Tailored Vacuum Chambers for AC Magnets
The proposed LAMPF-II accelerator has a 60-Hz booster synchrotron and a 3-Hz main ring. To provide a vacuum enclosure inside the magnets with low eddy-current losses and minimal field distortion, yet capable of carrying rf image currents and providing beam stabilization, we propose an innovative combination pipe. Structurally, the enclosure is high-purity alumina ceramic, which is strong, radiation resistant, and has good vacuum properties. Applied to the chamber are thin, spaced, silver conductors using adapted thick-film technology. The conductor design can be tailored to the stabilization requirements, for example, longitudinal conductors for image currents, circumferential for transverse stabilization. The inside of the chamber has a thin, resistive coating to avoid charge build-up. The overall 60-Hz power loss is less than 100 W/m.
Bench Measurements of the Energy Loss of a Stored Beam to Vacuum Components
Since 1975 measurements of higher order mode losses have been carried out at DESY. The method in use had been proposed by J. Rees and M. Sands): Short current pulses (2 ¿ = 100 psec) on a thin coaxial wire simulate a relativistic particle bunch. Changes in the bunch shape allow the determination of energy losses due to higher mode excitation. Measurements on simple cavity structures agree well with calculations. Results for a large variety of vacuum structures in the PETRA storage ring are given including structures, the losses of which can no longer be easily calculated. For these structures the results of the measurements described here are the only source of information for improvements.
Explicit solutions for N-dimensional Schrödinger equations with position-dependent mass
With the consideration of spherical symmetry for the potential and mass function, one-dimensional solutions of nonrelativistic Schrodinger equations with spatially varying effective mass are successfully extended to arbitrary dimensions within the frame of recently developed elegant nonperturbative technique, where the BenDaniel-Duke effective Hamiltonian in one dimension is assumed like the unperturbed piece, leading to well-known solutions, whereas the modification term due to possible use of other effective Hamiltonians in one dimension and, together with the corrections coming from the treatments in higher dimensions, are considered as an additional term like the perturbation. Application of the model and its generalization for the completeness are discussed.