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In this paper, we study the nonlinear evolution of a quadrupole wiggler free electron laser, in the presence of a helical wiggler, which increases adiabatically from zero to a constant level. To focus the electron beam, we apply an axial magnetic field. By using Maxwell equations and Lorentz force equation of motion for electrons, a set of coupled nonlinear equation is derived and solved numerically. The beam is cold and propagates with a relativistic velocity. Results are compared with dipole wiggler FEL.
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