Longitudinal and Transverse Impedances and Shielding Effectiveness of a Resistive Beam Pipe for Arbitrary Energy and Frequency

A. M. Al-khateeb
2005 AIP Conference Proceedings  
The longitudinal coupling impedance of a cylindrical beam pipe for arbitrary relativistic energy and mode frequency is obtained analytically for finite wall conductivity and finite wall thickness. Closed form expressions for the electromagnetic fields excited by a beam perturbation are derived analytically. General expressions for the resistive-wall impedance in the presence of a metallic shield and for the rf shielding effectiveness of the beam pipe have been obtained. The results are applied
more » ... o the GSI synchrotron SIS, where the thickness of the vacuum chamber in the dipole magnets is much smaller than the skin depth at injection energy. In addition, the transverse space-charge and resistive-wall impedances have been investigated analytically of a smooth cylindrical beam pipe of finite conductivity. Transverse beam charge distributions of a hollow beam and of a uniform beam are considered yielding different results. Closed form expressions for the excited electromagnetic fields in the beam-pipe-wall regions and for the corresponding total transverse impedance can be derived analytically for high energy beams.
doi:10.1063/1.1949565 fatcat:olm7pliddnewvdhiau6eeipgom