# I Can energy be extracted from a proton beam using a current transformer?

#### BrandonBerchtold

Suppose there exists a proton beam that is pulsed on and off. If this beam is aimed through a current transformer as in the attached image (the proton beam would act as the main primary conductor in this case), what would be the output of the transformer, and how would it affect the beam velocity?

The pulsed proton beam would effectively be creating a square wave of current flowing through the transformer. Transformers convert ac current from the primary winding to the secondary winding. Therefore, would the transformer slow the flow of the proton beam, and if so, by how much?

Basically I want to figure out how to extract the maximum amount of energy from a beam of protons and convert it into electrical energy.

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#### berkeman

Mentor
Basically I want to figure out how to extract the maximum amount of energy from a beam of protons and convert it into electrical energy.
Can you say what the source of the beam is? Do you have any voltage reference connection to the source of the beam? If you do, it may be easiest to just slow and stop the beam with a retarding voltage.

Otherwise, slowing it with a current transformer setup seems plausible. It may be most efficient to have a series of CTs to perform the slowing in stages, in order to be able to tune the number of turns and load impedance for each.

#### berkeman

Mentor
BTW, what are the frequency and duty cycle of the pulsed waveform? Depending on the duty cycle, the conversion may be fairly complicated...

#### BrandonBerchtold

Can you say what the source of the beam is? Do you have any voltage reference connection to the source of the beam? If you do, it may be easiest to just slow and stop the beam with a retarding voltage.

Otherwise, slowing it with a current transformer setup seems plausible. It may be most efficient to have a series of CTs to perform the slowing in stages, in order to be able to tune the number of turns and load impedance for each.
The beam originates from a set of parallel plates with a voltage difference of 100 KV between them. The beam then exits the parallel plate apparatus and travels down a vacuum tube. The goal is to convert ideally all of the kinetic energy of the beam into electrical energy that can be stored in a capacitor bank or equivalent storage device. How could one determine how much of the beam energy would be extracted by each current transformer stage? Is it just equal to the current through the secondary winding squared times the resistance in the secondary winding?

Originally I was planning on using a retarding voltage to slow the beam but was unsure how to extract electrical energy with that method since it would store the energy in the form of accumulated protons behind the retarding voltage stage.

The beam pulse duty cycle will be between 1% and 50% and will have a frequency in the MHz range (I assume this would complicate matters since this is in the radio frequency range).

#### berkeman

Mentor
The beam originates from a set of parallel plates with a voltage difference of 100 KV between them. The beam then exits the parallel plate apparatus and travels down a vacuum tube. The goal is to convert ideally all of the kinetic energy of the beam into electrical energy that can be stored in a capacitor bank or equivalent storage device.
This sounds pretty specialized. Is this for a design competition or olympiad, by any chance?

#### BrandonBerchtold

This sounds pretty specialized. Is this for a design competition or olympiad, by any chance?
It's mostly just a thought experiment at this point. I read up on some accelerator based fusion reactor designs and wanted to try simulating various subsystems of the device to get a better understanding of how feasible it could be.

#### berkeman

Mentor
It's mostly just a thought experiment at this point. I read up on some accelerator based fusion reactor designs and wanted to try simulating various subsystems of the device to get a better understanding of how feasible it could be.

#### BrandonBerchtold

Oh that's interesting. I knew that method was used for measuring flow rates of conductive fluids but I didn't think it would be able to be used as a means of generating electricity.

I'm not sure how efficient that would be in my application though since it seems to work primarily on the principle of charge separation and the majority of the energy in the proton beams I'm dealing with is in the form of kinetic energy.

Staff Emeritus
What you have posted has the proton beam going through a field free region. If you extract it's energy, where does it go? How are you extracting this energy?

#### BrandonBerchtold

What you have posted has the proton beam going through a field free region. If you extract it's energy, where does it go? How are you extracting this energy?
I envisioned something like in the attached sketch. Sorry if it's difficult to make out, but it's basically a ferrite core that has copper wire wound around it. The proton beam is a moving charge and therefore generates it's own magnetic field according to Biot Savart law. When the beam passes through the ferrite core, the beam induces a magnetic field in the core. This magnetic field induces a current in the wire wound around the ferrite core. This current passes through a diode and charges some sort of battery. I'm trying to figure out how much of the beams energy can be taken and stored in the battery. I would ideally like to be able to convert almost all of the kinetic energy in the beam into stored energy in the battery.

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#### berkeman

Mentor
I would ideally like to be able to convert almost all of the kinetic energy in the beam into stored energy in the battery.
Then at the very least, you should be using a full-wave rectifier...

#### BrandonBerchtold

Then at the very least, you should be using a full-wave rectifier...
Does it need a full wave rectifier? The transformer is fed a pulse train via the beam pulses, so the transformer input would peak at the beam current and have a minimum current of 0 A. The current should only ever be going in one direction, right?

Staff Emeritus
If I power up your toroid, there's no magnetic field in the interior, right? That's what you drew.

Therefore, if I put a field in the interior, it won't generate a current.

#### berkeman

Mentor
If I power up your toroid, there's no magnetic field in the interior, right? That's what you drew.

Therefore, if I put a field in the interior, it won't generate a current.
I think he's firing the pulsed beam through the middle of the CT. That will induce a voltage in the toroidal coil of the CT.

#### berkeman

Mentor
Does it need a full wave rectifier? The transformer is fed a pulse train via the beam pulses, so the transformer input would peak at the beam current and have a minimum current of 0 A. The current should only ever be going in one direction, right?
No. It sounds like you don't understand how transformers work yet.

#### BrandonBerchtold

No. It sounds like you don't understand how transformers work yet.
Oh whoops, yeah you're right, it does need a F-W rectifier. It's been a while since I've worked with transformers.

#### berkeman

Mentor
It's been a while since I've worked with transformers.
No worries. So now that you've reviewed transformer circuits you remember that the induced voltage in the CT coil is proportional to the change in the current through the CT. So for a pulse, there is only a change at the start and end of the pulse, right? So you could probably extract the most energy from a sinusoidally modulated beam if you only had one tuned CT.

For a pulsed beam, it seems like you would slow the start and end of each pulse because of the changing flux, so I'm not sure that what would do to the beam density and how best to extract the most energy from it.

Have you looked at using some sort of curved recovery mechanism? How complicated do you want this "thought experiment" to get?

And what is your background in physics? How much have you worked with the Lorentz force and beam shaping/focusing optics?

#### BrandonBerchtold

No worries. So now that you've reviewed transformer circuits you remember that the induced voltage in the CT coil is proportional to the change in the current through the CT. So for a pulse, there is only a change at the start and end of the pulse, right? So you could probably extract the most energy from a sinusoidally modulated beam if you only had one tuned CT.

For a pulsed beam, it seems like you would slow the start and end of each pulse because of the changing flux, so I'm not sure that what would do to the beam density and how best to extract the most energy from it.

Have you looked at using some sort of curved recovery mechanism? How complicated do you want this "thought experiment" to get?

And what is your background in physics? How much have you worked with the Lorentz force and beam shaping/focusing optics?
So the beam would likely be quite sinusoidal by nature. The idea is to send pulses of ionized gas into the beam accelerator and accelerate them in the presence of an axial magnetic field (in order to provide radial confinement). Due to the nature of valves, the plasma flow into the accelerator would begin slowly and increase until the valve is fully open, then it would decrease until the valve is fully closed. This would vary the beam density approximately sinusoidally.

Now, what if we simplify the problem a bit. What happens if we fire a single proton through a current transformer. How can we determine what forces act on the proton? The moving proton produces a magnetic field that induces a current in the secondary winding proportional to the fraction of the proton's magnetic field that is present inside the volume encircled by the secondary coil. Is it fair to assume then that the rate at which energy is taken from the proton is equivalent to the current in the secondary coil squared times the resistance of the secondary coil?

As for curved recovery mechanisms, I have looked into them but I'd prefer linear mechanisms since they're more compact and better suited for my purposes.

I am reasonably familiar with magnetic optics and the Lorentz force.

#### anorlunda

Mentor
Gold Member
Basically I want to figure out how to extract the maximum amount of energy from a beam of protons and convert it into electrical energy.
Do you mean practically or as an academic exercise?

Academically, If you take all the energy out of the beam, it becomes dispersed and motionless.

#### BrandonBerchtold

Do you mean practically or as an academic exercise?

Academically, If you take all the energy out of the beam, it becomes dispersed and motionless.
I'm interested in the practical amount of energy that could be extracted from the beam. Ideally I'd like to have a way of extracting upwards of 95% of the beam energy and converting it to storable electrical energy.

#### ZapperZ

Staff Emeritus
2018 Award
I'm interested in the practical amount of energy that could be extracted from the beam. Ideally I'd like to have a way of extracting upwards of 95% of the beam energy and converting it to storable electrical energy.
But why? Do you live near a constant source of proton beam?

It is more “practical” and efficient to directly use the energy needed to create and direct the proton beam than to tap the energy of the beam.

Zz,

#### anorlunda

Mentor
Gold Member
Is this question related to a SF story development?

#### BrandonBerchtold

But why? Do you live near a constant source of proton beam?

It is more “practical” and efficient to directly use the energy needed to create and direct the proton beam than to tap the energy of the beam.

Zz,
The reason I am interested in recapturing energy from the proton beam is because the beam is intended to strike a target and there is a very large probability that many of the protons will pass right through the target. As a matter of efficiency it would be nice to recapture some of the energy invested in these protons that pass through, especially if the beam is being run at higher energies.

#### BrandonBerchtold

Is this question related to a SF story development?
Unfortunately no, creative writing is definitely not my strong point. However I could see some interesting use cases for proton beam energy transfer or energy production in sci-fi :)

#### ZapperZ

Staff Emeritus
2018 Award
The reason I am interested in recapturing energy from the proton beam is because the beam is intended to strike a target and there is a very large probability that many of the protons will pass right through the target. As a matter of efficiency it would be nice to recapture some of the energy invested in these protons that pass through, especially if the beam is being run at higher energies.
What "target"?

If the aim here is to generate collision out of a stationary target, why should there be protons that will pass right through a target? After all, we DO have proton beam stops!

I've stopped 1 GeV electrons (which are waaaaay smaller than protons) with regular stainless steel vacuum chamber walls. It is not a big deal!

And you are also neglecting to see how much energy you can actually get out of such a thing. Do you know just how LITTLE current and amount of charge that is actually in a bunch of pulsed proton beam? Look at how much charge that is actually circulating around the LHC ring. Compare that to the amount of charge that you have in your ordinary copper conductor.

I mean, at some point, you need to do a back-of-the-envelope calculations on how feasible and how reasonable of a result that you should get, and whether this is all worthwhile. What is the investment that you need to put in, and what are the returns that you could get out of it? There are many so-called 'clever' ideas that do not produce anything worth considering.

Zz.

"Can energy be extracted from a proton beam using a current transformer?"

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