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.
An analytical solution for the Haissinski equation with purely inductive wake fields / R., Bartolini; J. I. M., Botman; G., Dattoli; L., Mezi; Migliorati, Mauro; C., Thomas. - In: EUROPHYSICS LETTERS. - ISSN 0295-5075. - 60:1(2002), pp. 66-71. [10.1209/epl/i2002-00319-x]
An analytical solution for the Haissinski equation with purely inductive wake fields
MIGLIORATI, Mauro;
2002
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
