Energy Loss to Coaxial Vacuum Chambers in LEP and LHC

In many hig-energy storage rings the beam chamber is connected to a separate pump chamber by a metallic wall with many holes or slots whic permits passage of the rest gas. In LEP, the pump chamber contains a metallic 'negstrip' pump, and thereby becomes a coazial transmission line. Also in LHC, a coaxial line is formed by the 'liner' and the surrounding cold vacuum chamber which it shields from heating by sznchrotron radiation. Since the phase velocity of electro-magnetic fields in a coax line is close to light velocity, the fields will be almost in sznchronism with the particle beam and the pump chamber, which may result in a large resistive impedance and could lead to isntability, loss of beam energy, and excessive heating of the chamber walls. Here we estimate the rate of field buildup analytically, and in a subsequent report we will compare these results with numerical computations using 3-D computer codes. The results are tested for diagnostic purposes on a 'slot coupler' with short and wide holes designed to extract energy efficiency.