I Best way to focus charged particles back to their source?

[CMTacoTophat]

TL;DR

What combination of electric and magnetic fields could direct the emitted charged particles, say alphas, back to the point source, while being able to monitor them or increase their energy?

Basically the TL;DR.

I was entertaining the idea of some sort of device as a challenge, but I couldn't think of a surefire way to capture as much of the output of, say, a collection of radionuclides, and direct the output charged particles back into them, while being in a form consistent and convenient enough for measurement, energy boosting (or degradation), etc.

I am sure there are varying solutions for different energy levels, especially with the equipment involved (like electrostatic vs. magnetostatic lenses), but I'm really looking for the simplest solution: low energy, even spread in all directions, etc.

So far my best design would be to have a cylindrical surrounding the source, with a magnetic field running axially, but getting stronger towards the shell radius so the particles would make tighter and tighter turns near the edge. This would hypothetically "reflect" them and contain them within the cylinder until accelerated enough or otherwise deflected to be split into two, even streams. Of course, I have no idea how to form that sort of field, or if it would even work.

Thanks in advance.

 

[anuttarasammyak]

Some alpha particles could be on circle track in constant kinetic energy and come back to the heavy source with a designed homogeneous magnetic field.

 

[CMTacoTophat]

Thanks for the reply. I've considered something along those lines, but the issue I always stagger with is the particles with velocities off-plane (the "plane" being defined as the one with the homogeneous field as its normal). Wouldn't they spiral away from that source? Forgive me if there's something obvious I'm missing.

 

[anuttarasammyak]

Applied magnetic field should be perpendicular to the velocity of the particle so that its track is a circle not a spiral.

 

[CMTacoTophat]

I think I get what you're implying: A magnetic field akin to that produced by a current wire, running circumferentially to an axis, with all emitted particles except those exactly aligned to the axis returning in a loop back to the source. How could you then, say, boost them? Would that require a series of banked rings with differing electric potentials? I apologize if any of my questions appear ill-informed.

 

[anuttarasammyak]

https://www.feynmanlectures.caltech.edu/II_29.html is a good one to know the fundamentals.

 

[CMTacoTophat]

Thanks for the resource - I haven't come across that one yet. However, it seems mostly concerned with point sources in 2D, and only capturing the emitted particles with a very particular range of velocities. I've been trying to figure out how to do so in 3D, and how to capture as many of them as possible. I get that they can loop back on themselves in a strong uniform magnetic field, but it would have to then be perpendicular to all surface normals of a (hypothetical, surrounding the point source) sphere, and the hairy-ball theorem then requires that it necessarily vanish in certain areas, thus preventing complete or near complete capture.