Title :
Control theory to accelerator research and self-focused bunched beam
Author :
Parsa, Z. ; Zadorozhny, V. ; Rudenko, A.
Author_Institution :
Dept. of Phys., Brookhaven Nat. Lab., Upton, NY, USA
Abstract :
A new approach to a nonlinear bunched beam dynamics based on the self-consistent Vlasov equation is presented. The main emphasis is given on the direct Lyapunov method in case of a vector field (on a compact manifold with a singular point) to finding a solution to Vlasov-Poisson equation (VPE). The VPE is transformed into a Fredholm equation in an attraction region. These properties are linked to the self-focusing and acceleration of a bunched beam.
Keywords :
Fredholm integral equations; Maxwell equations; Poisson equation; Vlasov equation; nonlinear differential equations; particle beam bunching; particle beam dynamics; particle beam stability; Fredholm equation; Maxwell equations; Vlasov-Poisson equation; attraction region; beam stability; compact manifold; control theory; direct Lyapunov method; nonlinear bunched beam dynamics; nonlinear evolutionary wave equation; self-consistent Vlasov equation; self-focused bunched beam; singular point; vector field; Acceleration; Control theory; Distribution functions; Force control; Kernel; Laboratories; Maxwell equations; Nonlinear equations; Particle beams; Poisson equations;
Conference_Titel :
Physics and Control, 2003. Proceedings. 2003 International Conference
Print_ISBN :
0-7803-7939-X
DOI :
10.1109/PHYCON.2003.1237040
