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We present a design methodology for developing ultrasmall electron injectors and accelerators based on cascaded cavities excited by short multicycle THz pulses obtained from laser-driven THz generation schemes. Based on the developed concept for optimal coupling of the THz pulse, a THz electron injector and two accelerating stages are designed. The designed electron gun consists of a four cell cavity operating at 300 GHz and a door-knob waveguide to coaxial coupler. Moreover, special designs are proposed to mitigate the problem of thermal heat flow and induced mechanical stress to achieve a stable device. We demonstrated a gun based on cascaded cavities that is powered by only 1.1 mJ of THz energy in 300 cycles to accelerate electron bunches up to 250 keV. An additional two linac sections can be added with five and four cell cavities both operating at 300 GHz boosting the bunch energy up to 1.2 MeV using a 4-mJ THz pulse

THz cavities and injectors for compact electron acceleration using laser-driven THz sources