Paper  Title  Page 

THAC2 
SpaceCharge Particle Resonances and Mode Parametric Resonances  


As the beam intensity increases in modern highpower accelerators, selffield effects of the beam become significant. There are two distinct families of spacecharge halo mechanisms in highintensity accelerators, and yet they need to be differentiated: resonances (particle resonances or incoherent resonances) and instabilities (parametric resonances or coherent resonances). What we call resonances are resonances of beam particles excited through the spacecharge nonlinear multipoles. What we call instabilities are instabilities of the beam modes. Instabilities are also called parametric resonances because they are parametric resonances of the VlasovPoisson equations. They would better be called mode parametric resonances to distinguish them from particle parametric resonances. Resonances and instabilities may look alike in the phase space, and yet they have distinct differences. Instabilities (or mode parametric resonances) do not have the resonant frequency component. Various orders of resonances and instabilities are presented along with the beam distributions with which the particular mechanism is observed.  
Slides THAC2 [5.680 MB]  
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