How To calculate the Power required for a Superconducting Magnet

[Sebastiaan]

Alright, I'm trying to calculate the power requirements for a 30 Weber =( 30 Tesla/m²) Strong magnet

According to this document it would require about 88 MW using a steady-state copper coil magnet

The question is, how much power is required to do the same using cryogenicly cooled superconducting magnet?

The Document does mention the following

As an example, consider a stress limited dipole magnet with 2.5 m radius and flux of 30 Wb. Such a superconducting coil would weight 3 tons, have a mean stress of 230 MPa, and carry a current density of 120 A/mm² - a value that is obtainable in currently available high temperature superconducting tapes

But how to convert this into power requirement into MegaWatt?

Here is one attempt:

120 A/mm² = 12.2e+8 m²

Weber = Joule / Ampere

Joule = Ampere * Weber = 12.2e+8 * 30 = 3600000000 J = 3600 MJ = 3.6 GJ

 

[phyzguy]

The magnet itself will not require any continuous power once the magnetic field is established, although it will require a burst of electrical power to establish the circulating current. The power requirements will be determined by the power needed for the cryogenic refrigeration units to keep the magnet cold. This will depend on the size of the magnet. By the way, you have your units wrong. 1 Tesla = 1 Weber/m^2. I suspect you mean that you want a magnetic field of 30 Tesla = 30 Weber/m^2. I think this is beyond the range of high-temperature superconductors, meaning you will probably need liquid helium refrigeration.

 

[Sebastiaan]

The magnet itself will not require any continuous power once the magnetic field is established, although it will require a burst of electrical power to establish the circulating current..

Interesting, so you would use a large bank of super capacitators charged to full power and then burst the magnetic field into life and then it is just a matter of maintaining below critical temperatures?

 

[phyzguy]

Intresting, so you would use a large bank of super capacitators charged to full power and then burst the magnetic field into life and then it is just a matter of maining below ciritical temperatures?

No, I think it would be more typical to ramp up the field more slowly. Maybe someone else with experience at the LHC would know how and at what rate they ramp up the field. This Wikipedia page gives some more detail.

 

[sophiecentaur]

@Sebastiaan : You ask a question about Power and provide a suggested answer in Energy. That doesn't actually make sense. The Energy in the field that you require can be supplied at almost any rate (Power) and it will just take different amounts of time.

 

[Dale]

Interesting, so you would use a large bank of super capacitators charged to full power and then burst the magnetic field into life and then it is just a matter of maintaining below critical temperatures?

Typically you just ramp a magnet to field using normal mains power. It can take a few hours, but the power is not particularly demanding.

 

[Sebastiaan]

@Sebastiaan : You ask a question about Power and provide a suggested answer in Energy. That doesn't actually make sense. The Energy in the field that you require can be supplied at almost any rate (Power) and it will just take different amounts of time.

Alright but how much power needs to be provided to get it fully charged? Does my 3.6 GigaJoule result make any sense? Also what would be the minimum amount of power to charge it?

 

[phyzguy]

Your energy calculation makes no sense. How did you go from 120 A/mm2 to 12.2e+8 m2? The units don't even agree. Then you ignored the m^2 in the next step of your calculation. The best way to do this is to figure out what the inductance of your coil will be. This will depend on the size of the coil. The energy to charge it is then given by 1/2*L*I^2. The power will then be this energy divided by how long you want to take to charge it up. But I suspect you will find that the refrigeration power will be the dominant power in your system.

How large is your magnet going to be?

 

[sophiecentaur]

Alright but how much power needs to be provided to get it fully charged?

It is the total Energy that determines conversation about when it is 'fully charged'. You cannot mix and match your units if you want a sensible conversation about Physics and EE.
Why would you want to charge the magnet up in any particular time? What would be the point of using 'super capacitors" which would, themselves, need to be charged at well.
3.6GJ can be supplied over any time you want. The formula E = Pt applies (or the Integral version when the supplied power is not constant.
Start with the basics.

 

[Sebastiaan]

Your energy calculation makes no sense. How did you go from 120 A/mm2 to 12.2e+8 m2? The units don't even agree.

Oh my mistake I meant 1.2e+8m². I wanted extrapolate 120 A/mm² to 1 square meter.
The goal is to find Joule = Amp * Wb

 

[Sebastiaan]

How large is your magnet going to be?

The diameter of the magnet would be 100 meter, the initial goal is to to create a 10 km diameter mini magnetosphere as described in the linked document. This is all hypothetically of cource!
The whole contraption would like something like this

 

[Sebastiaan]

Why would you want to charge the magnet up in any particular time? What would be the point of using 'super capacitors" which would, themselves, need to be charged at well.

I Want to make the magnetic field be able to quickly pulsate. I was hoping I could shift the energy between the super capacitors and the superconducting magnet. The Pulsating is required to make the mini mag become able to act as a magnetic scoop capable of collecting charged particles like solarwind ions

 

[sophiecentaur]

I Want to make the magnetic field be able to quickly pulsate. I was hoping I could shift the energy between the super capacitors and the superconducting magnet. The Pulsating is required to make the mini mag become able to act as a magnetic scoop capable of collecting charged particles like solarwind ions

You are proposing a resonant circuit now. This changes the situation somewhat. Supply power is not the only relevant factor here - you would still 'charge up' the resonator with energy slowly but now you have the resonant frequency of the LC oscillator to consider (the self Inductance of the coil) and, as you have heavy currents flowing in the leads to and in the massive C and the lead resistance would certainly not be Zero. Also, you could have significant peak volts across the capacitor. Super capacitors are not (afaik) high voltage devices.

 

[Vanadium 50]

This whole thread is a confused mismash of units, where units are misdefined, or used to represent the wrong thing, or equated when they are not equal. It's like trying to answer the question "how many calories are in a mile".

That said, if you are trying to have a field of that magnitude over that area with a magnet rise time of minutes, it will take gigawatts of power. You have to provide all the stored energy in the magnetic field from your power source. This will almost certainly destroy your magnet.

 

[Sebastiaan]

You are proposing a resonant circuit now. This changes the situation somewhat. Supply power is not the only relevant factor here - you would still 'charge up' the resonator with energy slowly but now you have the resonant frequency of the LC oscillator to consider (the self Inductance of the coil) and, as you have heavy currents flowing in the leads to and in the massive C and the lead resistance would certainly not be Zero. Also, you could have significant peak volts across the capacitor. Super capacitors are not (afaik) high voltage devices.

Ok, then how could we temporaily store the high current with high peak voltages?

 

[sophiecentaur]

Ok, then how could we temporaily store the high current with high peak voltages?

Did you read Vanadium's last post? He has introduced another thing for you to consider before you assume this is in any way workable.

 

[Sebastiaan]

You have to provide all the stored energy in the magnetic field from your power source. This will almost certainly destroy your magnet.

Besides making very gradual changes to the current, Is there anyway to prevent the edgy current causing a Magnet quench

 

[Vanadium 50]

Did you read Vanadium's last post?

Facts, schmacts.

 

[Sebastiaan]

Facts, schmacts.

Are you implying that based on your gut feeling it is imposible to create a pulsed magnetic field with super conducting magnets?

Ok but let me repharse my original question.

"How much power do you need to put into a 30 Weber super conduction magnet before it gets to full strength"

 

[anorlunda]

Are you implying that based on your gut feeling it is imposible to create a pulsed magnetic field with super conducting magnets?

Ok but let me repharse my original question.

"How much power do you need to put into a 30 Weber super conduction magnet before it gets to full strength"

Its time to clarify your question. Are you asking what's practically possible, or what may be theoretically possible in the future given infinite power and money?

The power needed depends on what you mean by "quickly pulsate." The quicker, the more power. Give us a number in hertz.

 

[Vanadium 50]

How much power do you need to put into a 30 Weber super conduction magnet before it gets to full strength

You see, that's mixing units again. How many volts are in a liter?

Are you implying that based on your gut feeling

More than a gut feeling. It's an order of magnitude calculation, by someone who actually knows what these units are. And who knows the difference between magnetic flux and magnetic fied.

 

[Sebastiaan]

You see, that's mixing units again. How many volts are in a liter?

sorry, I mean energy (in joules), not power (in voltage). Given is the Magnetic Flux strength of 30 Weber and current density of 120 A/mm² (= 1.2e+8 A/ m²?) , I know that Wb = J / A , can I use this to calculate J ?

 

[Sebastiaan]

Its time to clarify your question. Are you asking what's practically possible, or what may be theoretically possible in the future given infinite power and money?

What is theoretically possible given near outrageous power and money. I need it for the construction of a hard science-fiction game simulation. So as long as there are no fundamental physics laws broken and not too outrageous it can fly. Think 24 century level technology, not current 21 century technology

 

[Sebastiaan]

The power needed depends on what you mean by "quickly pulsate." The quicker, the more power. Give us a number in hertz.

I don't know but I guess it need to be fast enough to reel in the stuff catched in the magnetic field. My guess is it is linked to the speed of whatever I want to capture, which in the case of solar wind on average travels at 500 km/s. Given the radius of 5 km, a minimum pulse frequency Herz of 500 / 5 = 100 Herz is required

 

[Vanadium 50]

Then you need terawatts of power, not gigawatts. Probably several tens of terawatts, which exceeds all the power produced on earth. You might think this is acceptable in your story, but I can pretty much guarantee if you tried to feed your magnet this much power, it would vaporize.

 

[Sebastiaan]

Perhaps you are right, but could you please illustrate that with a calculation example?

 

[Vanadium 50]

Your picture gives a magnetic field strength. Energy density goes as the square of field strength, the volume is given, and the power goes as the frequency.

 

[f95toli]

Perhaps you are right, but could you please illustrate that with a calculation example?

Note also that creating a "pulsing" strong magnetic field is actually quite difficult since large inductance also implies a large time constant. Hence,. you want to keep the inductance as low as possible which means using a coil with fewer turns and instead using a large current. Now you have the problem that you have to find power supply that can generate a VERY large AC current; in your case the current would be so large that is probably not possible even in principle.
You also need even more energy since you have that W=LI^2/2

Experiments that require fast changes of large magnetic fields are very, very difficult and in some cases fairly extreme solutions are used. One way is to instead quickly change the geometry of the coil. This can also be used to generate very large magnetic fields; especially if explosives are used (there is actually a facility in the US where this is done)

 

[Sebastiaan]

You also need even more energy since you have that W=LI^2/2

Could you explain what "L" and "I" represent here? Or provide a reference?

 

[Asymptotic]

Could you explain what "L" and "I" represent here? Or provide a reference?

Energy stored in an electromagnetic field. L is inductance. I is current. Per Hyperphysics.