This manuscript presents a 2 + 2 metamaterial (MTM) transit-time oscillator (TTO) employing coaxial extraction, engineered to leverage the advantages of MTM and TTO. Cold cavity testing was conducted to examine the electromagnetic properties of the MTM resonator, revealing that at least 1/3 of the radial size can be reduced compared to traditional designs. Comparison of various energy extraction techniques has also been conducted, highlighting the effectiveness of coaxial method over other axial schemes. Computational simulations with electron beams, conducted under parameters of 650 kV, 5.36 kA, and 1.2 T magnetic field, yields a 1 GW microwave output at 1.54 GHz, exhibiting a stable, single mode without competition. This MTM integration significantly reduces the diode impedance in high-power microwave devices, resulting in a shorter axial length and achieving GW-level power output. This design suggests a potential step forward for MTM-based high-power microwave sources, offering the possibility of greater power density and compactness, and may contribute to the advancement of MTM applications in electron vacuum technology.
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