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.