Analytic approximation of the head-tail phase difference from continuous transverse excitation for measuring chromaticity

Abstract

We will explore a method for measuring chromaticity by continuously kicking the beam transversely. This is called the continuous head-tail method for measuring chromaticity. The complete analytic approximation in terms of trigonometric functions is derived for zero transverse emittance beam. A simple formula for calculating chromaticity from experimental data is also shown. Finally, the theory is compared with experimental data.