| Paper | Title | Page |
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| WEPLT092 | Equilibrium Longitudinal Distribution for Localized Regularized Inductive Wake | 2062 |
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In a recent paper [*] we have shown that a localized wake assumption and the Gaussian approximation for the longitudinal beam distribution function can be used to understand the nature of the stationary solutions for the inductive wake, by comparison between the resulting map and the Haissinski equation, which rules the (less realistic) case of a uniformly distributed wake. In particular we showed the non-existence of solutions of Haissinski's equation when the inductive wake strength exceeds a certain threshold [**] to correspond to the onset of chaos in the map evolving the moments of the beam distribution from turn to turn. In this paper we use the same formalism to confirm that as noted in [**] for Haissinski's equation, a steady state solution for the longitudinal phase space distribution function always exists if a physically regularized inductive wake, which satisfies an obvious causality condition, is used.
* S. Petracca and Th. Demma, Proc. of the 2003 PAC, IEEE Press, New York, 2003, ISBN 0-7803-7739-9, p.2996.** Y. Shobuda and K. Hirata, Part. Accel. vol. 62, 165 (1999). |
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| WEPLT093 | Electromagnetic Fields of an Off-axis Bunch in a Circular Pipe with Finite Conductivity and Thickness - I | 2065 |
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The electromagnetic field produced by a bunched beam in a circular pipe is usually computed under the assumption that the field penetration(skin depth) is far less than the wall thickness. Chao [*] gave a formula which exploits the wall thickness, but his result is restricted to the monopole term. Piwinski [**] treated the case of a metal coated ceramic wall, when the coating thickness is much smaller than the skin-depth, but his analysis is also limited to the monopole term.In this paper we solve the problem in full generality, by providing an exact (Green's functions) solution for the field of an off-axis point particle running at constant velocity in a circular pipe with finite wall conductivity and thickness.
* A.W. Chao, Phys. of Collective Beam Instab. in High En. Accel., Wiley,1993** S. Piwinski, DESY 1972/72 |
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| WEPLT094 | Electromagnetic Fields of an Off-axis Bunched Beam in a Circular Pipe with Finite Conductivity and Thickness - II | 2068 |
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The general exact solution exploited [*] is applied, introducing suitable dimensionless parameters, and using appropriate asymptotic limiting forms, to compute the wake field multipoles for the different paradigm cases of LHC and DAPHNE.
* R. P. Croce, Th. Demma, S. Petracca "Electromagnetic Fields of an Off-axis Bunch in a Circular Pipe with Finite Conductivity and Thickness", these proceedings |
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| WEPLT095 | Modified Polarizabilities and Wall Impedance for Shielded Perforated Beam Pipes with General Shape | 2071 |
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We extend previous results [*] concerning the modified polarizability of (electrically small) holes/slots in the wall of a circular beam liner surrounded by a coaxial circular tube to the most general liner and cold bore geometries. We obtain an equivalent wall impedance to describe the electromagnetic boundary conditions at perforated walls for this most general case, and use a general perturbational approach [**] for computing the pertinent longitudinal and transverse coupling impedances.
* R.L. Gluckstern, CERN SL 92-06 (AP), 1992, CERN SL 92-31 (AP), 1992; R.L. Gluckstern, B. Zotter, CERN SL 96-56 (AP), 1996.** S. Petracca, Part. Acc., {\bf 50}, 211, 1995; id., Phys. Rev. E, 60 (3),1999. |