Electromagnetic wave amplification in free electron lasers with a reversed guide field and a right-hand polarized wiggler field is considered both analytically and numerically. Electron bunch trapping by the high frequency electromagnetic field is used for efficiency optimization. Based on motion stability criteria, the possibility of bunch trapping by tapering the FEL parameters is shown. For this purpose any of the FEL parameters, such as the spatial periodicity of the wiggler or the electromagnetic wave, or the strength of the wiggler or guide field may be tapered. The stability analysis of the electron motion is based on Lyapunov theory, permitting the determination of the optimum tapering rate. A particle simulation was carried out for an FEL with a reversed guide field with only the wiggler field tapered. It was found that under the theoretically predicted tapering all electrons of the beam were trapped and it was possible to achieve as high an efficiency as allowed by the FEL mechanism. The interaction region lengthens in this case but is still experimentally realizable, In particular, for FEL parameters close to experimental ones (relativistic factor gamma = 4.75, wiggler field strength B-w = 2.8 kG, guide field strength B-0 = - 1.4 kG, operation wavelength lambda = 6.2 mm), it was found that the efficiency grew to over 50%, compared with about 20% efficiency in the homogeneous wiggler field case.
