The beam-wave interaction length is one of the key issues in designing THz extended interaction klystrons (EIKs). Four types of 0.65 THz EIKs with input and output cavities operating in $2 \pi$ -mode are analyzed. The first type with three $2\pi$ -mode idler cavities; the second type with three $\pi$ - mode idler cavities; the third type with two $2\pi$ -mode idler cavities and a feedback; the last type with two $\pi$ -mode idler cavities and a feedback. The particle-in-cell (PIC) results show that the output power is 1.125 W, 1.116W, 0.845 W and 0.813 W under input power of 1 mW and an ideal beam of 25.3 kV and 20 mA. The interaction lengths of four type EIKs are 25.61 mm, 21.11 mm, 16.65mm and 13.87 mm, respectively.