Reconnection in relativistic electron beams

The nonlinear dynamics of a relativistic, debunched electron beam in a linear accelerator, propagating along the z axis with a relativistic velocity e→zV, immersed in the magnetic field B→ is studied. The total field is conveniently expanded into cylindrical harmonics. In a linear accelerator, the dipolar component is absent, and the largest amplitude is that of the quadrupole, used for the beam focusing by the magnetic lenses, which are periodic along the beam. Also, small monopolar and octupolar components of the total magnetic field, which are homogeneous along the beam are accounted for. The monopolar Biot-Savart's field is produced self-consistently by the beam current, while the octupolar component is partially applied externally to achieve the fine tuning of the magnetic lenses, and a part of it arises accidentally, from the small errors in the quadrupolar coils