Chromaticity tracking using a phase modulation technique

In the classical chromaticity measurement technique, chromaticity is measured by measuring the change in betatron tune as the the RF frequency is varied. This paper will describe a novel way of measuring chromaticity: we will phase modulate the RF with a known sine wave and then phase demodulate the betatron frequency. The result is a line in Fourier space which corresponds to the frequency of our sine wave modulation. The peak of this sine wave is proportional to chromaticity. For this technique to work, a tune tracker PLL system is required because it supplies the betatron carrier frequency. This method has been tested in the Tevatron and we will show the results here.