Focusing effect and modulation mechanism of the beam self-fields on the electronʼs Larmor rotation in a free-electron laser with an axial guide magnetic field

► Beam self-field periodically acts on an electron with off-axis guiding center. ► This periodic varying field modulates the electronʼs Larmor rotation. ► Modulation results in a focusing effect on the e-beam transport at anti-resonance. ► Remarkable focusing effect relies on the beam current parameter.