Evolution of dense spatially modulated electron bunches

An analytical theory describing the dynamics of relativistic moving 1D electron pulses (layers) with the density modulation affected by a space charge has been revised and generalized for its application to the formation of dense picosecond bunches from linear accelerators with laser-driven photo injectors, and its good agreement with General Particle Tracer simulations has been demonstrated. Evolution of quasi-one-dimensional bunches (disks), for which the derived formulas predict longitudinal expansion, is compared with that for thin and long electron cylinders (threads), for which the excitation of non-linear waves with density spikes was found earlier by Musumeci et al. [Phys. Rev. Lett. 106(18), 184801 (2011)] and Musumeci et al. [Phys. Rev. Spec. Top. - Accel. Beams 16(10), 100701 (2013)]. Both types of bunches can be used for efficiency enhancement of THz sources based on the Doppler frequency up-shifted coherent spontaneous radiation of electrons. Despite the strong Coulomb repulsion, the periodicity of a preliminary modulation in dense 1D layers persists during their expansion in the most interesting case of a relatively small change in particle energy. However, the period of modulation increases and its amplitude decreases in time. In the case of a large change in electron energy, the uniformity of periodicity is broken due to different relativistic changes in longitudinal scales along the bunch: the "period" of modulation decreases and its amplitude increases from the rear to the front boundary. Nevertheless, the use of relatively long electron bunches with a proper preliminary spatial modulation of density can provide a significantly higher power and a narrower spectrum of coherent spontaneous radiation of dense bunches than in the case of initially short single bunches with the same charge.