Can nested solenoids trap particles?

[CMTacoTophat]

TL;DR

Could two nested solenoids, generating equal but opposite magnetic fields, radially confine any charged particles traveling through them

(NOTE: this is assuming trapping in 2 dimensions, with "axial" referring to a third orthogonal to both)

If there are two nested (ideal) solenoids of equal strength, pointing different directions (i. e., generating internal magnetic fields 180 degrees off from each other), then presumably they create a region of zero magnetic field in the very center, but a constant, axially-aligned magnetic field in between the two.

Now, if there is a transition between a region of zero magnetic field, and a constant, axially-aligned magnetic field, then any charged particles entering will turn some part of a cycle, and exit with the perpendicular component of their velocity (to the boundary between the fields) pointing in the opposite direction.

Therefore, with such a boundary existing completely around a certain radius, than any charged particles within cannot exit the apparatus (assuming the radius of their curvature is significantly less than the boundary/inner solenoid's radius), being contained without any concern of their velocity (as it does not affect the radius of curvature).

If this is true, it seems as if it would be pretty useful, but I don't hear it being used anywhere, so what part of my derivation is incorrect? If its mostly right but there's an "in-practice" reason for a lack of deployment, what would it be?

Thanks in advance.

 

[renormalize]

TL;DR: Could two nested solenoids, generating equal but opposite magnetic fields, radially confine any charged particles traveling through them

Your proposed configuration is hard for me to visualize. Could you provide a diagram which illustrates the solenoids, their magnetic fields and the desired current paths through those fields?

 

[CMTacoTophat]

Sure, here you go (sorry for the yellow - on - white, its the only full marker I have at the moment):

 

[A.T.]

sorry for the yellow - on - white

Don't eat the yellow snow!

 

[Ibix]

The field between the solenoids will be the (more or less) uniform interior field of the outer solenoid plus the non-uniform exterior field of the inner solenoid, so it won't be uniform. How non-uniform it is would need calculating. How strong it is would also need calculating, since the fields of the two solenoids are opposing.

I think the answer to your question depends on the details of the magnetic field (the non-uniformity might end up bending the particles away from axial motion) and the initial radial momenta of the charged particles.

 

[phyzguy]

I think what you are talking about is similar to the field reversed configuration, which is being studied as a possible path to controlled nuclear fusion.

 

[berkeman]

I think what you are talking about is similar to the field reversed configuration, which is being studied as a possible path to controlled nuclear fusion.

Interesting. But are folks still looking at it? It seems like the references are a bit old with no new work being done on it.

 

[phyzguy]

Interesting. But are folks still looking at it? It seems like the references are a bit old with no new work being done on it.

Oh yes. Helion energy is banking on it. They started construction on a power plant in July, 2025. Whether they will succeed is anyone's guess.

 

[berkeman]

Oh yes. Helion energy is banking on it. They started construction on a power plant in July, 2025. Whether they will succeed is anyone's guess.

Huh, interesting. I need to do more reading, but their system of direct energy extraction is interesting. I wonder how fast they are cycling their plasma volume...

Video about that part:

 

[CMTacoTophat]

Sorry for the late reply, I've been really busy the past couple of days.

Basically, it was supposed to be just two ideal solenoids, one inside the other, each generating a magnetic field of equal strength. Therefore, they would supposedly create a region of no B from 0 <= r < r_inner, and constant, axial B from r_inner <= r < r_outer.

My question is, could this configuration trap charged particles radially, if their orbit radius is much less than r_inner or r_outer? Because then it seems when they leave r_inner and enter the magnetic field of r_outer, they loop around and re-enter r_inner (in the radial plane - I assume this wouldn't affect their axial motion).

Of course, if this is wrong is some way, please let me know

 

[berkeman]

My question is, could this configuration trap charged particles radially, if their orbit radius is much less than r_inner or r_outer? Because then it seems when they leave r_inner and enter the magnetic field of r_outer, they loop around and re-enter r_inner (in the radial plane - I assume this wouldn't affect their axial motion).

Could you add to your sketch in post #3 to show the path of a negatively charged particle around the loop? I'm having trouble visualizing your written description. Thanks.

 

[CMTacoTophat]

 

[berkeman]

Sorry, that does not help; it is not the sketch that I asked for. What are you trying to accomplish?