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High levels of coherent current and energy oscillations appeared on an intense relativistic electron beam traversing a smooth drift tube in which two or more coaxial cavities were inserted. The frequency of oscillation depended strongly on the geometry of the drift region but only weakly on beam current and voltage. The frequency spectrum of modulation was monochromatic. By changing geometry, frequencies of up to 3 GHz were observed. Relativistic electron beams with voltages varying from 0.25 to 1 MeV and currents from 1 to 8 kA were modulated with efficiencies approaching 100%. The structure of the electron bunches was tailored by changes in the geometry. Both theory and particle simulation show that the presence of the cavities along the drift tube altered the simple streaming motion of the beam in a smooth drift tube resulting in a highly nonlinear beam behavior. The complex beam dynamics was governed by formation of virtual cathodes, reflexing electrons, and autoacceleration. Shaped electron bunches have many applications in collective acceleration, high power microwave production, and plasma heating.