Digital Generation of Noise-Signals with Arbitrary Constant or Time-Varying Spectra (A noise generation software package and its application)

Artificial creation of arbitrary noise signals is used in accelerator physics to reproduce a measured perturbation spectrum for simulations but also to generate real-time shaped noise spectra for controlled emittance blow-up giving tailored properties to the final bunch shape. It is demonstrated here how one can produce numerically what is, for all practical purposes, an unlimited quantity of non-periodic noise data having any predefined spectral density. This spectral density may be constant or varying with time. The noise output never repeats and has excellent statistical properties, important for very long-term applications. It is difficult to obtain such flexibility and spectral cleanliness using analogue techniques. This algorithm was applied both in computer simulations of bunch behaviour in the presence of RF noise in the PS, SPS and LHC and also to generate real-time noise, tracking the synchrotron frequency change during the energy ramp of the SPS and producing controlled longitudinal emittance blow-up. This successful experience indicates that this method can also be applied in the LHC.