Single-mode coherent synchrotron radiation instability

The microwave instability driven by the coherent synchrotron radiation (CSR) has been previously studied [G. Stupakov, S. Heifets, Phys. Rev. ST Accel. Beams 5, 054402 (2002)] neglecting effect of the shielding caused by the finite beam pipe aperture. The growth rate of the instability is large and, at low bunch density, is dominated by the long wavelength modes. Such modes may be close to the shielding threshold where the spectrum of the radiation in a toroidal beam pipe is discrete. In this paper we study the CSR instability in the case when it is driven by a single synchronous mode. Such a regime is different from the regime studied before where the continuous CSR spectrum was implied. We derive a system of equations for the beam-wave interaction and show its similarity to the 1D FEL theory. The growth rate of the instability is obtained and a transition to the case of continuous spectrum is discussed. Presented at the 2003 Particle Accelerator Conference (PAC 03) Portland, Oregon, May 12-16, 2003 ∗Work supported by Department of Energy contract DE–AC03–76SF00515. Single-mode coherent synchrotron radiation instability S. Heifets and G. Stupakov Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309