Beam Coupling Impedances of Obstacles Protruding into Beam Pipe

The beam coupling impedances of small obstacles protruding inside the vacuum chamber of an accelerator are calculated analytically at frequencies for which the wavelength is large compared to a typical size of the obstacle. Simple formulas for a few important particular cases, including both essentially three-dimensional objects like a post or a mask and axisymmetric irises, are presented. The analytical results are compared and agree with three-dimensional computer simulations. These results allow simple practical estimates of the broad-band impedance contributions from such discontinuities.Comment: 4 pages, LaTeX (REVTeX), 2 figures (eps); corrected and revised, comparison with simulations added; presented at PAC97 (Vancouver, May 97

Stability and Halo Formation in Axisymmetric Intense Beams

Beam stability and halo formation in high-intensity axisymmetric 2D beams in a uniform focusing channel are analyzed using particle-in-cell simulations. The tune depression - mismatch space is explored for the uniform (KV) distribution of the particle transverse-phase-space density, as well as for more realistic ones (in particular, the water-bag distribution), to determine the stability limits and halo parameters. The numerical results show an agreement with predictions of the analytical model for halo formation (R.L. Gluckstern, Phys. Rev. Letters, 73 (1994) 1247).Comment: 4 pages, LaTeX (REVTeX), 5 figures (eps); presented at PAC97 (Vancouver, May 97

A General Approach for Calculating Coupling Impedances of Small Discontinuities

A general theory of the beam interaction with small discontinuities of the vacuum chamber is developed taking into account the reaction of radiated waves back on the discontinuity. The reactive impedance calculated earlier is reproduced as the first order, and the resistive one as the second order of a perturbation theory based on this general approach. The theory also gives, in a very natural way, the results for the trapped modes due to small discontinuities obtained earlier by a different method.Comment: LaTeX, 3 pages (IEEE format), uses pac95.sty (20K

Transverse impedance of a resistive cylinder of finite length

In this report we calculate the transverse impedance of a charged particle beam, displaced from the axis of a circular cylindrical beam pipe which has finite resistivity only over a finite length. For this purpose we replace it with a cavity filled with the resistive material and connected to the region surrounding the beam by a gap of the same length. Matching of the electro-magnetic fields on both sides of the gap leads to an infinite set of linear equations for the field expansion coefficients with terms given by infinite sums over integrals which are evaluated by summing over their residues. By truncating these sums one can determine the transverse impedance and evaluate it numerically. Keeping only the lowest terms gives simple approximate expressions which are often sufficient to estimate the values and parameter dependence of the impedance

Halo Formation in Spheroidal Bunches with Self-Consistent Stationary Distributions

A new class of self-consistent 6-D phase space stationary distributions is constructed both analytically and numerically. The beam is then mismatched longitudinally and/or transversely, and we explore the beam stability and halo formation for the case of 3-D axisymmetric beam bunches using particle-in-cell simulations. We concentrate on beams with bunch length-to-width ratios varying from 1 to 5, which covers the typical range of the APT linac parameters. We find that the longitudinal halo forms first for comparable longitudinal and transverse mismatches. An interesting coupling phenomenon - a longitudinal or transverse halo is observed even for very small mismatches if the mismatch in the other plane is large - is discovered.Comment: 3 pages, 3 figures; presented at European Particle Accelerator Conference, Stockholm, Sweden (June 22-26, 1998