Electron orbits in combined rotating quadrupole and dipole magnetic fields

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Abstract
The single-particle trajectories of relativistic electrons in a magnetic field configuration which consist of a periodic wiggler field produced by a helical winding of two wires (‘‘dipole’’ magnetic field) superimposed on a helical winding of four wires (continuously rotating ‘‘quadrupole’’ magnetic field) are studied. The orbit equations can be reduced to a system of linear, inhomogeneous differential equations for variables related to transverse velocities. These equations are solved exactly and the stability region for the electron orbits in wide range of the parameters is obtained.