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Extending the method of Warnock and Ellison for the simulation of the Vlasov-Fokker-Planck equation for bunched beams [in Proceedings of the 2nd ICFA Advanced Accelerator Workshop on the Physics of High Brightness Beams, Los Angeles, CA, 1999 (World Scientific, Singapore, 2000)], we analyze arbitrary radio-frequency potentials and high- Q impedances and study instabilities in stretched bunches. Results for the microwave instability driven by a broadband impedance and instability driven by high- Q rf modes in stretched bunches are compared with measurements of the vacuum ultraviolet ring at the National Synchrotron Light Source. A method for the calculation of response functions is developed, and simulated response functions are compared to experimental results

Longitudinal simulations and measurements of stretched bunches