[en] Two types of thin septum magnets, direct drive and eddy current, were compared mainly in 2-D magnetic aspects. For the direct-drive type, the leakage field depended on the finite permeability of the magnet core and not on the thickness of the septum conductor. It was suggested that the leakage field be controlled by reducing the current in the septum conductor or by using a correction coil. There were no significant differences between the two types regarding thermal problems caused by high current densities in the thin septa. The leakage fields with 2-mm septum thicknesses were calculated using OPERA-2d to compare the two types. For the eddy-current type, the leakage fields calculated using OPERA-2d were compared with the calculations from Halbach's model. The leakage fields for the eddy-current type decayed with long time constants

[en] 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 δ, 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 << δ

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[en] Configuration of four-button beam position monitors (BPMs) employed in small-gap beam chambers is optimized from 2-D electrostatic calculation of induced charges on the button electrodes. The calculation shows that for a narrow chamber of width/height (2w/2h) >> 1, over 90% of the induced charges are distributed within a distance of 2h from the charged beam position in the direction of the chamber width. The most efficient configuration for a four-button BPM is to have a button diameter of (2-2.5) h with no button offset from the beam. The button sensitivities in this case are maximized and have good linearity with respect to the beam positions in the horizontal and vertical directions. The button sensitivities and beam coefficients are also calculated for the 8-mm and 5-mm chambers used in the insertion device straight sections of the 7-GeV Advanced Photon Source

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[en] Time-varying magnetic fields of magnets in booster accelerators induce substantial eddy currents in the vacuum chambers. The eddy currents in turn act to produce various multipole fields that act on the beam. These fields must be taken into account when doing a lattice design. In the APS booster, the relatively long dipole magnets (3 meters) are linearly ramped to accelerate the injected 325 MeV beam to 7 GeV. Substantial dipole and sextupole fields are generated in the elliptical vacuum chamber from the induced eddy currents. In this note, formulas for the induced dipole and sextupole fields are derived for elliptical and rectangular vacuum chambers for a time-varying dipole field. A discussion is given on how to generalize this derivation method to include eddy-current-induced multipole fields from higher multipole magnets (quadrupole, sextupole, etc.). Finally, transient effects are considered

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