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A premodulated electron beam on slow wave free electron laser (FEL) offers considerable enhancement in growth rate and efficiency when a guide magnetic field is used in the FEL device. A nonlocal theory of this process has been developed. The growth rate, efficiency and gain were evaluated based on experimentally known parameters relevant to slow wave free electron laser. It was found that the growth rate, efficiency and gain of the slow wave FEL increases with the modulation index Delta and has the largest value when the modulation index approaching unity in addition to the frequency and wave number of the premodulated beam are comparable to that of the radiation wave, i.e., omega0 ~ omega1 and k 0 ~ k 1. When the slow wave FEL has a guide magnetic field Bs, the transverse electron quiver velocity is enhanced via cyclotron resonance. This leads to a reduction in beam parallel velocity and reduction in radiation frequency omega1. The growth rate of the slow wave FEL instability decreases monotonically with the radiation frequency. Nonlocal effects reduce the growth rate of the slow wave FEL instability. The scheme seems to work well at millimeter and sub-millimeter wavelengths.