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?