| Incoherent synchrotron radiation from a relativistic electron beam circulating in the magnetic field configuration of the NRL modified betatron accelerator has been studied numerically and experimentally. Numerical studies show that, for relativistic electron energies up to approximately 2 MeV, the single particle spectrum of radiation is dominated by a peak in the intensity distribution at the Doppler-shifted cyclotron frequency about the toroidal field. This intensity distribution very closely approximates the distribution for a linear helical electron trajectory with relativistic velocity along the axis of the helix. The radiated electric field oscillations, however, are 'modulated' due to the curvature of the major radius. As the electrons accelerate above an energy of a few MeV, the modulation width becomes so narrow that even the fast gyro-oscillation about the toroidal field produces no significant variation in the total radiated fields. Thus, the amplitude, polarization, and frequency content in the spectrum approaches that of a purely circular orbit.; Experimental studies of the radiation have been conducted by monitoring the temporal evolution of radiated power during acceleration using fixed-frequency heterodyne receivers. Radiation was measured for electron beam energies in the range of 0.5 MeV to about 10 MeV, trapped beam currents up to approximately 500 A, and for values of toroidal guide field in the range of approximately 1900 to 3500 Gauss. At electron energies less than about 2 MeV, the polarization, amplitude, scaling with trapped beam current, and the temporal evolution of measured radiation during acceleration are in very good agreement with the predicted single particle spectrum. Furthermore, there is no evidence of collective emission at least within the frequency ranges 8 to 12 GHz and 26 to 40 GHz.; The only significant discrepancy between the experimental and predicted results is the apparent absence of the horizontally polarized radiation which is expected to dominate at energies above 2 to 3 MeV. The discrepancy is most likely due to the continuous loss of electrons resulting from beam expansion or the displacement of the beam centroid from the minor axis. |
