Tune variation and transverse displacement as a diagnostic for profiling beam energy

Abstract

In this paper we describe two methods that demonstrate an energy evolution at the ends of a long bunch. The first method is a nondestructive diagnostic that extends the response matrix technique, to provide insight into the time-sliced transverse behavior of a coasting bunch in a ring. This method uncovers intense beam physics from the resulting longitudinal energy variations at the ends of a rectangular bunch. Measurements of the tune profile, using this method, agree with analytical predictions resulting in a percent error of 0.32% and 2.45% (head and tail respectively). Measurements and calculations presented in this paper are presented for a beam with an intensity of 0.901 (beam current of 21 mA). The head and the tail tunes, averaged over four ring chambers, also illustrate the intensity variation axially along the bunch. This is exhibited through tune-shift measurements at the ends of the bunch. As confirmed through calculations, the measured tune shift at the head is smaller than the tail. This results from the sum of both the transverse coherent tune shift from image forces with the component from longitudinal space charge. The sum of the two components produces a smaller tune shift at the head of the beam and a larger tune shift at the tail. The second method presented in this paper optically illustrates the centroid “cork-screwing” motion within the beam ends, at a single location on the ring. The motion is resolvable using this diagnostic since it is capable of axially time-slicing regions of the beam with different energies. The difference between the two methods presented is that the first is a nondestructive diagnostic that can be extended to multiple turns whereas the second method is a destructive first turn imager.