It is shown that the frequencies of Trivelpiece-Gould (TG) modes in non-neutral plasma can get into the low-frequency range due to the Doppler shift caused by plasma rotation in crossed fields. TG modes interact with the ion modes that leads to plasma instability. In paper the frequency spectrum of "cold" electron plasma completely filling a waveguide and containing small density fraction of ions of background gas is determined numerically. For ions the kinetic description is used. Oscillations having azimuthal number m = 2 are considered. In this case both low- and upper-hybrid TG modes get into the low-frequency range. The spectrum consists of families of "modified" ion cyclotron (MIC) modes and electron TG modes with the frequencies equal to hybrid frequencies with the Doppler shift. The growth rates of upper-hybrid modes are much faster than the growth rates of low-hybrid and MIC modes.