I Paradox of Superconductivity

[Karmyogi01]

TL;DR

Inductance of a superconductive coil

For a series R-L circuit that uses superconductive components, how long would it take for current to build up after the power is turned on?

 

[berkeman]

TL;DR Summary: Inductance of a superconductive coil

For a series R-L circuit that uses superconductive components, how long would it take for current to build up after the power is turned on?

Why are you putting a resistor in series with a superconducting inductor? That kind of defeats the purpose, no?

 

[Karmyogi01]

Why are you putting a resistor in series with a superconducting inductor? That kind of defeats the purpose, no?

There is no resistor in series. All components are superconductive. R is vanishingly small

 

[berkeman]

What is the source impedance of the power supply that you are using to build the current? How is it connected to the superconducting coil?

 

[Karmyogi01]

What is the source impedance of the power supply that you are using to build the current? How is it connected to the superconducting coil?

I am assuming an ideal power source with zero impedance for clarity. However, the fundamental logic will not change even if it were not an ideal power source.

 

[Karmyogi01]

I am assuming an ideal power source with zero impedance for clarity. However, the fundamental logic will not change even if it were not an ideal power source.

For a series circuit the power supply is connected in series.

 

[Dale]

The time constant will depend on the radiation resistance of the superconductor. Superconductors have no resistance at DC, but at high frequencies they do have resistance and effective resistance.

 

[Karmyogi01]

The time constant will depend on the radiation resistance of the superconductor. Superconductors have no resistance at DC, but at high frequencies they do have resistance and effective resistance.

Good insight indeed! However, here we do not have the high frequency situation.

 

[renormalize]

Good insight indeed! However, here we do not have the high frequency situation.

Are you sure? The idealized version of "the power is turned on" is a step-function in time, which contains Fourier components with arbitrarily high frequency.

 

[Dale]

Good insight indeed! However, here we do not have the high frequency situation.

As @renormalize mentioned, you have arbitrarily high frequencies for switching on an ideal source.

 

[Baluncore]

For a series R-L circuit that uses superconductive components, how long would it take for current to build up after the power is turned on?

The series R+L will need a return circuit, that has not yet been defined.

In effect, R1+L1 is a transmission line operating against an unspecified environment. The superconducting resistor R1, will become a second series inductor, L2. The length of the combined L1+L2 surface, and the dielectric insulation, will determine the transit time, t. The open (or maybe closed) far end will reflect the initial turn on transient back to the input at t2 = 2*t.

The current through L1+L2 will continue to rise in 2t long steps forever, as the reflected wave bounces back and forth along the impedance of the transmission line, between the mismatched terminal impedances.

It will actually be more complex since the impedance of the R1 and L1 transmission lines may differ and so form different resonators. Also, the coupling between the turns of conductor on the inductor, and maybe wire wound resistor, could form a faster capacitor coupled ladder network.

 

[Karmyogi01]

Are you sure? The idealized version of "the power is turned on" is a step-function in time, which contains Fourier components with arbitrarily high frequency.

The radiation resistance is supposed to be very small and does not change the logic in a fundamental way. The time constant (TC) does not match what we observe. In addition, the question is not constrained to only an ideal power source.

 

[Dale]

the question is not constrained to only an ideal power source

I am assuming an ideal power source

Hmmm.

The time constant (TC) does not match what we observe.

What makes you think that? Do you have a reference that shows an experiment where it doesn’t match?

 

[Karmyogi01]

Hmmm.

What makes you think that? Do you have a reference that shows an experiment where it doesn’t match?

As stated above, I mentioned "ideal source" for the sake of clarity only and mentioned already that we do not necessarily have to assume that. I stated this already. To answer your question regarding TC, please tell me your estimate of "radiation resistance."

 

[berkeman]

As stated above, I mentioned "ideal source" for the sake of clarity only and mentioned already that we do not necessarily have to assume that.

Who is "we"? If we knew the actual application, that would help us to focus our responses.

 

[Dale]

, please tell me your estimate of "radiation resistance."

This depends on the geometry but is typically in the range of 50 to 300 ohms.

 

[Karmyogi01]

Thanks Dale for the info. So, this resistance would be a factor in the ramp up of voltage to V. If the ramp up is done very slowly, then the impact of the radiation resistance can be made insignificant. The real story begins after reaching the desired very small voltage V. From here on, the current would increase with a time constant (TC) being extremely large, especially for an ideal power source. We can expect the current to rise at a rate of about (V/L) amps/sec. in an almost linear fashion (initially) and take almost forever to reach its final value. This is contrary to our observations!

 

[sophiecentaur]

The radiation resistance is supposed to be very small and does not change the logic in a fundamental way. The time constant (TC) does not match what we observe. In addition, the question is not constrained to only an ideal power source.

Sorry but that doesn't make sense. If you have a circuit comprising only 'ideal' elements then you can draw no valid conclusions about how it will behave. If you say that the radiation resistance is very small then it will still be the highest value resistance in the circuit so it will, in fact be very big and it will be the resistance that determines the time constant.

in an almost linear fashion

What does that mean? There will be an exponential change as with any other 'time constant' (that's a definition of time constant). I'm afraid you're going round in circles with this argument. An example of where the time constant is frequently measured. Charging up a superconducting magnet takes many hours or even days (google time to switch on a superconducting magnet). That's a practical application for your question.

 

[renormalize]

The time constant (TC) does not match what we observe.

This is contrary to our observations!

You keep pointing to contrary "observations". To support that claim, please cite a scholarly reference that exhibits what is observed experimentally for the configuration you are discussing.

 

[Karmyogi01]

Sorry but that doesn't make sense. If you have a circuit comprising only 'ideal' elements then you can draw no valid conclusions about how it will behave. If you say that the radiation resistance is very small then it will still be the highest value resistance in the circuit so it will, in fact be very big and it will be the resistance that determines the time constant.

What does that mean? There will be an exponential change as with any other 'time constant' (that's a definition of time constant). I'm afraid you're going round in circles with this argument. An example of where the time constant is frequently measured. Charging up a superconducting magnet takes many hours or even days (google time to switch on a superconducting magnet). That's a practical application for your question.

That's not what I said. Please read the whole post. Your first paragraph states the obvious!

 

[Baluncore]

We can expect the current to rise at a rate of about (V/L) amps/sec. in an almost linear fashion (initially) and take almost forever to reach its final value. This is contrary to our observations!

The physical arrangement of the circuit components will be important. You have not described the complete circuit. Depending on the construction of the inductor, you may have a slow-wave structure that ignores the bulk inductance.

How about actually describing the physical layout, and what current you actually observe when you arbitrarily "power" the circuit, is that with a ramp, or a step.

A circuit and its response are never paradoxical, you get a paradox when you do not understand the circuit you are working with. Your inability to describe the circuit explains your paradox.

 

[Dale]

in an almost linear fashion (initially) and take almost forever to reach its final value. This is contrary to our observations!

Ramping up a MRI magnet is almost linear, it takes a few hours which is not almost forever, and I don’t see what you think is contrary to what in any of that.

You are making random assertions of some contradiction, please post the professional scientific reference that describes the actual observations you are discussing. So far it just seems like your unfounded opinion

 

[Karmyogi01]

Ramping up a MRI magnet is almost linear, it takes a few hours which is not almost forever, and I don’t see what you think is contrary to what in any of that.

You are making random assertions of some contradiction, please post the professional scientific reference that describes the actual observations you are discussing. So far it just seems like your unfounded opinion

Thanks for making my point! Yes, “hours” is not forever! However, the analysis says times required are likely to be much longer than that. I am calling it a “paradox” and NOT a contradiction. I believe there is an explanation, but the discussion here has not yet yielded the resolution! Following your advice, I will try to post a scientific paper. I honestly appreciate the valuable inputs from all. Please, stay tuned! I expect to find the resolution soon and post it here.

 

[Dale]

However, the analysis says times required are likely to be much longer than that.

What analysis? All I have seen is your unfounded assertions to that effect.

Following your advice, I will try to post a scientific paper. I honestly appreciate the valuable inputs from all. Please, stay tuned! I expect to find the resolution soon and post it here.

Indeed. Please do.

 

[sophiecentaur]

Ramping up a MRI magnet is almost linear, it takes a few hours which is not almost forever, and I don’t see what you think is contrary to what in any of that.

If you measure a linear ramp then the source impedance must be designed to be constant current. No problem but one can't draw conclusions about a circuit where 'R' varies.

It would be nice to be given the full story from the OP - with some evidence and a description of the system.

When there's any implied claim about a paradox, one has to be skeptical.

 

[Dale]

It would be nice to be given the full story from the OP - with some evidence and a description of the system.

When there's any implied claim about a paradox, one has to be skeptical

Agreed. You could design circuits with a superconducting component and a long time constant and you could design circuits with a superconducting component and a short time constant. So this personal-opinion-in-place-of-evidence approach is not a sound basis on which to claim a contradiction

 

[sophiecentaur]

You could design circuits with a superconducting component and a long time constant

Yes - merely by increasing the source resistance but there's a lot of energy stored in a big magnet and you would want an efficient charging system which would not be a simple resistive source (with I squared R losses) . So the term should be something like "charge time" and not "time constant".

I'd suggest that no real system would have a simple time constant so that 'paradox' flies out of the window.