CST – Computer Simulation Technology

Simulation of Cold-Test Parameters for Slow-Wave Structure using Eigenmode Solver

Cold-test parameters of a slow-wave structure can be obtained using CST MICROWAVE STUDIO® (CST MWS) Eigenmode solver without considering the input and output couplers. As depicted in Fig. 1, a single period helical slow-wave structure is simulated in the Eigenmode solver with periodic boundary defined in the longitudinal direction (z-axis).

Figure 1: Geometry of a single period circular helix

The single period helix is extended periodically and infinitely in the longitudinal direction. The phase shift of the periodic boundary, which is corresponding to the phase constant, β, can be defined in the ‘Phase Shift/Scan Angles’ property page. The number of modes to be calculated can be specified in the Eigenmode solver setting. For each eigenmode, the field distribution of the mode and the corresponding eigenfrequency can be obtained. Figure 2 shows the field distributions for the fundamental mode....

figure2a Figure 2a
Figure 2b figure2c
Figure 2c

Figure 2: Field distribution of the circular helix: (a) E field, (b) H field, and (c) surface current for the fundamental mode

The phase shift of the periodic boundary is defined as a parameter and sweeping of this parameter was performed from 5- to 175-degree with a step size of ten degrees. Template based post-processing can be defined to obtain several cold-test parameters such as phase constant, normalized phase velocity, normalized group velocity and power-flow. These results are shown in Figure 3. An application note on obtaining cold-test parameters using Eigenmode solver is available on the CST support website [1].

Figure 3a
Figure 3b Figure 3c Figure 3d Figure 3: Cold-test parameters obtained from parameter sweep of the phase. (a) phase constant, (b) normalized phase velocity, (c) normalized group velocity, and (d) power-flow. (x-axis: Frequency in GHz)

Interaction impedance is an important parameter for slow-wave structure design as it directly affects the gain of a traveling wave tube. In this example, the interaction impedance is obtained directly by evaluating the following formula through the template based post-processing:

where Ez,n(0) is the on-axis longitudinal electric field magnitude of the nth space harmonic; βn is the axial phase constant of the nth space harmonic; P is the power flow through the structure. Ez,n(0) can be obtained by performing Fourier analysis on the total on-axis axial electric field:

where βn can be obtained from:

where β is the fundamental axial phase constant and L is the helix pitch. The on-axis phase constant, βn, electric field, Ez,n(0), and interaction impedance, kn, for the fundamental and the non-fundamental space harmonics (n= 1, 0, and -1) are shown in Figure 4. The space harmonics at different off-axis positions [2] can be obtained by simply modifying the evaluation location of the E-field in the post-processing.

Figure 4a Figure 4b Figure 4c Figure 4: Fundamental and higher order space harmonics analysis for (a) phase constant, (b) axial electric field and (c) interaction impedance. (x-axis: Frequency in GHz)


[1] CST Application Note: “Slow Wave Structure Postprocessing (#3359),” CST Knowledge Base.

[2] Ajith Kumar M.M., S. Aditya, and C. Chua, “Interaction impedance for space harmonics of circular helix using simulations,” IEEE Trans. Electron Devices, vol. 64, no. 4, pp. 1868-1872, Apl. 2017.

Rate this Article

4.5 of 5 Stars
5 Stars
4 Stars
3 Stars
2 Stars
1 Stars
contact support

Your session has expired. Redirecting you to the login page...

We use cookie to operate this website, improve its usability, personalize your experience, and track visits. By continuing to use this site, you are consenting to use of cookies. You have the possibility to manage the parameters and choose whether to accept certain cookies while on the site. For more information, please read our updated privacy policy

Cookie Management

When you browse our website, cookies are enabled by default and data may be read or stored locally on your device. You can set your preferences below:

Functional cookies

These cookies enable additional functionality like saving preferences, allowing social interactions and analyzing usage for site optimization.

Advertising cookies

These cookies enable us and third parties to serve ads that are relevant to your interests.