Title :
A new approach to potential well bunch deformation
Author :
Hagel, J. ; Zotter, B.
Author_Institution :
CERN, Geneva, Switzerland
Abstract :
A stationary solution to the Vlasov equation fulfils a nonlinear integral equation of the Volterra type known as Haissinski´s equation. It describes the shape of a bunch of particles as function of the current and the impedance of the surrounding structure. An analytic technique is described for solving this integral equation which is based on transforming the Volterra integral equation into one of Fredholm type with fixed integration limits, using a Fourier expansion for the discontinuous integrand. The results are applied to LEP (Large Electron-Positron colliding beam accelerator) at injection energy, and are found to be in excellent agreement with measurements of the bunch length in the potential well regime.<>
Keywords :
electron accelerators; integral equations; particle beam diagnostics; storage rings; synchrotrons; Fourier expansion; Haissinski´s equation; LEP; Large Electron-Positron colliding beam accelerator; Vlasov equation; Volterra integral equation; discontinuous integrand; nonlinear integral equation; potential well bunch deformation; Acceleration; Electrons; Impedance; Integral equations; Kernel; Potential well; Radio frequency; Shape; Storage rings; Voltage;
Conference_Titel :
Particle Accelerator Conference, 1991. Accelerator Science and Technology., Conference Record of the 1991 IEEE
Conference_Location :
San Francisco, CA, USA
Print_ISBN :
0-7803-0135-8
DOI :
10.1109/PAC.1991.164343
