Abstract

The authors evaluate the longitudinal coupling impedance of a toroidal chamber with rectangular cross section in the frequency domain below the synchronous resonant modes. With infinite wall conductivity the impedance is purely reactive and consists of a space charge term, proportional to gamma /sup -2/, and a curvature term which survives at large gamma . The curvature term is well represented as a quadratic function of frequency. Consequences for beam stability, if any, arise from high-frequency resonances, which can produce values of several ohms for Z/n. >

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