[Spehro Pefhany]

How do I analyze a circuit that has two connected superconducting
loops with persistent currents i1 and i2. Suppose L1 and/or L2 vary,
what will happen to the currents? Do they interact?


i1 -> i2 ->
.--------------.---------------.
| | |
C| i3 | C|
C| | C|
L1 C| | | C| L2
| v | |
| | |
'--------------'---------------'

(view with monospaced font only)

 

[Spehro Pefhany]

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.

 

[[email protected]]

How do I analyze a circuit that has two connected superconducting
loops with persistent currents i1 and i2. Suppose L1 and/or L2 vary,
what will happen to the currents? Do they interact?


i1 -> i2 ->
.--------------.---------------.
| | |
C| i3 | C|
C| | C|
L1 C| | | C| L2
| v | |
| | |
'--------------'---------------'

(view with monospaced font only)

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?

 

[[email protected]]

Of course Vl1 = Vl2. Both are zero.

John

Yeah, too fast on the reply.

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

 

[Jasen Betts]

How do I analyze a circuit that has two connected superconducting
loops with persistent currents i1 and i2.

Kirchoffs node law looks apropriate.

Suppose L1 and/or L2 vary,
what will happen to the currents? Do they interact?

Are they magnetically coupled?

i1 -> i2 ->
.--------------.---------------.
| | |
C| i3 | C|
C| | C|
L1 C| | | C| L2
| v | |
| | |
'--------------'---------------'

(view with monospaced font only)

bye

 

[M Kiviranta]

: 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)

 

[Jeroen Belleman]

: How do I analyze a circuit that has two connected superconducting
: loops with persistent currents i1 and i2.

The Kirchoff laws

[...]

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?

Jeroen Belleman

 

[Rich Grise]

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

What does it mean anyway?

Thanks,
Rich

 

[Rich Grise]

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...

Jeezee Cry, Guy, grow a skin and quit sniveling.

Remember: You can't please everybody, so you might as well try to please
yourself - but first you have to learn to ignore the assholes.

Cheers!
Rich

 

[M Kiviranta]

: 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