Abstract
A linear theory of generalized circular free electron lasers (FEL) is presented. A relativistic electron beam rotates azimuthally under an axial magnetic field and/or a radial electric field, superimposed by an azimuthally periodic wiggler magnetic field in the radial direction. The characteristics of these circular FELs depend largely on the effective azimuthal inertia of the equilibrium circular motion. The electric field type, in which only a radial electric field force is applied to balance the centrifugal force, has the maximum growth rate among circular FELs. The growth rate of the magnetic field type, in which only an axial magnetic field is applied, is as high as that of the electric field for highly relativistic cases. In these two types, the weak pump regime found in conventional linear FELs is replaced by a negative mass instability regime. The crossed field type, in which both fields are applied to balance the centrifugal force, has a very small growth rate for highly relativistic cases.
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