Longitudinal impedance of LHC version-1 stripline beam position monitor

The electrodes in the first version of the LHC beam position monitor are 50 \W striplines. An enlarged aperture is required to keep the inner face of the electrodes in the shadow of the mechanical aperture of the machine. The longitudinal impedance of this device consists of two distinct components, one from the cavity and the other from the electrodes. The cavity part of the impedance can be reduced by inter-electrode shields as proposed by G. Lambertson. A complementary way of reducing this part of the impedance is to use tapered edges. The cavity wake potential of the beam position monitor is computed both with the 3D code MAFIA and analytically for a very short bunch (20 mm) and for a normal high energy LHC bunch (75 mm). The computation is done separately for the inter-electrode shields and for the tapered ends. The agreement between the two methods is very good, hence it can be concluded that the cavity impedance of the monitor cavity is well known up to the cut-off frequency of the LHC pipe (5.1 GHz). The impedance reduction by the shields and tapers can best be appreciated on the Z/n impedance plots. Finally, the wake field for the complete monitor which now also includes 4 striplines, is computed analytically for the two types of bunches.