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Mode interactions in coaxial gyrotrons are studied numerically using the Maryland gyrotron code (MAGY), which has recently been modified to treat coaxial structures. Simulations are focused on the study of the FZK 170 GHz coaxial gyrotron. This device is being considered for electron cyclotron plasma heating in International Thermonuclear Experimental Reactor; however, current performance is below expectations based on previous simulations. The mode competition process during the voltage rise includes at least six modes in two groups (corotating and counterrotating with an electron beam). Simulations show that the sequence of modes achieving a measurable level of output power during start-up depends on several electron beam parameters: voltage, current, beam radius, beam thickness, pitch angle, and spread in transverse velocity. MAGY simulations made with nominal parameters confirm the results of previous simulations. Two beam parameters are not well characterized: pitch angle and spread in transverse velocity. We found that the measured results are consistent with a decrease in the pitch angle and a 3% transverse velocity spread. Also, the effect of modes at the cyclotron harmonic on the fundamental cyclotron harmonic modes is studied and discussed.