Resonance analysis for a space charge dominated beam in a circular lattice

Abstract

We use the linearized Vlasov-Poisson equations to study the response of a Kapchinskij-Vladimirskij beam to magnetic multipole errors in a circular lattice. This work extends the calculation of Gluckstern [Proceedings of the Linac Conference, 1970 (Fermilab, Batavia, IL, 1970, p. 811] to the case of nonideal periodic lattices. The smooth approximation is assumed. We determine the resonance conditions as well as the amplitude of the excited collective modes as a function of the error size outside the stopbands. We find that the frequencies associated with lattice resonances are a subset of the beam natural eigenfrequencies. The result is used to study the motion of test particles crossing the boundary of the beam core. Close to resonance the model predicts the emergence of a halo if sufficiently large gradient errors are present. Application is made to the University of Maryland Electron Ring.

Accelerator Design Study for a Soft X-Ray Free Electron Laser at the Lawrence Berkeley National Laboratory

“…6.5. The period of this modulation is consistent with expectations from the linear analysis [Heifets et al, Huang et al 2002, Venturini 2007b of the microbunching instability. The spectral properties of the instability are determined by the gain function through the bunch compressor shown in Fig.…”

“…In addition to macroparticle simulations we have also pursued an alternative approach based on the use of grid-based direct methods to solve the Vlasov equation describing the beam dynamics [Venturini et al 2007a[Venturini et al , 2007b. The beam density in phase space is represented on a grid and therefore is immune to sampling noise that occurs when the number macroparticles is significantly smaller than the bunch population.…”

Half-integer resonance crossing in high-intensity rings

“…More than that, using the KV (Kapchinsky-Vladimirsky) beam, it is easy to show [5,10] that the effect of gradient errors in the lattice is exactly compensated by the spacecharge perturbation induced by those errors if n inc n͞2. A similar result can be obtained for the high-order resonances using the Vlasov equation [11].…”

“…The corresponding coefficients C m can be easily extracted from Refs. [6,11,12] and are summarized, for example, in Ref. [9].…”

Effect of Space Charge Rotation with Kapchinskiy-Vladimirskiy Distribution Function in Quadrapole

“…The issue of envelope resonances and instabilities has received new attention in several papers [1,2,3,4], where as the effect of space charge on linear coupling due to skew drift. In this paper we discuss about Rotation with KapchinskiyVladimirskiy Distribution Function (KV) in [5,6] and effect on the focusing and defocusing on quadrupole and very important on the designing of accelerators.…”