Supeconducting circuits

LI is conserved in each loop, wot? Assuming no L in the middle leg.

John

Okay. Faraday's law, essentially. And of course energy (I^2*L) is not conserved. Good insight, thanks, John.

It depends. Changing L1 & L2 will do work on the system, just as in a parametric amp. If you change L2, say, a voltage V will appear across the system in order that d/dt(L2*i2**2/2) = V*i2 (power conservation). That will cause a change in i2 and i3 that will be in proportion to the reciprocal of their inductances (the inductance of the centre path will not really be zero).

Cheers,

Phil Hobbs

It depends. Changing L1 & L2 will do work on the system, just as in a parametric amp. If you change L2, say, a voltage V will appear across the system in order that d/dt(L2*i2**2/2) = V*i2 (power conservation). That will cause a change in i2 and i3 that will be in proportion to the reciprocal of their inductances (the inductance of the centre path will not really be zero).

Cheers,

Phil Hobbs

What all this chilly stuff about anyhow?

John

What do you mean by "superconducting loops"?

Do you mean two real superconducting loops connected with real wire with real resistance and real inductance or do you mean an idealized circuit where the resistance of the inductors and wires is zero?

The currents don't "interact", but if the wire is zero resistance, V(L1) = V(L2).

Which means V(t) = L1 di1(t)/dt = L2 di2(t)/dt and i3 = i1 + i2.

What are you attempting to analyze?

--
Jim Pennino

Remove .spam.sux to reply.

Of course Vl1 = Vl2. Both are zero.

John

Yeah, too fast on the reply.

If everything is ideal, there is no voltage or current.

--
Jim Pennino

Remove .spam.sux to reply.

In sci.electronics.design Spehro Pefhany wrote: : How do I analyze a circuit that has two connected superconducting : loops with persistent currents i1 and i2.

The Kirchoff laws

(i) sum of currents to every node equals zero (ii) sum of voltages around every loop equals zero

apply to the superconducting circuits as well as odinary circuits, except that the latter should be modified into

(iib) sum of time integrals of voltages (i.e. up to an integration constant, magnetic fluxes) around every loop equals zero.

Not relevant to the original question, the integration constants (equal to trapped flux) should additionally be integer multiples of the flux quantum,

2.07E-15 webers. : Suppose L1 and/or L2 vary, : what will happen to the currents? Do they interact?

If the leg carrying i3 has a finite inductance, the currents do interact. If it has zero inductance, the leg must geometrically shrink to a point (a node)and you can no longer assign a vector quantity (a current) to it. All this is assuming that there is no mutual inductance between L1 and L2.

Regards, Mikko

: i1 -> i2 ->

: .--------------.---------------. : | | | : C| i3 | C| : C| | C| : L1 C| | | C| L2 : | v | | : | | | : '--------------'---------------'

: (view with monospaced font only)

They pretty much have to be. Ignoring certain specific geometries and perfect magnetic shields (talk to a real superconductor expert to learn about those), Inductors couple to each other, as do capacitors. You can easily make the coupling as small as you wish simply by using longer wires and putting them farther away from each other (this assumes that the wires are not inductors, of course, something that I suspect violate the basic laws of physics). IANASCEE.

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Guy Macon

Is that really true? SQUIDs may constrain the flux through them to some integer multiple of 2e/h, but is it the same for a continuous superconducting loop?

Jeroen Belleman

Stop that IANASCEE stuff, OK? It's pompous and annoying.

John

I will do whatever you want, but I really am at a loss as to how to make you happy. If I post anything on a topic without being an expert in all areas of the topic, I get flamed for "pretending to be an expert." If I signify that I am not an expert, you say that I am being "pompous and annoying." And if I do something that displeases someone, they tell me that it displeases them, and I immediately apologize and stop doing it, I still get flamed about it months or years later. God forbid that I make an actual technical error...

I just want to have technical discussions without having to walk on eggshells trying to avoid offending the sensibilities of someone here and having the technical discussion thrown away to make room for another boring flamfest. I have been around Usenet long enough that the flames don't bother me, but the hijacking of an interesting technical discussion

*does* bother me.

I am not trying to be difficult here. I really am at a loss as to how to avoid offending you. As always, I will comply with any reasonable request in an attempt to get back to discussing technical issues. Just tell me what you want.

--
Guy Macon

What does it mean anyway?

Thanks, Rich

"I Am Not A State Certified Electrical Engineer"?

I Am Not A SuperConductor Electrical Engineeer

Jeroen Belleman wrote: : M Kiviranta wrote: : > Not relevant to the original question, the integration constants (equal to : > trapped flux) should additionally be integer multiples of the flux quantum, : > 2.07E-15 webers.

: Is that really true? SQUIDs may constrain the flux through them to some : integer multiple of 2e/h, but is it the same for a continuous superconducting : loop?

I think so. A mere perfect conductor can trap an arbitrary amount of flux (flux changes are prevented by screening currents which arise in the loop), but for a superconductor the trapped flux is a multiple of the flux quantum. The reason is that the mechanism behind superconductivity (when contrasted against a hypothetical *classical* mechanism giving rise to zero resistivity) requires the quantum phase of the electrons (more accurately: phase of the order parameter of the condensate) to change by an integer multiple of 2pi radians when traversing around the loop. Thus even the flux threading an enormous persistent current magnet (like an MRI magnet or a fault limiter) should consist of an integer number of flux quanta, however enormous the number might be.

It is actually hard to think of any mechanism which would give rise to zero resistivity and would *not* imply some sort of a flux quantization. Zero loss suggests that electrons must travel ballistically around the loop (no collisions), and uniqueness requirement of their wave functions then dictates that quantum phase must shift by integer times 2pi around the loop.

Some ways out would be to find some charge carriers which don't come associated with a quantum phase, or to find a collision mechanism which could scramble the quantum phase but conspire in such a way that no net energy loss takes place. I guess such mechanisms are probably forbidden by some conservation law or another. Actually, the, conspiring-collisions mechanism sounds a bit like the Frölich interaction, which *does* lie behind the BCS superconductivity, but even there the loss of quantum phase of the individual electrons magically re-appears elsewhere, as the boundary condition of the order parameter.

This is quite far from the original question, by the way...

Regards Mikko