Can Protons Be Accurately Aimed in a Nuclear Reactor?

[x_engineer]

Seems to me that a nuclear reactor is an extremely random process with lots of variable and large delays. A neutron generated by one fission goes by an incredible number of nucleii before it actually hits one that absorbs it.

So how accurately can you aim a proton? Let's go with them for the moment since we have good electromagnetic ways of controlling them. Also, does a nucleus stay within a nuclear diameter in a solid at room temperature?

 

[Bill_K]

So how accurately can you aim a proton?

Well for starters, the LHC beams are focused down to 16 microns at the collision points.

Also, does a nucleus stay within a nuclear diameter in a solid at room temperature?

Not by any means. It depends on the material of course, but figure that lattice vibrations are not much different from the lattice spacing, which is of the order of an Angstrom.

 

[x_engineer]

I was thinking of a device like an electron microscope operated in reverse. According to Wikipedia, it can have 0.2nm resolution. Would a proton microscope be able to get to femtometre resolution? (Nucleii are femtometres in size). Can you operate it in reverse and get a proton to pass reliably within that distance of some arbitrary point in space?

<<<lattice vibrations are not much different from the lattice spacing, which is of the order of an Angstrom>>>
Thats a bummer - it does not matter what CEP your missile has if you can't tell whether the target is going to be within the kill radius!

Anyway to get a nucleus to "hold still" in at least 2 dimensions? I don't care if you can't tell within a centimetre (maybe even a meter) where it is in the third dimension.

 

[eXorikos]

If you can accelerate a proton to the same velocity as the electron, you have an even better resolution for your proton microscope.

It depends on what you call reliable. You will be unable to pass 100% of your beam within any arbitrary distance. This all comes down to Heisenberg really. If you want to control your resolution, you need to control the momentum and you lose information about the position. So you won't be able to control if it passes in an arbitrary distance to a point. The uncertainty principle gives a limit for it.

 

[x_engineer]

The idea is to get nearly 100% of the proton/neutrons to hit a target nucleus. If it was one target and one projectile, you need to be able to aim, and to know something about where the target is. I think the Heisenberg principle limits both if your setup needs to know both position and momentum to ensure a collision.

A nuclear reactor gets around the problem by assembling a ***very*** large number of targets and not caring which ones the wandering neutrons hit.

If we had good neutron mirrors (we dont) we could accomplish the same thing with far fewer targets by simply giving the neutrons multiple chances at the same set of targets. The limiting factor then would be the lifetime of the neutron.

If you can reduce the degrees of freedom of motion to one dimension, you again don't need to know precisely where the target or projectile are going to be. (But is this itself a violation of the Heisenberg principle - it isn't just position and momentum - e.g. energy and time are also linked variables)

 

[edguy99]

Seems to me that a nuclear reactor is an extremely random process with lots of variable and large delays. A neutron generated by one fission goes by an incredible number of nucleii before it actually hits one that absorbs it.

So how accurately can you aim a proton? Let's go with them for the moment since we have good electromagnetic ways of controlling them. Also, does a nucleus stay within a nuclear diameter in a solid at room temperature?

Great question, here are three different answers, I wonder which is right:

1. The proton charge radius is 0.8768 femtometers

2. Studies have found an empirical relation between the charge radius and the mass number, A, for heavier nuclei (A > 20):
R ≈ r0*A^⅓ where r0 is an empirical constant of 1.2–1.5 fm.
This gives a charge radius for the gold nucleus (A = 197) of about 7.5 fm.

3. Neutron and x-ray scattering cross-sections compared.

Note that neutrons penetrate through Al much better then x-rays do, yet are strongly scattered by hydrogen.

 

[x_engineer]

This response is some kind of joke, right?

 

[x_engineer]

TO Edguy99:

I guess you are trying to tell me I am using Newtonian concepts that don't work at the nuclear level.