Calculation of pulsed kicker magnetic field attenuation inside beam chambers.

摘要

The ceramic beam chambers in the sections of the kicker magnets for the beam injection and extraction in the Advanced Photon Source (APS) are made of alumina. The inner surface of the ceramic chamber is coated with a conductive paste. The choice of coating thickness is intended to reduce the shielding of the pulsed kicker magnetic field while containing the electromagnetic fields due to the beam bunches inside the chamber, and minimize the Ohmic heating due to the fields on the chamber [1]. The thin coating generally does not give a uniform surface resistivity for typical dimensions of the ceramic chambers in use. The chamber cross section is a circular or an elliptic shape. The chamber or its wall thickness refers to the conductive coating in the following sections. This note calculates the penetration of the kicker magnetic field inside the beam chamber. The kicker field is assumed to be a half-sine pulse and be spatially uniform over the chamber dimensions. The purpose of the calculation is to be able to deduce the average surface resistivity of a chamber by fitting the measured magnetic field data with the calculation inside the chamber. In the following section, assuming that the coating thickness d is much smaller than the classical skin depth {delta}, the penetrated field inside the chamber is calculated by subtracting the shielding field due to the eddy currents. In Section 3, for the kicker fields parallel and perpendicular to the axis of a circular beam chamber, the fields inside the chamber with an arbitrary wall thickness are calculated. For both directions of the kicker fields, the approximations made for d << {delta} achieve the same results as given in Section 2. For elliptic chambers, the calculations for the vector potentials are not completed because of the tedious approximation procedure with Mathieu functions. Instead, the results in Section 2 and the time constants calculated for the elliptic geometries in Table 1 could be used for the purpose of this note.