Linearization of the Fermilab recycler high level RF

In studying the recycler high level RF, it was found that at 89 kHz, the lowest frequency required by the system, some nonlinearities in magnitude and phase were discovered. The visible evidence of this was that beam injected in a barrier bucket had a definite slope at the top. Using a network analyzer, the S-parameter S₂₁ was realized for the overall system and from mathematical modeling a second order numerator and denominator transfer function was found. The inverse of this transfer function gives our linearization transfer function. The linearization transfer function was realized in hardware by summing a high pass, band pass and low pass filter together. The resulting magnitude and phase plots, along with actual beam response will be shown.