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This paper investigates the antenna waveguide (launcher), the main component of the quasi-optical mode converter of a 2-MW 170-GHz TE34,19 coaxial cavity gyrotron, which is under development within the European Union. For coaxial gyrotrons operating in very high-order cavity modes like the TE34,19, due to the ratio of the caustic to cavity radius of 0.323, the transformation of the high-order cavity mode into a nearly Gaussian distribution cannot be done as good as for gyrotron modes where the ratio of caustic to cavity radius is approximately 0.5. The simulation results for the TE34,19 mode show that the average and peak values of the power density at the edges of the cuts of a conventional dimpled-wall launcher are approximately 32.3 W/cm2 and 63.8, respectively, which will produce diffraction losses and reflection of power from the cuts. This paper reports on an advanced launcher for which average and peak values of power density of 1.9 and 5.4 W/cm2 at the edges of the cuts are achieved, and a well-focused field at the aperture with a scalar Gaussian mode content of 94.8% is obtained.