Fig 4 The interaction structure of the designed tube .
The start oscillation length of the competition mode is a consideration in the design of the L1 and L2 sections. Under the condition that the working voltage is 75kV, the radius of the guide center is Rc=0, and the radius of the waveguide is Rw=5.5mm, the variation of the starting length of each mode in the lossless waveguide with the current is shown in Figure 5. When the working current I=9A, the corresponding start length of TE31 and TE41 are 50.2mm and 101.3mm, respectively, so the length of the lossless section L1should be less than 50.2mm. Under the same conditions, the start oscillation length and oscillation frequency of the TE31mode, which has smaller oscillation length than TE41mode, vary with the logarithm of the ratio between the resistivity of the dielectric and of copper, π‘™π‘œπ‘”10(𝜌/πœŒπ‘π‘œπ‘π‘π‘’π‘Ÿ) (πœŒπ‘π‘œπ‘π‘π‘’π‘Ÿ= 1.72e-8 S/m), as shown in Figure 6. According to the resistivity of the dielectric rings in the laboratory, the length of dielectric-loaded section L2, should be less than 271 mm.
The dielectric ring in the interaction structure is made of AlN-SiC ceramics, as shown in Figure 7a. The ceramics has high thermal conductivity of 60 W/m. K and a certain mechanical strength. The loss amount is easy to control by the period number. Its relative permittivity is Ξ΅r=12, the loss tangent tanΞΈ=0.16, and the effect of beam-wave interaction is the best in simulation when the thickness d=1.8mm. Figure 7b shows the loss of ceramics to microwaves in the operating frequency band of working mode TE21, and it can be seen that the actual measured values are close to the simulation values according to the comparison. Figure 8a and 8b only show the simulation results of the loss of the ceramic ring near the start frequency of the competition modes TE31 and TE41, which are also relatively close to the real situation. (TE31 and TE41 mode converters are not prepared).