Applications of cavity transverse modes in accelerators

Different applications of TE modes in accelerator physics are discussed. In this discussion, the Fourier transform of the squared axial component of magnetic field, B_z²(z), plays an important role. If it turns out to be zero, the rf field-particle energy transfer is negligible and the focal length of the TE mode lens is phase independent. Such rf lens focuses continuous beams just as a solenoid. In order to compensate spherical aberrations and emittance growth caused by field nonlinearities of a focusing solenoid, the rf focusing is used also even if the beam space charge is taken into account. If the transform has its maximum, excitations of TE mode resonances and electron beam self-focusing are possible. Furthermore, the rf field of the TE mode can be used to expand the radial acceptance of a FEL for the THz region.