the situation of the Kerr black-hole uniqueness proofs, since in these proofs very strong symmetry requirements are made, which are inconsistent with the generic condition: The generators of the Kerr event horizon, for example, never feel tidal forces. However, the black-hole uniqueness theorems are frequently used to argue that the final black-hole state is of Kerr type; the symmetry requirements are then not expected to hold exactly for all time, just approximately in the limit of a long time after the black hole formation. In this actual physical case the generic condition does hold, for the reasons given on page 101 of HE. Thus Theorem 2 tells us that although there may be nonsingular causality-violating black-hole solutions, they would have to satisfy strong symmetry requirements exactly over their entire history. In other words, the existence of CTL would be an unstable property of black holes. Hence, no physically realistic, causality-violating, nonsingular black-hole solutions exist.

The behavior of standing wave accelerator tanks, made up of chains of resonant cavities, is investigated using a coupled resonator model. This model gives accurate predictions of the behavior of such a cavity chain, including tolerances to errors in manufacture, cavity feed distributions, and transient response. The parameters necessary in the theory, the cavity couplings, Q's, and frequencies, may easily be determined by experiment. Extension of the simple chain to a more complex chain with double periodicity and second nearest neighbor coupling is demonstrated. Advantages of operating such accelerators in the π/2 mode are shown.

The design and operation of resonant linear accelerator tanks suitable for use in high energy proton and electron linacs is described. It is shown that construction of these tanks to operate in the π/2 mode yields systems with extraordinary field stability. Theoretical expressions and corresponding experimental observations are obtained for the behavior of cavity chains operating in the π/2 mode. The synthesis of the side coupled cavity chain, a biperiodic chain which combines high acceleration efficiency with π/2 mode field stability, is described. Extensions of π/2 mode operation to nonperiodic chains is also demonstrated.

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