  In this paper, we use an envelope equation-based approach to obtain
analytical scaling laws for the shortest pulse length achievable using
radiofrequency (RF) based bunch compression. The derived formulas elucidate the
dependencies on the electron beam energy and beam charge and reveal how to
obtain bunches containing 1 million electrons with single-digit fs pulse
lengths; relativistic energies are strongly desirable. The effect of the
non-linearities associated with the RF curvature and the beam propagation in a
drift is shown to strongly limit the attainability of extreme compression
ratios. Using an additional higher frequency RF cavity is proposed as a method
to linearize the bunch compression and enable the generation of ultrashort
beams in the sub-femtosecond regime.
