Simulation study of beam extraction from a synchrotron using colored noise with digital filter

A simulation program is developed for a slow-extraction method using a fast Q magnet (FQ) and an RF-knockout. In this extraction method, after the separatrix is produced with excitation of sextupole magnets, a required quantity of circulating beam is extracted by shrinking the separatrix with excitation of the FQ. Then the emittance of circulating beam is diffused to an original size with the RF-knockout. This process is repeated with required timing until the entire circulating beam is completely extracted. An algorithm using a digital filter and white noise is proposed for a colored noise as a signal source for the RF-knockout. Spill structures with the present computing method were similar to the results obtained using a conventional algorithm with the sum of cosines of many frequency components. The results are also in agreement with the experimental results using the HIMAC synchrotron. The computing time of colored noise for simulation of 106 turns was 0.5 h for the filter method and 5.0 h for the conventional one. It is indicated that a colored noise with a wider frequency bandwidth gives a better spill structure that smoothly increases with time.