An analytical solution for the Haissinski equation with purely inductive wake fields
TU/e - Eindhoven, The Netherlands
2 ENEA - Frascati, Roma, Italy
3 Università di Roma “La Sapienza” - Roma, Italy
Accepted: 17 July 2002
The static solution of the Fokker-Planck equation, known as the Haissinski equation and governing the longitudinal evolution of an electron beam moving in a Storage-Ring which is subject to an inductive wake field, can be expressed in an analytical form, using the Lambert W-function. We show how the use of this analytical tool allows a better understanding of the validity of the numerical solutions and the distribution normalization properties.
PACS: 41.75.-i – Charged-particle beams / 29.27.-a – Beams in particle accelerators / 02.30.Hq – Ordinary differential equations
© EDP Sciences, 2002