Particle transverse autophasing in weak focusing linear accelerators

The transverse autophasing conditions in high-energy linear accelerators with weakly focusing lattice have been studied. A solution has been developed which does not require an additional correlated energy spread in the beam along the linear accelerator. The main features of the solution are that the focusing lattice is not scaled along the linac and the autophasing regime is provided only by initial correlated energy spread. The matching of the amplitudes of dispersive and wakefield terms (the autophasing regime) in equation of motion is accomplished by accelerating the bunch behind the crest of the radio-frequency wave at the low-energy part of the linac. The analytical study is confirmed by particle tracking simulations in TeV Energy Superconducting Linear Accelerator (TESLA).