A fast beam-ion instability

Mutually driven transverse oscillations of an electron beam and residual gas ions may result in a fast transverse instability. This effect arises either during a single pass of a train of electron bunches or it is caused by ionization electrons oscillating within a single positron bunch. In both cases, the beam oscillations grow exponentially with an exponent proportional to the square root of time. In this report, instability rise times are calculated analytically and compared with computer simulations. The effect considered could be a significant limitation in many future designs