Frequency-selective harmonic retrieval for Schottky mass spectrometry.

Nuclear mass measurements by means of Schottky mass spectrometry critically rely on an accurate determination of revolution frequencies of the circulating ions in a storage ring. Such a harmonic retrieval problem is conventionally tackled via the periodogram of the Schottky data, where the ion peaks are identified and their spectral locations are obtained by fittings. However, the discrete frequency grid of the periodogram has unfortunately hampered a fine resolution of two closely spaced harmonics. We thereby propose a method based on the state space representation in the frequency domain to overcome this limit. Moreover, its frequency-selective merit has allowed the method to focus only on a narrow band and thus greatly reduced the computational cost while still retaining superb accuracy. With the real Schottky data from an isochronous-Schottky beam time at the experimental cooler-storage ring in Lanzhou, the accuracy of the retrieved harmonics is demonstrated to be around 1 ppm, as limited by the anisochronism effect of the ion optics.