The ring cyclotron as a kaon-neutron generator

We examine the status of the existing π-meson facilities and their prospects for development. We discuss the designs of K-meson and neutron facilities. Oh the basis of numerical modeling of the dynamics of the proton with the complete equations of motion on a computer, we establish the slow passage of the integral resonance with respect to the radial betatron oscillations $Q_{R}= 2(~845) MeV in an isochronous ring cyclotron, with the subsequent acceleration to $Q_{R} = 2.3(~1200 MeV). We detect the previously unknown phenomenon of strong postresonance(as opposed to the known adiabatic) damping of the amplitudes of the free radial oscillations of the charged particles perturbed in traversing the integral resonance as the radius of the orbit increases. This damping is due to the drift of the frequency of the radial oscillations from the resonance in the spatially varying magnetic field. The parameters of the ring cyclotron as a generator of kaons and neutrons are given for a proton energy of ~4.2 GeV.