| Issue |
Europhys. Lett.
Volume 60, Number 1, October 2002
|
|
|---|---|---|
| Page(s) | 66 - 71 | |
| Section | Atomic and molecular physics | |
| DOI | https://doi.org/10.1209/epl/i2002-00319-x | |
| Published online | 01 September 2002 | |
An analytical solution for the Haissinski equation with purely inductive wake fields
1
TU/e - Eindhoven, The Netherlands
2
ENEA - Frascati, Roma, Italy
3
Università di Roma “La Sapienza” - Roma, Italy
Received:
31
January
2002
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
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