Simulations of axial B-dot monitors inside a groove in the beam pipe

Beam tilt measurement is important for understanding the beam dynamics. Our previous theoretical studies and simulations have shown that the axial B-dot in smooth beam pipe can be used to measure the beam tilt directly. Practical azimuthal B-dot loops typically are placed inside a groove in the beam pipe to avoid direct beam interception. For the same purpose, practical axial B-dot loops should also be placed inside such a groove. In this paper, responses of axial magnetic field to the beam tilt and to the beam offset, in the presence of the groove, are investigated by simulations. The simulation results show that the axial magnetic field in the central plane of the groove is proportional to the beam tilt and independent on the centroid position. The ratio between the axial magnetic field and the beam tilt depends on the position of the axial B-dot loop and the dimensions of the groove.