# Electromagnetic potential well, impossible?

Waxbear
I was having a discussion with my friend the other day. He had just attended a lecture about Paul traps. He told me that the Paul trap potential has a stationary point in the middle, which is a saddle point, and that the 2 pairs of opposite poles are oscillating between being positive and negative, such that the 'hills' and 'valleys' of the potential are constantly switching place. Then anything placed near the saddle point will find itself on a slope most of the time and thus be relatively trapped. When i asked why it had to be a saddle point and not just a constant minimum, he said that it was because it is impossible to create a consant electromagnetic potential well.

I remember hearing a bit about this during my introductory electromagnetism course. But that was well over a year ago and i can't remember the argument for this. A google search didn't give me anything either. So is there a law or an equation you can point me to, which will make this obvious to me? Maybe it comes out easily from one of Maxwell's equations. I took EM1 and EM2 (which makes it slightly embarassing that i don't know this) so you know my prerequisites for understanding your explanations.

## Answers and Replies

Q-reeus
This one may only apply to fluids, but have a look: www.nano-optics.ethz.ch/publications/krishnan.pdf [Broken]

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Waxbear
Well yes, in that article it certainly seems like they are able to make an electrostatic potential well. So it seems to be possible. I wonder why Paul traps are so complicated then.

Q-reeus
Well yes, in that article it certainly seems like they are able to make an electrostatic potential well. So it seems to be possible. I wonder why Paul traps are so complicated then.
Yeah, just looking at http://en.wikipedia.org/wiki/Quadrupole_ion_trap, complication is the word. At the bottom, you might like to Google-chase on the Linear and Cylindrical traps mentioned there - they seem to be purely electrostatic going by brief descriptions offered.

Waxbear
Looking at Linear Ion Trap: "or as an actual trap by creating a potential well for the ions along the axis of the electrodes." So it seems that it is possible to create an electromagnetic potential well after all.

Q-reeus
Looking at Linear Ion Trap: "or as an actual trap by creating a potential well for the ions along the axis of the electrodes." So it seems that it is possible to create an electromagnetic potential well after all.
Sorry to say I gave you a wrong steer on the linear trap thing. Take a look here:
First part of intro reads:
Linear ion traps are finding new applications in many areas of mass spectrometry. In a linear ion trap, ions are confined radially by a two-dimensional (2D) radio frequency (RF) field, and axially by stopping potentials applied to end electrodes.
So still needs an rf field. I really haven't checked through the Swiss team's arrangement, but it may critically depend on non-linear dielectric effects in fluids - not sure and not willing to dig deep there. Good hunting.