Transverse-longitudinal temperature equilibration in a long uniform beam

Computer simulations are employed to examine the transfer of transverse thermal energy to the longitudinal direction via a collective electrostatic instability which is driven by an initial temperature anisotropy. The nature of the instability is illustrated using electrostatic particle-in-cell simulations in an axisymmetric geometry, but with three components of the velocity. Results are presented for a long coasting space-charge-dominated beam, propagating in a uniform focused channel to illustrate the development of a coherent mode structure with an axial wavelength comparable with the beam diameter, and growth times comparable with the betatron period.