Coherent nonlinear longitudinal phenomena in unbunched synchrotron beams

Coherent nonlinear longitudinal dynamics have been investigated in unbunched hadron beams [1]. These phenomena may be described using a theoretical framework originally developed to describe interactions in plasmas [2]. Processes exhibiting the weakest degree of nonlinearity are known as wave-wave interactions. Manifestations of these interactions may be used to help characterize a beam. Echoes have been used to measure the collisional damping rate of weak diffusive processes which degrade a stored beam. Further information is contained in the echo shape, which depends on the form of the particle energy distribution. The echo shape may also be modified by the presence of wakefields, or nonlinearities in the machine lattice which affect the longitudinal motion of the particles.