In this paper, beam-wave interaction analysis in a Ka-band periodically ceramic loaded gyrotron traveling-wave tube (gyro-TWT) amplifier is investigated using particle-in-cell (PIC) simulation. The simulations predict that the interaction structure can produce more than 80-kW output power, 50-dB saturated gain, and 3-dB bandwidth is 2.56 GHz for 65 kV and 5-A electron beam with velocity ratio of 1.2. The dispersion and interaction impedance characteristics of the ceramic-loaded gyro-TWT amplifier are also determined using 3-D simulator CST-microwave studio. This paper describes the design and simulation of a high performance 35-GHz mode gyro-TWT that applies the same technique of employing a periodic dielectric loaded interaction structure to achieve stability and wide bandwidth. The stability of this gyro-amplifier is excellent and demonstrates that the ceramic loading is highly effective for suppressing the spurious oscillations in gyro-TWT.