Transverse beam echoes can be excited with a single dipole kick followed by a single quadrupole kick. They have been used to measure diffusion in hadron beams and have other diagnostic capabilities. Here we develop theories of the transverse echo nonlinear in both the dipole and quadrupole kick strengths. The theories predict the maximum echo amplitudes and the optimum strength parameters. We find that the echo amplitude increases with smaller beam emittance and the asymptotic echo amplitude can exceed half the initial dipole kick amplitude. We show that multiple echoes can be observed provided the dipole kick is large enough. The spectrum of the echo pulse can be used to determine the nonlinear detuning parameter with small amplitude dipole kicks. Simulations are performed to check the theoretical predictions. In the useful ranges of dipole and quadrupole strengths, they are shown to be in reasonable agreement.

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An improved mathematical model was developed to design a continuous sterilizer for liquid fermentation media containing suspended solids. Unsteady-state energy balances were used to determine the temperature distribution in the liquid medium and in the solid particles as a function of time and position within the particle, as the medium flows through the sterilizer. Such temperature profiles were used to determine the level of microbial reduction achieved by each component of the sterilizer and by the entire sterilization process. A considerable difference exists between the temperature in the particle core and in the surrounding liquid. This has a significant impact on the degree of sterility achieved by the process. The level of microbial reduction in the particles was found to be tens and or even hundreds of order of magnitude lower than the corresponding level achieved in the liquid. The role of the particle material on the degree of sterilization was also investigated. Solid materials typically found in fermentation media, such as wood or flour clumps were found to offer considerable resistance to the sterilization of the organisms lodged inside them.