Nonlinear Longitudinal Waves in High Energy Stored Beams
arXiv:physics/9907043 · doi:10.1063/1.1301899
Abstract
We solve the Vlasov equation for the longitudinal distribution function and find stationary wave patterns when the distribution in the energy error is Maxwellian. In the long wavelength limit a stability criterion for linear waves has been obtained, and a Korteweg-de Vries-Burgers equation for the relevant hydrodynamic quantities has been derived.
arXiv commentLaTeX, 10 pages