principle of superposition correctly you will find things are not as you now seem to believe.
So - first what is the killer flux argument?
Given flat plates a surface charge of 50C/m^2 would lead to fields of 7MV/u in the gap between the plate charge and the (opposing) dielectric charge. This field is high enough to ionise any lattice, therefore such surface charge can't exist.
There are a number of subtleties about this argument. The first issue is that you could it appears use it to show that normal ceramic capacitors don't work:
Given flat plates a surface charge of 0.25C/m^2 would lead to fields of 35,000V/u in the gap between the plate charge and the (opposing) dielectric charge. This field is high enough to ionise any lattice, therefore such surface charge can't exist.
The induced field still looks probably too high! But that leaves out the dielectric. If you have ionic polarization equal to this surface charge there is no field on distances larger than the charge movement distance for ionic polarization: less than one lattice cell. So all is OK. The problem with killer flux is that the surface charge is higher than any possible ionic polarization. What makes ionic polarization so special? We have other polarization methods after all. It is that it happens with very small charge movements. So does classic electronic polarization, and that would do equally well but does not to give k much higher than 2 or so. Such a low k does not reduce the killer flux's killer field enough to be helpful.
So flux kills when it cannot be (nearly) balanced by polarization. The limit for electronic and ionic polarization with all charges bound to a lattice cell is around 1C/m^2. If you allow charge exchange polarization between the ions in a bicubic cell the limit goes up to maybe 1.5C/m^2.
The second issue is the gap between the plates and the opposing charge. You might argue this is so small that the killer field does not have enough room to develop, and quantum effects save the day. The trouble is that quantum effects also limit the volume charge density in material to around 1 electron per lattice cell. Pauli exclusion means that piling lots of electrons into a small volume is impossible without giving them extra energy. The effect is that at the edges of charged conductors charge spreads out a bit into the interior.
At 50C/m^2 this spreading out effect is large. How large TP can perhaps help us with. I suspect there are some nice formulae we could use to approximate it. Anyway, I'll investigate further if challenged on this point. I maintain large enough that the depth of uncancelled surface charge, and hence volume which experiences killer field, is large enough for voltage to exceed bandgap by a large factor, even given some cancellation from electronic polarization (inner electron shells). Suppose the k from these inner electron shells is 7 (a gross overestimate). There remains 1MV/u or 1000V/nm field. So one lattice cell (0.4nm typically) of this is enough to give 400V - much larger than any bandgap.
One amusing issue of this nanoscopic view of the killer field is that it kills only by making whatever it touches conduct. So killer field inside the metal plate is fine, because charge is free to move to an equilibrium position and conduction no problem. Why can't we have conduction everywhere? Something insulating must separate the plate killer charge from the opposing charge. Otherwise Coulomb attraction between the two would mean that they cancelled each other out, and are capacitor becomes a conductor. It does not matter whether the opposing charge is another plate, or space charge moving inside a dielectric: it must the the same size as the plate charge, and there must be an insulating barrier to stop it joining the space charge. That barrier is made to conduct by the killer field from the two sets of opposing charge.
You don't need Gauss to calculate this - you can do it all by considering Coulomb force on any charge in the insulating barrier (that is just another way of describing the induced filed of course).
What about space charge inside the dielectric? The best way to think of this is to ask: "what is it that stops the space charge from moving all the way through the dielectric?". Whatever that insulating section is, the killer field argument will then apply to it.
The third issue is what if the plates are not really flat? For example suppose the plate (or dielectric) has conducting needles, like a forest, which interlock with similar needles from the other plate. Charge is free to move along each needle (because it conducts) but not to hop between adjacent needles.
The effect here is to make the plates much higher effective surface area than they appear to be. And it really is a get-out for the killer flux argument, because the effective surface charge is now divided by the "fractal expansion ratio" - the amount the plates have increased in surface area.
If anyone wants to kill the killer flux argument for this reason I agree. I stated this as a caveat "fractal plates" three years ago (?) when I first wrote up killer flux in detail. All that has changed since then is I understand more about how difficult it is for fractal plates to store high ED. Here is what I was summarising two years ago, which still seems about right. I'd link the original Gauss disproof threads but can't seem to find them.
Theoretically, if fractal plates could be made with a weird dielectric (and TP, always the optimist, sees this as likley) they could just nicely explain the current EEstor measurements. They could however not go much higher than 1000J/cc - as TP and others would agree.
Now I await with baited breath for PeterP's argument against this. He is clear that I don't understand electrostatics. Fair enough - let us have some better understanding posted here.
Thread rules: stick to electrostatics and related matters.
What calculations? The material polarizes to the degree it does. Its not a calculation. Its not as if The Great Designer in the Sky said to His Helpers, "ok, today I'm creating barium titanate with a k of so and so. Just go down there, measure it and make certain its the right value." There isn't anyone who knows the first principle- the k is whatever you measure it to be.
You discuss fractal plates and Gauss in the topics below.