Why do inductors need such high voltage for fast current rise?

[nemesiswes]

Hi I have been researching pulsing Electromagnets (inductors) and I have run into a problem. I have been using this formula for figuring out how fast a current will rise if powered with a ceratin voltage and the coil inductance.

L (uh> / V = Time to 1 amp ( in MicroSecond)

According to this which I found seems to be accurate, says that if you want a current to rise to 1 A in say 1 microsecond on a inductor of inductance 10 mH, then the voltage required would be 10,000 Volts.

10,000 (uH)/ 1 (microseconds) = 10,000 Volts

That seems like awful lot of voltage and it get's even more outrageous if you plot in larger inductors and smaller time-frames

1,000,000 (uH) / .001 (microseconds = 1,000,000,000 Volts

Doesn't that sound too high, 1 Billion Volts just to pulse a 1 H coil to 1 Amp in 1 Nanosecond, ? If you were to repeat that pulse a 500 million times a second, then I think you would be using 500 Million Watts of power! since the duty cycle would 50%.

I'm just going to go ahead and assume something is wrong here like always, lol. So can someone please explain too me why this is wrong, if it is. If it is not wrong then why does it take so much voltage which usually also means high power since the current here is 1 amp and it's not just one pulse but many over a second.

 

[sophiecentaur]

You could, perhaps, achieve faster times if you use a Capacitor to resonate with the Inductor. But if you remember that what you are trying to achieve is to store a lot of magnetic energy in a very short time. That involves High Power. You are contemplating accelerating a railway train from zero to 100mph in 2 seconds.

One possible trick would be to build up a high voltage on an LC resonator (different L) and then. when at the peak of volts, switch over to the 'Magnet'. The stored energy would then be dumped where you wanted it. This is the principle of some Capacitor Discharge Ignition systems.

 

[Bob S]

You could, perhaps, achieve faster times if you use a Capacitor to resonate with the Inductor. But if you remember that what you are trying to achieve is to store a lot of magnetic energy in a very short time. That involves High Power. You are contemplating accelerating a railway train from zero to 100mph in 2 seconds.

One possible trick would be to build up a high voltage on an LC resonator (different L) and then. when at the peak of volts, switch over to the 'Magnet'. The stored energy would then be dumped where you wanted it. This is the principle of some Capacitor Discharge Ignition systems.

Blumlein pulse generators are often used to get very fast, very HV pulses. See
http://www.pulsedpower.eu/pulsedpower_engineering.html
See for example the plot of a 30 kV, 10 ns wide pulse in article.

 

[sophiecentaur]

I'm just going to go ahead and assume something is wrong here like always, lol. So can someone please explain too me why this is wrong, if it is. If it is not wrong then why does it take so much voltage which usually also means high power since the current here is 1 amp and it's not just one pulse but many over a second.

You are reasonable to doubt it when you get any massive answer but your figures show you that you are in the right ball park.

BUT what is going to happen to all this magnetic energy after your pulse? You don't have to dump it all in a massive resistor (not a trivial thing to do either). Why not store it in a massive capacitor, use it for the next pulse, and save a lot on your electricity bill (and on re-wiring the house!).

Can I ask what is the application?

 

[nemesiswes]

Well there really is no application, I was just interested researching pulsed power, and after researching a little, I found it odd that the power use would be so high. I know if it is just one pulse then it is not bad, but if you were to do it multiple times a second like say 50% duty cycle then power use can reach insane levels.

Too sopiecentaur, I do like the analogy you used though

" But if you remember that what you are trying to achieve is to store a lot of magnetic energy in a very short time. That involves High Power. You are contemplating accelerating a railway train from zero to 100mph in 2 seconds. "

It kind of puts what I am talking about into perspective, lol.

 

[sophiecentaur]

The actual amount of Energy involved is fairly modest but, as Power is the rate of Energy transfer, it's the short time that makes the power so high.
A camera Flash is an excellent example of this. The energy for the flash is obtained by charging a Capacitor (about 100μF) to about 200V. This is done over a second or so using energy from a humble battery (you will have heard the whistle from the charging circuit). The energy stored in the Capacitor is 2J. But this energy is delivered to the flashtube in about 1ms - giving a Power of 2kW!. All from a couple of AA cells.

In your case, the power is enormous but the Energy, as well as being fairly modest, can mostly be reclaimed as the Magnetic field collapses by 'catching it' in a resonating Capacitor. If you are prepared to wait for a few seconds for the initial Energy to build up then you only need to delover a small amount of Energy for each pulse, to make up for any resistive losses in the circuit during each pulse.

Actually, all of the more expensive flash guns can control the length of the flash (to get the exposure right at the time) and they re-direct the unused energy which was stored in the capacitor, into an inductor and then back into the capacitor in order to reduce battery drain.

 

[nemesiswes]

Actually I know I said there really is no application but there is. I am trying to create a ultra high powered Rail gun, well at least design one for fun, maybe not actually create since the cost's would be huge, lol

This other thread of mine probably also makes more sense when you put the two together, lol
https://www.physicsforums.com/showthread.php?t=594146

So I guess all this might make a little more sense now that you know why I am trying to find out why it takes so much power and how the magnetic fields really work, lol.

One question I have regarding capturing the collapsing field to help reduce the total energy used is when the rail gun fire's, the magnetic field rises in both the stationary coil and the moving coil attached to the round. How much of that field can actually be captured back since it was used to do work, move the round forward?

Another question is since the faster it pulses, the more power (same amount of energy) you can deliver to the coil in a smaller amount of time and because of that, at the time scales I am talking about which will be around 1 Nano-second, how will the coil size come into play? I want to power a big coil, let's say 1 Henry, a coil of that size would be about 2500 turns on a 12 inch long x 12 inch wide with about 8 layers. Now since it is to reach full power in 1 nS, that is only 1 ft of length, but the total wire length is 12 x 3.141 x 2500turns = 94,230 inches or 7,852.5 ft, about 1.5 miles! Would the information that the coil is on have to travel each inch of that wire around the coil before it was fully on or would the electric field from the wire intersect each wire around it and so on, so it would only actually travel a maximum of 12 inches (because both length and diameter are the same) and thus it would be able to reach full power in 1 nS?

I have more to say but I want to hear what others have to say first, Some of the questions I have rely on these ones being answered.

 

[sophiecentaur]

If you are using Energy from this to power a rail gun then, of course, the energy that goes into the KE of the projectile can't be recovered.
As you have a specific requirement for this energy, have you thought how much speed the projectile must have? This will determine the Kinetic Energy (and power) that your magnet system will need to supply and, over the length of track involved, this will tell you the current pulses needed. BTW, why do these pulses need to be so short?