Radial dependence of the self-magnetic field in a free-electron laser

The self-magnetic field due to wiggler-induced transversal velocity in a free-electron laser (FEL) has not attained accuracy so far. This self-field has gained constant expression in recent studies. However, to get a precise result, a self-magnetic field's variation by radial coordination (r) must be considered. In the current study, the calculation of self-magnetic field due to wiggler-induced transverse velocity in an FEL with a helical wiggler and axial magnetic field is presented with consideration of self field's variation by r. This calculation is performed using the Frobenius series method. Results showed that the self-magnetic field has a diamagnetic effect for group I and a paramagnetic effect for group II.