Railgun and energy considerations

[ZeroGravity]

Hi forum
Can anyone explain where the energy is ...

Consider a railigun, a voltage is put across the two parallel rails, a current starts building up, whille some energy is stored in the magnetic field inside the current loop.

The energy stored in the magnetic field is:

U=0.5*L*I^2 I being the current and L the self inductance of the loop.
As the projectile moves the area of the loop increases.

I would expect that the self inductance of the loop then was decreasing, lowering the energy in the magnetic field while accelerating the projectile...but it seems that it is the other way around...(using https://www.eeweb.com/tools/rectangle-loop-inductance to calculate the inductance for different values)
Where is the energy coming from ?

 

[Dr.D]

The energy comes from the external current source driving the rail gun.

 

[ZeroGravity]

The energy comes from the external current source driving the rail gun.

But why is it energetically favorable for the system to increase the area?

 

[Windadct]

The same amount of magnetic flux over a large area (loop) is lower energy than a smaller one, lower flux density.

 

[ZeroGravity]

The same amount of magnetic flux over a large area (loop) is lower energy than a smaller one, lower flux density.

Can you give any mathematical support for your statement?
I would like to get the same result from the lorentz force as for the relation F=0.5*L'*I^2 ...i.e. the derivative of the magnetic energy...
Bur the magnetic energy should diminish right?

 

[jartsa]

The energy stored in the magnetic field is:

U=0.5*L*I^2 I being the current and L the self inductance of the loop.
As the projectile moves the area of the loop increases.

Does the power source keep the current constant?

If so, then the energy stored in the magnetic field increases as the area of the circuit increases.

That part of the rail where there is a current repels the opposite rail, IOW it has magnetic potential energy. That part is getting longer as the projectile moves. That is how the gun is gaining more magnetic potential energy.

 

[Dr.D]

The current in a rail gun is far from constant. It is a mighty surge that drops fairly rapidly to zero. It is usually either (1) a capacitor discharge, or (2) a very rapidly spinning alternator (called a pulsed alternator) that converts kinetic energy to electrical energy. When I worked on such things a decade or more back, we were looking at peak current around 5 mega-amps.

 

[jartsa]

The current in a rail gun is far from constant. It is a mighty surge that drops fairly rapidly to zero. It is usually either (1) a capacitor discharge, or (2) a very rapidly spinning alternator (called a pulsed alternator) that converts kinetic energy to electrical energy. When I worked on such things a decade or more back, we were looking at peak current around 5 mega-amps.

Yes. But we are talking about a rail gun that is idealized in some way, question is what idealization have we chosen.

In the following idealization the energy of the magnetic field is decreasing when the area of the circuit is increasing. I guess the current that is the source of the magnetic field must be decreasing in this case. (Because magnetic energy=0.5*L*I²)

First energy from the power source is used to create the magnetic field, then the energy from the magnetic field is used to accelerate a projectile.

(Something holds the projectile still while the current is being ramped up)

 

[Dr.D]

Yes. But we are talking about a rail gun that is idealized in some way, question is what idealization have we chosen.

Your idealization is so far from reality as to be meaningless, but go ahead, have fun with your fiction.

What is the point of holding the projectile still? I always understood rail guns as mass accelerators. What power sources can you suggest that are capable of sustained current at those levels (the military wants to know about them).

 

[ZeroGravity]

How would you convince youself that the magnetic energy is decreasing as the area is increasing?
Calculating the volume integral og the magnetic flux density seems cumbersome...Any suggestions?
Should the self inductance not decrease as the area is increased? in order for the magnetic energy to decrease?

 

[Dr.D]

I really cannot say what happens to the self-inductance, but I can observed that rail gun builders go to extreme lengths to reduce all forms of inductance (and resistance) to the smallest possible values. This is the only way you can deliver the massive current required to get the thing to work at all.

 

[ZeroGravity]

I can see that you would want to minimize the resistance, but why the selfinductance?, and how?

 

[Dr.D]

The burst of current that drives the rail gun has many frequency components. Whatever inductance there may be increases the reactance and tends to limit the current. It is an all out push to get as much current to flow as possible.