Oscilloscope measurement of the synchronous phase shift in an electron storage ring

We present a new technique to measure the synchronous phase shift in an electron storage ring. A digi- tal sampling oscilloscope is used to observe the cavity and beam signals simultaneously, and the amplitude and relative phase are obtained from a Fourier transform of the time-domain data. This procedure gives 6 mdeg resolution and is largely insensitive to input signal amplitude variations. The measurement system was used to study the dependence of the synchronous phase shift on beam current, gap voltage, and beam energy in the Brazilian Synchrotron Light Source electron storage ring. The measurement of the shift in the phase of the stored electron beam with respect to the cavity voltage (the syn- chronous phase shift (1)) is a well-known procedure to de- termine various important beam parameters in an electron storage ring. The variation of the synchronous phase shift as a function of gap voltage has been used to determine the energy loss to synchrotron radiation (2), and its variation as a function of beam current has been used in several ma- chines (2- 5) to determine parasitic mode losses. In most of these measurements, rf phase detection techniques are used and commercial vector voltmeters or network ana- lyzers are often the instruments of choice. More recently, a novel method was proposed by Podobedov and Siemann (6) to mix the cavity and beam signals down to audio fre- quencies, thus allowing the use of a fully digitized lock-in amplifier for the phase detection. Their work demonstrated the possibility of measuring the very small phase shifts to be expected from the newer low impedance machines. All of these measurements suffer from various diffi- culties, including electronic noise and various systematic errors (e.g., slow phase drifts due to cable temperature variations), that make accurate determinations of the phase shifts difficult. One important source of uncertainty in phase measure- ments is the inherent dependence of the measured phase on the signal amplitude for rf phase detectors. The depen- dence of the measured phase on amplitude is a basic feature of most rf phase detectors based on mixing techniques, and a typical value of the phase measurement variation due to input signal amplitude variation for a commercial rf vector voltmeter is 50 mdegdB (4).