Digital Generation of Noise-Signals with Arbitrary Constant or Time-Varying Spectra

Noise sources in the RF system of an accelerator produce longitudinal emittance increase or particle loss. This noise is inherent, from the beam-control system electronics, external sources or high power components, or can be purposely injected for a specific need such as bunch distribution modification or controlled emittance increase. Simulations to study these effects on the beam require precise reproduction either of the total noise measured on the hardware, or of the noise spectrum to be injected and optimized to produce the desired changes. In the latter case the 'optimized' noise source has also to be created in real-time to actually excite the beam via the RF system. This paper describes a new algorithm to create noise spectra of arbitrary spectral density varying with cycle time. It has very good statistical properties and effectively infinite period length, important for long simulation runs. It is spectrally clean and avoids undesired mirror spectra. Coded in C++, it is flexible and fast. Used extensively in simulations it has also successfully created controlled emittance increase in the SPS by the injection of artificial real-time RF noise.