Abstract: The effects of the beam thickness and the conducting wall in a free electron laser with a linearly polarized wiggle magnetic field and an axial magnetic field are investigated within the framework of fluid-Maxwell equations. The growth rate of free electron laser instability is obtained, in which the nonlinear volume and surface current density are simultaneously considered. The numerical calculations indicate that the volume coupling is dominant. There is a particular value of the beam thickness and the separation between the conducting wall and the beam for which the growth rate becomes maximum.