Transverse resistive wall impedances and shielding effectiveness for beam pipes of arbitrary wall thickness

Transverse Schottky spectra and beam transfer functions (BTFs) of coasting ion beams were measured in the heavy ion synchrotron SIS-18 in order to study the impact of space charge on the transverse beam dynamics. The particle number in the beam was varied to investigate the intensity dependence of the space-charge effect. No cooling was applied to the beams throughout the experiment. The expected deformation of the Schottky spectra and BTFs is observed. An analytic model with linear space charge is employed to describe the deformed Schottky and BTF signals. In this model, the incoherent space-charge force and the coherent forces due to impedances are treated separately. Using the model, the space-charge induced tune shift is evaluated both from the position and the form of the signals. The data are well described by the model, only in the high-intensity BTFs deviations are observed. The stability diagrams are shifted according to the space-charge parameter obtained from the BTFs. In addition, the tune shift is estimated by virtue of measured beam profiles and particle numbers. The estimated tune shift is of the same order of magnitude but smaller than the measured one. Possible explanations for deviations between the measurements, the model, and the estimation are discussed.

Section: Schottky and Transverse Btf Diagnosticsmentioning

confidence: 99%

Transverse Schottky and beam transfer function measurements in space charge affected coasting ion beams

Paret

Kornilov

Weiland

2010

“…(A3). More refined treatments are available -see [12] and references therein. The qualitative features of the results presented in this paper are likely to remain unchanged because the wakefield model only determines the constant numerical values of the coefficients of x in Eq.…”

Section: Tracking Simulationmentioning

confidence: 99%

Time evolution of coupled-bunch modes from beta function variation in storage rings

Hock

Wolski

2007

We present an analytical and numerical study of the equations of motion for bunches coupled by transverse wakefields. We base our study on a recent lattice design for the damping rings in the baseline configuration of the International Linear Collider. Using the macroparticle model, and assuming resistive wall wakefield coupling, we present numerical results on the time evolution of the multibunch modes. Decay modes display growth after initial decay, and mode amplitudes exhibit high-frequency oscillations. These phenomena are not expected if the beta function is assumed to have a constant, averaged value. We show analytically that they can come from coupling between modes caused by variation of the beta function in a real lattice. The effect is shown to be comparable to the effect of a nonuniform fill pattern and significantly larger than that of the higher-order mode wakefield localized in the rf cavities. Turning to the case of constant beta function, we develop a more complete treatment of the equations of motion. We derive general formulas for the bunch trajectories, and show that such formulas can only be valid in the limit of small wakefield coupling.

“…In addition to the standard references on im-pedance problems [4,13], this paper rests on and has profited from the various publications at GSI [14], FNAL [15], DESY [8,16], and primarily the experimental and theoretical work at CERN for the LHC collimator [17][18][19]. The analytic treatments of both the transverse and longitudinal beam tube impedances suffered from a tenuous agreement with experimental data in the low-frequency regime; this issue was addressed successfully in a recent comprehensive paper [20], although, seemingly, further work may be needed.…”

Section: Introductionmentioning

confidence: 99%

Matrix solution for the wall impedance of infinitely long multilayer circular beam tubes

Hahn

2010

The coupling impedance of beam tubes is a long-standing important topic for particle accelerators that many authors have addressed. The present study was initiated in view of a specific problem, but its novel approach is broadly applicable to the longitudinal and transverse coupling impedances of coated beam tubes or multilayer tubes. The matrix method presented here derives the wall impedance by treating the radial wave propagation of the beam-excited electromagnetic fields in full analogy to longitudinal transmission lines. Starting from the Maxwell equations, the radially transverse magnetic field components are described for monopole and dipole modes by a 2 Â 2 matrix. Assuming isotropic material properties within one layer, the transverse field components at the inner boundary of a layer uniquely are determined by matrix transfer of the field components at its outer boundary. By imposing power-flow constraints on the matrix, wave impedance mapping and field matching between layers is enforced and replaced by matrix multiplication. The longitudinal and transverse coupling impedances are derived from the wall impedance at the innermost boundary, and the different procedures for its determination are discussed. The matrix method is demonstrated via selected yet representative examples of the welldocumented cases of a stainless-steel tube, and of a graphite collimator.