Is there a different behavior between proton and antiproton beams at the Tevatron? This question has its origin to the reference on the Aegis experiment at CERN where they aim to produce super cooled antihydrogen and detect whether its reaction to gravity is negative.
It set me thinking that the beams in the Tevatron circulate for more than a second and everything falls about 4.9 meters in a second, so the bunches must be falling too. This of course will be compensated by the fields  that keep the bunches in track among all the other corrections necessary. If though the antiprotons  have a different behavior under gravity, this difference would appear in the orbits of protons and antiprotons.
The question has two points:
a) since the beams are travelling equal and opposite paths through the magnetic circuit, a negative gravity effect on antiprotons would disperse the antiproton beam up with respect to the path of  the proton one. Could one get a limit on the magnitude of the gravitational effect difference between protons and antiprotons from this?
I found one reference where the antiproton   beam has a different behavior in chromaticity than the proton one, and it is explained away. 
Now I am completely vague about beam dynamics which I have filed under "art" rather than "physics" but 
b) am wondering whether this observed difference could be interpreted as a gravitational field difference in a dedicated experiment.
Maybe there are beam engineers reading this list. 
My feeling is that if antiparticles  had negative gravity interactions , beam engineers would have detected it since the first e+e- machine, but feelings can be wrong.
 A: The vertical position of the beams is maintained by quadra-pole (and possibly other high n-pole configurations, I'm not actually familiar with the details of the Tevatron) magnets in the ring as part of the general positioning and focusing mechanism.
Because of the difference in coupling strength between gravity and magnetism, any difference due to different behavior in the beams would be too small to measure with the available equipment (or indeed anything you could install in the ring).
There was a proposal to measure $g$ for anti-matter at Fermilab that's been floating around for some time, but the PAC has turned it down repeatedly and now made the decision to alter some of the hardware it would have relied upon. So, the idea is dead for the time being.
I believe the reasoning went like this


*

*It ought to work, but no one has used all these principle in one experiment at one time before.

*It would be a moderately expensive, single measurement experiment

*It's a good idea, but it doesn't really fit in with our future plans. I mean, it not really "intensity frontier" physics, is it?

A: I am not good at all in all that but as soon as the particles in accelerators are charged and relativistic, the gravity force is always negligible with respect to other forces present. I think it is like trying to measure the gravity effect on a beam of light.
