CST

Periodic Eigenmode Simulation of a Travelling Wave Tube

This example demonstrates an eigenmode calculation using periodic boundaries in z-direction. The phase shift of the periodic boundary is defined as a parameter which is swept from 5 degrees to 175 degrees with a step size of ten degrees. CST MWS's Eigenmode solver is ideal for this task.


Geometry reduced to a single helix turn
Figure 1: Geometry reduced to a single helix turn

The frequency range is defined up to 10 GHz. The boundary conditions are set to "electric" except for the two boundary conditions in the z direction, which are defined as "periodic" in order to model the periodicity of the helix. A parameter "phase" is assigned to the periodic boundary, so that the phase shift can be used in a parameter sweep.


E, H fields and surface currents obtained from the periodic eigenmode solution
Figure 2: E, H fields and surface currents obtained from the periodic eigenmode solution

All Fields for periodic phase shift may be plotted as in figure 2 where the E and H Fields are shown.


Dispersion characteristics obtained from parameter sweep of the phase
Figure 3: Dispersion characteristics obtained from parameter sweep of the phase

Figure 3 shows the dispersion curves obtained from the parameter sweep via post-processing templates. The phase velocity is shown here as a function of  frequency. The eigenmode solver delivers any aribitrary number of desired modes, 3 of which are shown in the plot.


Pierce Impedance extracted via template-based post-processing of the parameter sweep results
Figure 4: Pierce Impedance extracted via template-based post-processing of the parameter sweep results

Figure 4 shows the Pierce Impedance obtained as a post-processing step. The powerflow in the tube is also an additional post-processing quantity that may be calculated.


CST Article "Periodic Eigenmode Simulation of a Travelling Wave Tube"
last modified 30. Apr 2013 9:56
printed 4. Aug 2015 1:16, Article ID 123
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