An operator of the permittivity can completely describe alone a microwave response of conductors with the spatial dispersion. A wave problem is formulated to search the eigenvalues of the permittivity operator, similar to the problem of the wave propagation in hollow waveguides and resonators, but non-self conjugated. Dispersion relations and general solutions are obtained. A significant role of the spatial-type force resonances is considered. Due to the self-consistency of a kinetics problem, the spatialtype force resonances are added to and usually dominate over the influence of boundary conditions. The obtained resonances include particular solutions corresponding to the surface impedances for the anomalous skin effect, for superconductors, as well as four novel solutions. The general frequency dependence of the surface impedance is derived for all solutions except that for a superconductor.

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At the present time, there are about 40 thousand particle accelerators in the world. The present review article describes their role in various realms of human activities, including industry, fundamental science, and medicine. Data presented in various sources, such as scientific articles and reports and International Atomic Energy Agency (IAEA) publications, over the past fifty years are analyzed. Emphasis is placed on the importance of nuclear-physics methods for medicine.

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