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, πππ10(π/πππππππ) (πππππππ= 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).