## Capacity of a superconducting loop?

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zenten
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### Capacity of a superconducting loop?

I can't seem to find any details on this, which seems strange as it seems like a basic question really.

What are the factors for determining the capacity of a superconducting loop? Does it depend on the material type? I'm assuming that the thickness of the wire and the circumference of the loop would be relevant, but I have no idea what the actual formula might be.

eSOANEM
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### Re: Capacity of a superconducting loop?

Do you mean capacitance?

If so, yeah, it is a simple calculation. In fact, most calculations of capacitance for a given geometry assume it has no resistance i.e. it is a superconductor. As such, if you look up a formula for the capacitance of a certain geometry, chances are it'll actually be for the superconducting case.
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zenten
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### Re: Capacity of a superconducting loop?

eSOANEM wrote:Do you mean capacitance?

If so, yeah, it is a simple calculation. In fact, most calculations of capacitance for a given geometry assume it has no resistance i.e. it is a superconductor. As such, if you look up a formula for the capacitance of a certain geometry, chances are it'll actually be for the superconducting case.

I don't think so, but I'm getting a bit confused by the terminology.

Basically, if you use that loop like a battery, how much can it store, using the same sort of terms you would use for a battery?

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### Re: Capacity of a superconducting loop?

Do you mean, if you use a superconducting loop as a superconducting magnet, how much energy can it store?
In that case, you should look up the energy stored in an ideal inductor, since again, the calculation assumes superconductivity.

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### Re: Capacity of a superconducting loop?

A superconducting loop can store energy in its magnetic field by acting as an inductor; W=½LI². See https://en.wikipedia.org/wiki/Inductanc ... its_in_air for a formula for the inductance of a wire loop. An inductor is very much unlike a battery, though.

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### Re: Capacity of a superconducting loop?

Yeah, batteries derive their power through chemical processes. A superconducting coil does not have access to any of these. It can however store energy like and inductor or a capacitor (provided you have some other electrode somewhere even if it is out at infinity).
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idobox
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### Re: Capacity of a superconducting loop?

I think he is referring to the maximum current a superconductor can carry.
Apparently, when the magnetic field is too strong, the material stops being superconducting. This critical point depends on temperature, and I found this applet that calculates it for you. http://hyperphysics.phy-astr.gsu.edu/hbase/solids/scbc2.html
The relation of current to magnetic field will depend on geometry.
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zenten
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### Re: Capacity of a superconducting loop?

eSOANEM wrote:Yeah, batteries derive their power through chemical processes. A superconducting coil does not have access to any of these. It can however store energy like and inductor or a capacitor (provided you have some other electrode somewhere even if it is out at infinity).

Right, I get the process is totally different from a battery. But what I meant is unlike any practical capacitors that we have it can store energy for a very long time, so in theory it could be used for some of the same applications as a battery.

idobox wrote:I think he is referring to the maximum current a superconductor can carry.
Apparently, when the magnetic field is too strong, the material stops being superconducting. This critical point depends on temperature, and I found this applet that calculates it for you. http://hyperphysics.phy-astr.gsu.edu/hbase/solids/scbc2.html
The relation of current to magnetic field will depend on geometry.

Ah, thanks, that seems to be exactly what I was thinking of.

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### Re: Capacity of a superconducting loop?

zenten wrote:
eSOANEM wrote:Yeah, batteries derive their power through chemical processes. A superconducting coil does not have access to any of these. It can however store energy like and inductor or a capacitor (provided you have some other electrode somewhere even if it is out at infinity).

Right, I get the process is totally different from a battery. But what I meant is unlike any practical capacitors that we have it can store energy for a very long time, so in theory it could be used for some of the same applications as a battery.

idobox wrote:I think he is referring to the maximum current a superconductor can carry.
Apparently, when the magnetic field is too strong, the material stops being superconducting. This critical point depends on temperature, and I found this applet that calculates it for you. http://hyperphysics.phy-astr.gsu.edu/hbase/solids/scbc2.html
The relation of current to magnetic field will depend on geometry.

Ah, thanks, that seems to be exactly what I was thinking of.

The thing is that, because the process is completely different, you get completely different properties. The problem with capacitors isn't that they can't store the energy for a long time, it's that, when they do give it out they do so very quickly. This is a fundamental property of how capacitors work and you can't get round it through geometry or superconductivity.

Also, whilst the maximum amount of current you can fit through a superconducting coil could be called its capacity, that is in a completely unrelated sense to it being used as a battery (or anything like one) and is more a measure of the maximum energy that can be stored in it when it's used as an inductor (although again, inductors behave in a fundamentally very different way to a battery).
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idobox
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### Re: Capacity of a superconducting loop?

zenten wrote:Right, I get the process is totally different from a battery. But what I meant is unlike any practical capacitors that we have it can store energy for a very long time, so in theory it could be used for some of the same applications as a battery.

They can, and they are used for that. http://en.wikipedia.org/wiki/Superconducting_magnetic_energy_storage.
The problem is that they're expensive, fragile, need to be cooled and can't store that much energy. Their main advantage is that you can dump or drain massive energies in very short times. As a result, they are mostly used for short term storage and regulating power supplies.

eSOANEM wrote:The thing is that, because the process is completely different, you get completely different properties. The problem with capacitors isn't that they can't store the energy for a long time, it's that, when they do give it out they do so very quickly. This is a fundamental property of how capacitors work and you can't get round it through geometry or superconductivity.

Also, whilst the maximum amount of current you can fit through a superconducting coil could be called its capacity, that is in a completely unrelated sense to it being used as a battery (or anything like one) and is more a measure of the maximum energy that can be stored in it when it's used as an inductor (although again, inductors behave in a fundamentally very different way to a battery).

The term capacitance is specific in electric engineering, and is the ratio of charge over voltage. Capacity is often used in that meaning, but it just means the ability to contain or carry stuff, and is much less precise.

Now, what you say about capacitors is mostly inaccurate. Capacitors all have leakage, and can't store energy for very long periods (it can be days, but not months or years like some batteries). And with charge pumps or switched-mode power supplies can extract energy from capacitors at a slow rate with no problem. The main problem with capacitors is that they don't store a lot of energy per unit of volume. People are working on increasing the energy density by using nanotubes or other magic stuff,, but right now, they lag far behind chemical batteries.
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eternauta3k
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### Re: Capacity of a superconducting loop?

At what point in calculating capacitance do you assume 0 resistance? That I recall, you only assume linear media.
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DanD
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### Re: Capacity of a superconducting loop?

idobox wrote:The problem is that they're expensive, fragile, need to be cooled and can't store that much energy. Their main advantage is that you can dump or drain massive energies in very short times. As a result, they are mostly used for short term storage and regulating power supplies.

They can also be charged extremely quickly, which makes them (conceptually) attractive for things like electric vehicles. And they are extremely efficient, with essentially zero storage losses (and low transmission losses). If we find a superconductor which operates at true high temperature (at or above room temperature), and has a high capacity, they will be extremely attractive. But finding such is in the "fundamental breakthrough" rather than the "incremental improvement" category, which means it isn't practical to predict when such a discovery might occur.

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### Re: Capacity of a superconducting loop?

eternauta3k wrote:At what point in calculating capacitance do you assume 0 resistance? That I recall, you only assume linear media.

You assume that the surface of it is at a constant voltage. This is only true either in superconductors or once they've been held at a constant voltage for a long time.
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### Re: Capacity of a superconducting loop?

It's impossible to find superconductors today that have a combination of high critical temperature, high critical field, and ease of large-scale manufacturing into wire or tape suitable for constructing coils with. A material like that usable even at 77K would revolutionise the cost and usability of superconductors.

That's why most real-world applications of superconducting magnets - say, NMR spectroscopy and medical imaging, advanced tokamaks such as ITER and accelerators such as RHIC and LHC are made of niobium-titanium alloy cooled with expensive, scarce liquid helium, as opposed to a high-Tc cuprate material such as YBCO which is familiar in classroom demonstrations of Meissner-effect levitation, which can be cooled below Tc with dirt-cheap, abundant liquid nitrogen. (Materials like YBCO are often of limited usefulness in applications like this both because of the low critical current and also because of the material working properties for manufacturing the conductor.)
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eternauta3k
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### Re: Capacity of a superconducting loop?

eSOANEM wrote:
eternauta3k wrote:At what point in calculating capacitance do you assume 0 resistance? That I recall, you only assume linear media.

You assume that the surface of it is at a constant voltage. This is only true either in superconductors or once they've been held at a constant voltage for a long time.

If you're working in timescales shorter than this relaxation time then you can't model it as a simple capacitor.
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