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  1. The temporal resolution of ultrafast electron diffraction at weakly relativistic beam energies (≲100 keV) suffers from space-charge induced electron pulse broadening. We describe the implementation of a radio frequency (RF) cavity operating in the continuous wave regime to compress high repetition rate electron bunches from a 40.4 kV DC photoinjector for ultrafast electron diffraction applications. Active stabilization of the RF amplitude and phase through a feedback loop based on the demodulated in-phase and quadrature components of the RF signal is demonstrated. This scheme yields 144 ± 19 fs RMS temporal resolution in pump–probe studies. 
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  2. We present 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 relativistic energies are strongly desirable to obtain bunches containing 1 million electrons with single-digit femtosecond pulse lengths. However, the non-linearities associated with the RF curvature and the beam propagation in drift spaces significantly limit the attainability of extreme compression ratios. Therefore, an additional higher frequency RF cavity is implemented, which linearizes the bunch compression, enabling the generation of ultrashort beams in the sub-femtosecond regime. 
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