Novel trapped-particle asymmetry modes propagate on cylindrical electron co
lumns when axial variations in the wall voltage cause particle trapping. Th
ese modes consist of E x B drifts of edge-trapped particles, partially shie
lded by axial flows of interior untrapped particles. A simple model agrees
well with the observed frequencies and eigenfunctions, but the strong mode
damping is as yet unexplained. These modes may be important in coupling tra
p asymmetries to particle motions and low frequency E x B drift modes.