Transverse-longitudinal Energy Equilibration in a Long Uniform Beam

Evidence is presented to show the transfer, via a collective electrostatic instability, of transverse energy to the longitudinal direction if the axial temperature of a beam is sufficiently low. Two-dimensional r,z electrostatic PIC simulations of a long coasting space-charge-dominated beam propagating in a uniform focused channel are presented to illustrate, for typical parameters, the development of a coherent mode structure with an axial wavelength comparable to the beam diameter, and growth times comparable to the betatron period.