Linear dynamics of charged particles in the main lattices of storage rings

To study the characteristics of synchrotron radiation in magnetic fields of accelerators first the author was necessary to obtain a continuous solutions of Hill’s equation. For this purpose the gradient or the components of magnetic field were developed in a series. The same procedure is followed now in the case of storage rings. This approach proved to be interesting not only from the point of view of describing the motion of partiles in ordinary three-dimensional space but also in the fact that we get new differential equations. This brief review can be regarded as an introduction to the proposed method. The next step may be to add nonlinearities. This would be the best approximation to the determination of betatron oscillations in the existing accelerators.