Coupling Impedances of Small Discontinuities: Dependence on Beam Velocity

The beam coupling impedances of small discontinuities of an accelerator vacuum chamber have been calculated [e.g., S.S. Kurennoy, R.L. Gluckstern, and G.V. Stupakov, Phys. Rev. E 52, 4354 (1995)] for ultrarelativistic beams using the Bethe diffraction theory. Here we extend the results to an arbitrary beam velocity. The vacuum chamber is assumed to have an arbitrary, but uniform along the beam path, cross section. The longitudinal and transverse coupling impedances are derived in terms of series over cross-section eigenfunctions, while the discontinuity shape enters via its polarizabilities. Simple explicit formulas for two important particular cases - circular and rectangular chamber cross sections - are presented. The impedance dependence on the beam velocity exhibits some unusual features: for example, the reactive impedance, which dominates in the ultrarelativistic limit, can vanish at a certain beam velocity, or its magnitude can exceed the ultrarelativistic value many times. In addition, we demonstrate that the same technique, the field expansion into a series of cross-section eigenfunctions, is convenient for calculating the space-charge impedance of uniform beam pipes with arbitrary cross section.Comment: REVTeX, 11 pages, 6 figures. Submitted to Phys. Rev. ST - Accel. Beam

Nonlinearities and Effects of Transverse Beam Size in Beam Position Monitors (revised)

The fields produced by a long beam with a given transverse charge distribution in a homogeneous vacuum chamber are studied. Signals induced by a displaced finite-size beam on electrodes of a beam position monitor (BPM) are calculated and compared to those produced by a pencil beam. The non-linearities and corrections to BPM signals due to a finite transverse beam size are calculated for an arbitrary chamber cross section. Simple analytical expressions are given for a few particular transverse distributions of the beam current in a circular or rectangular chamber. Of particular interest is a general proof that in an arbitrary homogeneous chamber the beam-size corrections vanish for any axisymmetric beam current distribution.Comment: REVTeX, 8 pages, 9 figures. Corrected Eqs. (7),(22),(25) and Figs. 2-9. Expande

Wake Field Effect Analysis in APT Linac

The 1.7-GeV 100-mA CW proton linac is now under design for the Accelerator Production of Tritium (APT) Project. The APT linac comprises both the normal conducting (below 211 MeV) and superconducting (SC) sections. The high current leads to stringent restrictions on allowable beam losses (<1 nA/m), that requires analyzing carefully all possible loss sources. While wake-field effects are usually considered negligible in proton linacs, we study these effects for the APT to exclude potential problems at such a high current. Loss factors and resonance frequency spectra of various discontinuities of the vacuum chamber are investigated, both analytically and using 2-D and 3-D simulation codes with a single bunch as well as with many bunches. Our main conclusion is that the only noticeable effect is the HOM heating of the 5-cell SC cavities. It, however, has an acceptable level and, in addition, will be taken care of by HOM couplers.Comment: 3 pages, 6 figures; presented at European Particle Accelerator Conference, Stockholm, Sweden (June 22-26, 1998

Polarizabilities of an Annular Cut in the Wall of an Arbitrary Thickness

The electric and magnetic polarizabilities of an aperture are its important characteristics in the theory of aperture coupling and diffraction of EM waves. The beam coupling impedances due to a small discontinuity on the chamber wall of an accelerator can also be expressed in terms of the polarizabilities of the discontinuity. The polarizabilities are geometrical factors which can be found by solving a static (electric or magnetic) problem. However, they are known in an explicit analytical form only for a few simple-shaped discontinuities, such as an elliptic hole in a thin wall. In the present paper the polarizabilities of a ring-shaped cut in the wall of an arbitrary thickness are studied using a combination of analytical, variational and numerical methods. The results are applied to estimate the coupling impedances of button-type beam position monitors.Comment: Uuencoded gzipped PS-file, 7 pages, 5 figures (110K) Submitted : IEEE Transactions on Microwave Theory and Technique

Cavity Loss Factors For Non-Ultrarelativistic Beams

Cavity loss factors can be easily computed for ultrarelativistic beams using time-domain codes like MAFIA or ABCI. However, for non-ultrarelativistic beams the problem is more complicated because of difficulties with its numerical formulation in the time domain. We calculate the loss factors of a non-ultrarelativistic bunch and compare results with the relativistic case.Comment: 3 pages, 3 figures; presented at European Particle Accelerator Conference, Stockholm, Sweden (June 22-26, 1998

Effects of Transverse Beam Size in Beam Position Monitors

The fields produced by a long beam with a given transverse charge distribution in a homogeneous vacuum chamber are studied. Signals induced by a displaced finite-size beam on electrodes of a beam position monitor (BPM) are calculated and compared to those produced by a pencil beam. The non-linearities and corrections to BPM signals due to a finite transverse beam size are calculated for an arbitrary chamber cross section. Simple analytical expressions are given for a few particular transverse distributions of the beam current in a circular or rectangular chamber. Of particular interest is a general proof that in an arbitrary homogeneous chamber the beam-size corrections vanish for any axisymmetric beam current distribution

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