Creating a solenoid with varying magnetic field

[CMTacoTophat]

TL;DR

How would you create a magnetic field within a solenoid that varies with radius?

I'm posing this question because it seems like it should have a simple answer, but I can't for the life of me figure it out. It seems a setup like this could be very useful; if there were charged particles inside, and the magnetic field was stronger going from the center to the shell radius, then they could reasonably be "reflected" to remain inside. I believe this could happen if, should they travel closer to the wall, the turn radius decreases, and they bend back from the shell.

So far, all I've been able to envision is a varying winding pattern of wire coils, but I'm not so sure how it could be achieved in practice, if possible.

Any insight helps - thanks in advance.

 

[berkeman]

TL;DR: How would you create a magnetic field within a solenoid that varies with radius?

What radius? Can you upload a sketch of what you want to do? And in what way do you want the field to vary? (linearly, inverse square, etc.)

 

[CMTacoTophat]

I don't think the way in which the field varies matters too much (as long it's not, say, a jump at the very end). This sketch should help: