Beam-shape distortion caused by transverse wake fields

As a particle bunch in a storage ring passes through a region with a transverse impedance, it generates a transverse wake electromagnetic field that is proportional to the transverse displacement of the bunch in the region. The field acts back on the bunch, causing various effects (such as instabilities) in the motion of the bunch. We study one such effect in which a transverse impedance causes the beam to be distorted in its shape. Observed at a fixed location in the storage ring, this distortion does not change from turn to turn; rather, the distortion is static in time. To describe the distortion, the bunch is considered to be divided longitudinally into many slices and the centers of change of the slices are connected into a curve. In the absence of transverse impedance, this curve is a straight line parallel to the direction of motion of the bunch. Perturbed by the transverse wake field, the curve becomes distorted. What we find in this paper is the shape of such a curve. The results obtained are applied to the PEP storage ring. The impedance is assumed to come solely from the rf cavities. We find that the beam shape is sufficiently distorted and hence that loss of luminosity due to this effect becomes a possibility