Varying the Coulomb Potential of Metal Tube. MOT secondary flashover.

[seanlogan]

Hello,

   I have a length of steel pipe which I would like to charge negative.  I want to vary the charge (the Coulomb Potential) of the pipe with respect to time, but always keep it negative -- it should never swing positive.

  My experimental setup, circuit schematics, and computer simulation of the Fields can be found here:

https://spaz.org/~magi/elec/pulse/pulse.html

  I am using the secondary of a Microwave Oven Transformer (MOT) as a choke, and a vacuum relay as a switch.  When the switch closes, current begins ramping up through the choke.  When the switch opens, the choke kicks out a spike of (negative) high voltage.

   The problem is that if I use more than 9 or 10 volts, the choke arcs over purple lightning, and eventually destroyed the diodes in my power supply.

   Can you recommend a more appropriate choke to use?  Or a different approach?  I want the Coulomb Potential of the pipe to vary with respect to time, but always be negative, as shown in the second image on this page:

https://spaz.org/~magi/elec/cw/cw.html

   My setup is similar to the experimental setup proposed by Yakir Aharonov and David Bohm in their 1959 paper on "The Significance of the Electromagnetic Potentials in the Quantum Theory".  The Coulomb Potential is high inside a charged pipe, but the Electric Field is nearly zero inside.

   I am considering using a "DC" 30kV power supply which uses ferrite-core transformers, driven at a few kHz, with diodes on the secondary.  I will connect the positive lead to Earth Ground, and the negative lead to the pipe.  I am hoping the ripple on the output will be large.

Thank you,
Sean Logan

[Luca c.]

hi, I think that for your application a van de Graff generator or any other electrostatic generator might be better.
For example using a van de Graff you might be able to control very accurately the potential varying the speed of the belt in the machine, because the electric field and so the potential is in direct relationship to the number of charged ions contained in a given volume, in the atmosphere the charge accumulated by a Van de Graaff generator are naturally dissipated by the ions flowing away in the air, so you have a situation where you can control the total number of charge in a given volume by balancing the input flow of charge versus the output flow, if you want to raise the potential, the speed of the motor is increased, the rod accumulates more charge than what can leave and so the potential is increased.
This setup would be more stable in terms of ripple compared to the 30KV generator, but I think it would also be more useful because accurately controlling the flow of charge from a flyback transformer would be very hard, and even if you can do that you would be limited by the 30KV that is not that high compared to what you might be able to reach with an electrostatic generator.
can I ask for what kind of experiment you need this setup?

[seanlogan]

Dear Luca,

   Yes, a Van de Graaf generator sounds like a good idea.  I recently attended an antique radio swap meet (https://www.pugetsoundantiqueradio.com/) at which a gentleman gave a demonstration of a home made Van de Graaf generator.  I don't know how much charge could be held on a metal tube, as opposed to a sphere, but it would be interesting to find out.

   I am curious about the  Coulomb Potential in regions of space where the Electric Field is zero, such as inside a charged metal tube.   I discovered that two physicists, Yakir Aharonov and David Bohm, were thinking along similar lines in 1959.  To quote from their paper:

In classical mechanics, we recall that potentials cannot have such significance because the equation of motion involves only the field quantities themselves. For this reason, the potentials have been regarded as purely mathematical auxiliaries, while only the field quantities were thought to have a direct physical meaning.

In quantum mechanics, the essential difference is that the equations of motion of a particle are replaced by the Schrodinger equation for a wave. This Schrodinger equation is obtained from a canonical formalism, which cannot be expressed in terms of the fields alone, but which also requires the potentials. Indeed, the potentials play a role, in Schrodinger's equation, which is analogous to that of the index of refration in optics, The Lorentz force does not appear anywhere in the fundamental theory, but appears only as an approximation holding in the classical limit. It would therefore seem natural at this point to propose that, in quantum mechanics, the fundamental physical entities are the potentials, while the fields are derived from them by differentiations.

The main objection that could be raised against the above suggestion is grounded in the gauge invariance of the theory. In other words, if the potentials are subject to the transformation [...], then all the known physical quantities are left unchanged. As a result, the same physical behavior is obtained from any two potentials, A„(x) and A„'(x), related by the above transformation. This means that insofar as the potentials are richer in properties than the fields, there is no way to reveal this additional richness. It was therefore concluded that the potentials cannot have any meaning, except insofar as they are used mathematically, to calculate the fields.

We have seen from the examples described in this paper that the above point of view cannot be maintained for the general case. Of course, our discussion does not bring into question the gauge invariance of the theory. But it does show that in a theory involving only local interactions (e.g., Schrodinger's or Dirac's equation, and current quantum-mechanical field theories), the potentials must, in certain cases, be considered as physically effective, even when there are no fields acting on the charged particles.

Reference:

Aharonov, Yakir. Bohm, David. "Significance of Electromagnetic Potentials in the Quantum Theory". The Physical Review, Volume 115, Number 3, August 1st, 1959.

https://spaz.org/~magi/ref/aharonov.pdf