Using the quadrupole moment frequency response of bunched beam to measure its transverse emittance

The quadrupole moment measured with a quadrupole pickup has been used to measure the transverse emittance of the beam. Unfortunately, the poor S/N ratio in the measurement makes it difficult to produce good and consistent emittance results. One way to enhance the S/N is to kick the beam with a quadrupole kicker and then measure its quadrupole frequency response (QFR) with a quadrupole pickup. This paper will show that if the bunched beam is extremely short, the quadrupole tunes are well decoupled and far apart, and the quadrupole tune spread is smaller than the synchrotron tune, then the emittance can be extracted from the QFR.