We present data from our study of a device known as the inverse free electron laser. First, numerical simulations were performed to optimize the design parameters for an experiment that accelerates electrons in the presence of an undulator by stimulated absorption of radiation. The Columbia free electron laser (FEL) was configured as an auto-accelerator (IFELA) system; high power (MW's) FEL radiation at {approximately}1.65 mm is developed along the first section of an undulator inside a quasi-optical resonator. The electron beam then traverses a second section of undulator where a fraction of the electrons is accelerated by stimulated absorption of the 1.65 mm wavelength power developed in the first undulator section. The second undulator section has very low gain and does not generate power on its own. We have found that as much as 60% of the power generated in the first section can be absorbed in the second section, providing that the initial electron energy is chosen correctly with respect to the parameters chosen for the first and second undulators. An electron momentum spectrometer is used to monitor the distribution of electron energies as the electrons exit the IFELA. We have found; using our experimental parameters, that roughly 10% ofmore » the electrons are accelerated to energies as high as 1100 keV, in accordance with predictions from the numerical model. The appearance of high energy electrons is correlated with the abrupt absorption of millimeter power. The autoaccelerator configuration is used because there is no intense source of coherent power at the 1.65 mm design wavelength other than the FEL.« less