In this paper we describe a new microbunching instability occurring in charged particle beams propagating along a straight trajectory. The nature of these exponentially growing plasma oscillations gave the reason for its name: plasma-cascade instability. Such instability can strongly amplify longitudinal microbunching originating from the beam’s shot noise, even to the point of saturation. Resulting random density and energy microstructures can drastically reduce beam quality. Conversely, such instability can drive novel high-power sources of broadband radiation or can be used as a broadband amplifier. We discovered this phenomenon in a search for such amplifier in the coherent electron cooling scheme [Phys. Rev. Lett. 102, 114801 (2009)PRLTAO0031-900710.1103/PhysRevLett.102.114801] without separation of electron and hadron beams. In this paper we present a brief analytical theory of this new phenomenon, detailed numerical studies, the results of experimental demonstration as well as control of the longitudinal plasma-cascade instability.