DocumentCode :
334677
Title :
Stability diagrams for Landau damping
Author :
Berg, J. Scott ; Ruggiero, Francesco
Volume :
2
fYear :
1997
fDate :
12-16 May 1997
Firstpage :
1712
Abstract :
Coherent modes which are present when there is no incoherent tune spread may be absent when such a spread exists. Such modes are “Landau damped”. There is instead an incoherent spectrum, a continuum of an infinite number of frequencies, which will decohere (filament), thus not leading to collective instabilities. A stability diagram indicates when Landau damping will be effective. It divides the effective impedance plane, or equivalently the plane of coherent frequency in the absence of tune spread, into regions. The region which contains +i∞ corresponds to instability. Thus, one can substitute a simpler computation (finding discrete eigenvalues) for a more complex computation (solving an eigenvalue system with both a discrete and a continuous eigenvalue spectrum). We present stability diagrams assuming a linear tune shift with amplitude, allowing tune spread in two transverse planes or in the longitudinal plane alone. When there is longitudinal tune spread, this can not be done exactly, and we describe approximations which make the computation tractable
Keywords :
particle beam stability; Landau damping; coherent frequency; collective instabilities; continuous eigenvalue spectrum; effective impedance plane; incoherent spectrum; incoherent tune spread; linear tune shift; longitudinal plane; stability diagram; stability diagrams; transverse planes; tune spread; Damping; Eigenvalues and eigenfunctions; Frequency conversion; Gaussian distribution; Impedance; Integral equations; Laboratories; Lattices; Stability; Transfer functions;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Particle Accelerator Conference, 1997. Proceedings of the 1997
Conference_Location :
Vancouver, BC
Print_ISBN :
0-7803-4376-X
Type :
conf
DOI :
10.1109/PAC.1997.750810
Filename :
750810
Link To Document :
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