Volume 60, Number 1, October 2002
|Page(s)||66 - 71|
|Section||Atomic and molecular physics|
|Published online||01 September 2002|
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.