Measuring the ISR Impedance at Very High Frequencies by Observing the Energy Loss of a Coasting Beam

A slow energy loss of unbunched protons and antiprotons in the ISR has been observed which is larger than expected for interactions with the residual gas and for synchrotron radiation., It can be explained as a parasitic mode loss due to the wall currents induced by the longitudinal Schottky noise. This noise as seen at the wall of a circular chamber of radius a extends to a typical frequency of the order ¿ ~ c¿/a limited by the finite opening angle of ~1/¿ of the fields created by a relativisitic particle. Due to the statistical longitudinal distribution of the particles the total energy loss due to the induced wall current is proportional to the total number of particles and the loss per particle becomes independent of current. This loss leads to a steady decrease of the orbit radius which can be observed for long storage times. Using these results obtained at different energies, the frequency dependence of the resistive longitudinal impedance in the range of several tens of GHz is obtained. This impedance is compared with the prediction of the diffraction theory.