The high-frequency electromagnetic field generated by a density-modulated, helical electron beam propagating in a magnetized plasma is calculated. The magnetic fluctuations are found to exhibit spatially localized ~evanescent! resonances at harmonics of the electron-cyclotron frequency, whose width is determined by the pitch angle of the beam, and whose existence is a consequence of the helical geometry. In addition, electrostatic modes are radiated near the hybrid frequencies, and electromagnetic modes are radiated above the upper-hybrid frequency. The predicted frequency spectrum and mode structure in configuration space are in good agreement with experimental observations of discrete emission lines at the electron-cyclotron harmonics.