RF undulator field and ion beam acceleration in linac

The possibility of using radiofrequency undulator fields for ion beam focusing and acceleration in a linac is discussed. In the periodic structure, we consider it has no space harmonics in synchronism with the beam. The accelerating force is produced by the combination of two or more space harmonics of the RF undulator field. The particle motion equations in Hamilton´s form are devised by means of a smooth approximation. The analysis of the 3D effective potential permits one to find the conditions under which focusing and acceleration of the particles occur simultaneously. Examples illustrating the efficiency of the proposed method of acceleration are given for longitudinal and transverse undulators. The results are compared with a conventional linac and the other possibility of ion beam acceleration in UNDULAC-E(M) where electrostatic and magnetic fields are used