CST Studio Suite® can provide accurate simulations of cavity parameters. We have performed simulations on a simple pillbox to verify the simulation results and compare them with analytical and those of Superfish simulation code. First, the following points might be interesting:
Use of symmetry axes
In CSR, each symmetry axis reduces the calculation domain in half. But in order to use the symmetry axes, one must enter the full geometry first. It should be noted that depending on the symmetry plane, some modes are not possible, so these should be chosen with care.
Eigenfrequency and Q
In the eignemode solver, it is convenient to carve away the geometry from within the background which is made of perfectly electrical conductor PEC, instead of creating a positvie geometry. In the post processing step, the PEC is considered as copper for loss calculations. One can choose how many modes the solver should calculate, using the meshing scheme. The eigenfrequencies will be calculated.
Simulation of Rs/Q
The characteristic impedance (sometimes called the geometric factor) Rs/Q can be calculated in the post processor form 2D and 3D fields results → 3D Eigenmode Result. In the menu the direction and length of integration can be entered, whereas either maximum longitudinal extension or a section can be specified. Like in Superfish, CST uses the following definition for the calculation of the shunt impedance and Rs/Q $$R_s=\dfrac{U^2}{P_L}$$
The effect of the transit time factor TTF can be turned off resulting in the so called frozen shunt impedance, which is more suitable for comparison with bench-top measurements. This option is called “consider particle velocity”
By fixing the direction of integration path, but changing the transversal offset, one can calculate the longitudinal Rs/Q for each transversal position. To achieve this, a post processing rule must be added manually for each point, say e.g. for every 5 mm.
Update 2019
The newest version of CST allows parameter sweeping in the schematic section. First create the cavity in the 3D model, then click on the schematics. In the schematics create a new variable, then add a new task “Block”. Inside “Block” you choose project type “High Frequency” and Solver type “Eigenmode”. Then you add a second task which is a sweep task for the variable, and inside the sweep task, put the template based post processing inside of the sweep loop.
Power loss and Energy
The values of power loss and total stored energy are scaled such that the total energy is 1 Joule. Considering the relationship of Q value the power loss is scaled accordingly.
Length and size of the beam pipe
The beam pipes should in principle not contribute to the overall impedance of the cavity, so beam pipes can be omitted in the simulation. While this is true for beam pipes with small radii, larger beam pipes affect the whole cavity geometry in a way, that fields extend into the pipe region. So the value of Rs/Q or shunt impedance will not be accurate if calculated over the whole longitudinal extension of the design.
The field extension can be plotted in the post processor 2D and 3D fields results → Evaluate field in arbitrary coordinates. The value at the FWHM of this curve can be used as a starting point for the calculation of the impedance integrals. In order to compare the results with bench top measurement (bead pull measurements), also there the value at FWHM can be used.
One last hint for test pillboxes: Although it mostly does, sometimes a very small extension, like 1 or 2 mm is needed to make sure the solver converges.
Comparing transit time factors
In the following we consider a copper pill box resonator with radius 30 cm and depth 9 cm, using PEC (i.e. copper in the post processing) The results which are summarized in the following table, show an extremely agreement. In order to compare the results of MWS and Superfish, it is important to know the differences in the presentation of their results. By sweeping in microwave studio, one can not obtain the transit time factor directly, but needs to divide the resulting R/Q sweep by the R/Q value without transit time factor i.e. $\widehat{R/Q}$. The resulting values are squares of the transit time factor $\Lambda$ since $$R/Q = \widehat{R/Q}*\Lambda^2(\beta)$$
Also in Superfish the excitation fields are normalized on some arbitrary value, while in MWS the resulting electric field energy is normalized to one joule.
| 1st Mode | Analytic | SUPERFISH | CST |
| $f_0$ [MHz] | 382.475 | 382.475 | 382.475 |
| Q | 20310 | 20486 | 20485.7 |
| Rs/Q w.o. TTF | 111 | 111.04 | 110.9 |
| Power Loss [W] | 1.16E+5 | 1.17E+5 | 1.17E+5 |