The betatron part of the equations of motion of an electron beam, propagating in a linearly polarized undulator, can be derived from a quartic anharmonic oscillator Hamiltonian coupling the vertical and radial components. The relevant Liouville equation is solved, providing the evolution of the e-beam phase-space distribution, and analyze the variation, during the transport of quantities of physical interest. In particular, radial and vertical phase-space contour plots which exhibit distortions, due to nonlinear effects, and consequent emittance growth are discussed. The integration method employed is based on a symmetric split technique of the evolution operator associated to the Liouville equation under study. Previous results from a macroparticle simulation are used as benchmark. Finally, the split operator technique naturally leads to area preserving maps. © 1995 American Institute of Physics.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy (miscellaneous)
Dattoli, G., & Ottaviani, P. L. (1995). Electron beam propagation in linearly polarized undulators: The effect of the anharmonicity on the spatial and phase-space distributions. Journal of Applied Physics, 78(2), 1348 - 1357. https://doi.org/10.1063/1.360309