Two designs of Ka-band 34.2 GHz three-cavity coaxial gyroklystrons that might be applied to driving high gradient linear accelerators are presented. The input, buncher and output cavities operate in the TE_(011), TE_(021) and TE_(041) modes, respectively. The buncher cavity doubles the signal frequency and the output cavity quadruples it. The electron beam current of 540 A and voltage of 460 kV are used in both designs. The simulations show that for the first design, a maximum efficiency of 15%, a maximum gain of 31 dB and a bandwidth of 1 MHz can be realized for an orbital-to-axial velocity ratio at the entrance to the microwave circuit of α_0=1.6. The efficiency and gain for the second design are 16.3% and 42.1 dB, respectively, at α_0 = 1.3; but the bandwidth is reduced to 600 kHz. For both designs the output cavity is zero-drive unstable.
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