Chapter 2 – Simulation Workflows¶

CST Studio Suite for Particle Dynamics Simulation is designed for ease of use. However, to get started quickly, you need to know a few things. The main purpose of this chapter is to provide an overview of the software’s capabilities. Read this chapter carefully, as this may be the fastest way to learn how to use the software efficiently.

This chapter covers three different workflow examples for Particle Tracking, Particle in Cell (PIC) and Wakefield computations:

1. Workflow Example: Particle Tracking¶

1.1. Model and simulate a simple electron gun, including a particle simulation (static approximation)
1.2. Parameter studies of the model and automatic optimization of the structure

2. Workflow Example: Electromagnetic Particle in Cell¶

2.1. Model and simulate a simple output cavity

3. Workflow Example: Wakefield¶

3.1. Model and simulate a simple pillbox cavity

Simulation Workflow: Particle Tracking¶

The following example shows, how to set up and run a simple Particle Tracking simulation. Studying this example carefully will allow you to become familiar with many standard operations that are necessary to perform a Particle Tracking simulation within CST Studio Suite. For more information on the physics that can be modelled with the Tracking solver, an overview is provided in Chapter 3 – Solver Overview : Particle Tracking Solver.

Go through the following explanations carefully even if you are not planning to use the software for Particle Tracking simulations. Only a small portion of the example is specific to this particular application type since most of the considerations are general and apply to all solvers and application domains.

At the end of this example, you will find some remarks concerning the differences between the typical simulation procedures for electrostatic and magnetostatic calculations and some useful hints for setting up the Particle Tracking and gun algorithm.

The following explanations always describe the menu-based way to open a particular dialog box or to launch a command. Whenever available, the corresponding toolbar item is displayed next to the command description. Due to the limited space in this manual, the shortest way to activate a particular command (i.e. by pressing a shortcut key or activating the command from the context menu) is omitted. You should regularly open the context menu to check available commands for the currently active mode.

The Structure¶

Usually an electron gun is only one part of a complex device, for example a particle accelerator. The gun is used to create a collimated particle beam, so that other parts of the device are supplied with a beam of good quality.

The way this gun works is quite simple. Electrons are emitted from a cathode by a particle source based on space charge limited emission. These particles are accelerated and focused by an anode. Additional focusing is realized by a set of magnets behind the anode.

The following picture shows the structure of interest. It has been sliced open to aid visualization. Anode and cathode consist of perfect electrical conductor (PEC) material whereas the magnetic structure above the anode consists of iron and permanent magnets.

Before you start modeling the structure, let us spend a few moments discussing how to describe this structure efficiently.

In the CST Studio Suite, the user can define the properties of the background material. Anything you do not fill with a particular material will automatically be filled with the background material. For this structure it is sufficient to model anode, cathode, two iron discs and three permanent magnets of the electron gun. The background properties will be set to vacuum.

Your method of describing the structure should therefore be as follows:

1. Model cathode and anode of the electron gun.
2. Model the two iron discs.
3. Model the three permanent magnets.

Create a New Project¶

After launching the CST Studio Suite, you will enter the start screen showing you a list of recently opened projects and allowing you to select the application that best suits your requirements. The easiest way to get started is to configure a project template, which defines the basic settings that are important for your typical application. Therefore, click on the New Template button in the New Project from Template section within the New and Recent tab.

Next, you should choose the application area, Particle Dynamics for the example in this tutorial, and then select the workflow by double-clicking on the corresponding entry.

graph LR
  A["Static / Low Frequency"] --> B["Microwaves & RF/OPTICAL"]
  B --> C["EDA/Electronics"]
  C --> D["EMC/EMI"]
  D --> E["Particle Dynamics"]
  E --> F["Static Dynamics"]

For the electron gun, please select Vacuum Electronic Devices Particle Gun Particle Tracking .

Finally, you are requested to select the units that best fit your application. For this example, please select the dimensions as follows:

For the specific application in this tutorial the other settings can be left unchanged. After clicking the Next button, you can specify a name for the project template and review a summary of your initial settings:

Finally, click the Finish button to save the project template and to create a new project with the respective settings. CST Studio Suite for Particle Dynamics Simulation will be launched automatically due to the choice of this specific project template within the application area Particle Dynamics.

Please note: When you click again on the File: New and Recent you will see that the recently defined template appears below the Project Templates section. For further projects in the same application area you can simply click on this template entry to launch CST Studio Suite for Particle Dynamics Simulation with useful basic settings. It is not necessary to define a new template each time. You are now able to start the software with reasonable initial settings quickly with just one click on the corresponding template.

Please note: All settings made for a project template can be modified later during the construction of your model. For example, the units can be modified in the units dialog box (Home: Settings Units ) and the solver type can be selected via the Home: Simulation Setup Solver drop-down list.

Open the Tracking QuickStart Guide¶

An interesting feature of the online help system is the QuickStart Guide, an electronic assistant that will guide you through your simulation. If it does not show up automatically, you can open this assistant by selecting QuickStart Guide from the dropdown list next to the Help button in the upper right corner.

The following dialog box should then be visible at the upper right corner of the main view:

As the project template has already set the solver type, units, background material and boundary conditions, the Particle Tracking Analysis is preselected and some entries are marked as done. The blue arrow always indicates the next step necessary for your problem definition. You do not have to follow the steps in this order, but we recommend to follow this guide at the beginning to ensure that all necessary steps have been completed.

Look at the dialog box as you follow the various steps in this example. You may close the assistant at any time. Even if you re-open the window later, it will always indicate the next required step.

If you are unsure of how to access a certain operation, click on the corresponding line. The QuickStart Guide will then either run an animation showing the location of the related menu entry or open the corresponding help page.

Define the Units¶

The Particle Gun template has already applied some settings for you. The defaults for this structure type are geometrical units in mm and time in s. You can change these settings in the units dialog box (Home: Settings Units ), but for this example you should just leave the settings as specified by the template. Additionally, the used units are also displayed in the status bar:

Define the Background Material¶

As discussed above, the structure will be described within vacuum. The material type Normal is set as default background material in the Particle Gun template. For this example, you do not need to make any changes as the default properties of the material type Normal are those of vacuum. In case you need to change the properties, you may do so in the corresponding dialog box Simulation: Settings Background

Model the Structure¶

The basic settings have been made, now we are able to set up the structure. Since the electron gun is rotationally symmetric, a special but very efficient technique can be used to design the structure. First, the cathode is created.

1. Open the Rotate Profile dialog box Modeling: Shapes Rotate Face to create the cathode.
2. Press the ESC key to show the dialog box. Do not click a point in the working plane.

1. Enter the name "cathode" and choose Z as axis of rotation. Set the material to PEC. Now enter the polygon data as shown in the table below.

1. You may click the Preview button during the construction to get a preview of the solid. This makes it easy to detect any possible mistakes when entering the data.

The dialog box should now look like in the picture above. Click the OK button to confirm your settings and to construct the cathode.

1. The structure is displayed in the working plane and now your cathode should look like this:

One part of the cathode is still missing, the inner cylinder. We will need this inner cylinder to define the particle source. To create this cylinder, open the Cylinder dialog Modeling: Shapes Cylinder . Press the ESC key to show the dialog box.

Change the name the name to "cathode_inner", enter an Outer radius of 1.5 and Zmax of 0.5. Click the OK button to confirm your changes. The cylinder should fit perfectly into the hole of the solid cathode:

1. The construction of the cathode is completely finished and now we will construct the anode in the same way as we constructed the outer cathode. Open the Rotate Profile dialog box Modeling: Shapes Rotate Face .

2. Press the ESC key to show the dialog box. Do not click a point in the working plane.

3. Enter the name "anode" and choose z as axis of rotation. The material PEC should be automatically selected.

Now enter the polygon data as shown in the following table:

Your dialog box should now look like in the picture above. Click the OK button to confirm your changes. The creation of the anode is complete and the whole structure should look like this (rotated for better visibility):

1. As you might have noticed, the magnetic part of the structure is still missing. First, we will construct the three vacuum discs that will serve as permanent magnets. To create one disc, open the Cylinder dialog box Modeling: Shapes Cylinder . Press the ESC key to show the dialog box.
2. Enter the name "magnet", outer radius 32.8 and the inner radius 5.8. The z range extends from 31 to 37.9 mm. Change the material to vacuum. Click the OK button to confirm your changes.

1. Since the same cylinder exists three times, we will use the transform dialog box to create the missing two cylinders. First, select the solid "magnet" in the navigation tree NT: Components \(\Rightarrow\) component 1 magnet.

1. Open the Transform Selected Object dialog box Modeling: \(T o o I s \hookrightarrow T r a n s f o r m \tilde { \mathbf { a } } ^ { \perp }\) to copy the cylinder.

Enable the checkbox Copy. Then enter a translation of 10 in z-direction. Change the Repetition factor to 2 and click the OK button to confirm your changes. The structure should now look like this:

1. Before the iron discs will be defined, we create a new and simple iron material. To do this, open the material dialog box Modeling: Materials New/Edit New Material. Change the Material name to "Iron", the Color to red and value of Mu to 100 like in the picture below. Now we have quickly defined a simple iron material. Click the OK button to confirm your changes and to leave this dialog box.

1. The iron discs are created in the same way as the magnets. Open the cylinder dialog Modeling: Shapes Cylinder . Press the ESC key to show the dialog box.

1. Enter the Name "iron", an Outer radius of 32.8 and Inner radius of 5.8. The z range extends from 37.9 to 41 mm. Change the material to the new material \(" \ln 0 \mathsf { n } " .\) . Your dialog box should now look like the above picture.
2. Finally click the OK button and confirm your changes. To create the second iron disc, we will use the transform mechanism again. Select the solid \(" \mathsf { i r o n " }\) in the navigation tree.

graph TD
  A["Components"] --> B["component1"]
  B --> C["anode"]
  C --> D["cathode"]
  D --> E["cathode_inner"]
  E --> F["iron"]
  F --> G["magnet"]
  G --> H["magnet_1"]
  H --> I["magnet_2"]

1. Open the Transform Selected Object dialog box Modeling: Tools Transform \(\hat { \mathbf { a } } ^ { \tt a }\) to copy the cylinder.

1. Select Copy and enter a translation of 10 in z-direction. Click the OK button to confirm your changes. Now the structure should look like this:

1. The structure creation part is finished and we can start to define the sources, i.e. potentials, magnets and particle sources.

Congratulations! You have just created your first Particle Tracking structure within CST Studio Suite.

Define Potentials and Magnets¶

With all components for the electrostatic part of the configuration defined, the appropriate potentials can be set. First, define the potentials of the cathode and anode:

1. Select Simulation: Sources and Loads Static Sources Electric Potential and double-click on the surface of the “cathode” solid in the working plane. Press the Return key to finish your selection and to open the Define Potential dialog box.

1. Enter the name "cathode_pot" and a value of -3e4 V. As usual, click the OK button to confirm your changes.
2. In the same way, the potential for the anode is defined. Select Simulation: Sources and Loads Static Sources Electric Potential and double-click on the surface of the anode. Press the Return key to finish your selection and to open the Define Potential dialog box.
3. Enter the name "anode_pot" and a value of 0 V. Click the OK button to confirm your changes.

1. If you now select the potential folder in the navigation tree your structure should look like the picture below:

Note: As the solids "cathode" and "cathode_inner" are in direct contact, both have the same potential. That means "cathode_inner" also has a potential of -30 kV.

1. After the potential definition is finished, we will create three permanent magnets for the three vacuum discs. To define the first magnet select Simulation: Sources and Loads Static Sources Permanent Magnet .
2. Then select the solid that should become a permanent magnet. Thus, double-click on the vacuum disc named "magnet".

1. The Define Magnet dialog box opens. Ensure that the vector components are set to X: 0, Y: 0, Z: 1 and Inverse direction is not checked. Enter a value of 0.02 T for the remanent flux. Leave the other settings unchanged and click OK to confirm.

1. In the same way, define magnets for the vacuum solids "magnet_1" and "magnet_2" in z-direction. The solid "magnet_1" should be the vacuum disc in the middle of the three discs.

1. If you now select the Permanent Magnets folder in the navigation tree you should see the following picture:

1. Potential and magnet definitions are now complete.

In practice, it is advisable to visualize and refine the mesh before the particle source is defined. The reason is that the number of emission points of the particle source can depend on the mesh settings. This matter is discussed in detail in the later chapter Define Particle Sources.

Visualize and Refine the Mesh¶

By default, the Particle Tracking solver uses a hexahedral mesh for computing electrostatic and magnetostatic fields. This is the optimal choice for axis-aligned structures as used in this example. However, especially when surfaces in the vicinity of the particle trajectories are curved, their representation by tetrahedral mesh cells might be better-suited and will deliver more accurate results. In order to keep the focus on the simulation workflow itself, we will deal with tetrahedral meshes in a later, more specialized section.

The mesh generation for the structure’s analysis is performed automatically based on an expert system. However, in some situations it may be helpful to inspect the mesh to improve the simulation speed by changing the parameters for the mesh generation.

The mesh can be visualized by entering the mesh view Home: Mesh Mesh View . For this structure, the mesh information will be displayed as follows:

One 2D mesh plane is visible at a time. You can modify the orientation of the mesh plane by adjusting the selection in the Mesh: Sectional View Normal dropdown list or just by pressing the X/Y/Z keys. Move the plane along its normal direction using the Up/Down cursor keys. The current position of the plane will be shown in the Mesh: Sectional View Position field.

There are some thick mesh lines shown in the mesh view. These mesh lines represent important planes (so-called snapping planes) at which placement of mesh lines is considered necessary by the expert system. You can control these so-called snapping planes in the Special Mesh Properties dialog by selecting Simulation: Mesh Global Properties Specials Snapping.

In many cases, the automatic mesh generation will produce a reasonable initial mesh, but in our case, we will refine the mesh in the cathode region to have a finer mesh resolution for the particle beam.

1. Make sure you are in the mesh view mode. Select the solid cathode in the navigation tree NT: Components component1 cathode.

1. Open the dialog box Mesh: Mesh Control Local Properties to modify the local mesh settings of the cathode. In the General tab, choose Absolute value from the Volume refinement drop-down list. This brings up the Use same setting in all three directions checkbox. Uncheck that box and change the step width in x and y to a value of 0.4.

1. Confirm your changes as usual by clicking on the OK button. The dialog box closes and you can see the modified mesh.

The number of mesh cells should be 497,536. You can get this information from the status bar.

You can now leave the mesh inspection mode via Mesh: Close Close Mesh View .

Define Particle Sources¶

A particle source is a shaped surface of a component where charged particles enter the computational domain under a specific emission condition, which is determined by the emission model settings. Such a source is often located on the surface of a PEC solid, but it can also be defined on the surface of any arbitrary material. In our case the particle source will be placed on the inner cathode. To facilitate the selection of the surface of the inner cathode, some solids will be hidden.

1. Select "cathode" and "cathode_inner" in the navigation tree. Use the Shift key for multi-selection. Select the option View: Visibility Hide Hide Unselected. Now we are able to define the particle source.

graph TD
  A["Components"] --> B["component1"]
  B --> C["anode"]
  C --> D["cathode"]
  D --> E["cathode_inner"]
  E --> F["iron"]
  F --> G["iron_1"]
  G --> H["magnet"]
  H --> I["magnet_1"]
  I --> J["magnet_2"]

1. Select Simulation: Sources and Loads Particle Sources Particle Area Source and select the inner surface of the solid "cathode_inner" by doubleclicking it. Make sure that the surface is highlighted when you move the mouse cursor away from the surface.

1. After selecting the emission surface, press the Return key to open the Define Particle Area Source dialog box. Here, the particle type and particle density at the previously selected surface are adjustable. Change the Tracking emission model to Space charge. The blue points in the preview visualize the particle emission points. Their density can be influenced using the Number of emission points slider. An increase of the number of emission points leads to a smoother current density. The checkbox Adjust density to mesh should be enabled if the emission model Space charge is chosen. Otherwise, the number of emission points might be too low to obtain good simulation results and then has to be increased manually when refining the mesh.

Note: As seen in the lower part of the dialog box, standard or user-defined particle types can be specified. A particle definition library allows you to export such user-defined particle definitions to a database and also to import them. This library is accessible through the Load and Save buttons. In this example, we keep the default particle type electron.

1. Move the Number of emission points slider until the number is 375. For finecontrol, you can use the left/right arrow keys while the slider is focused. To change the emission model settings, click the Edit button next to the emission model drop down list. The SCL Emission Settings dialog box opens:

1. An emission model describes the conditions particles need to fulfill in order to be emitted into free space. For instance, the space charge emission model allows particles to be emitted as long as an electric field perpendicular to the emitting surface is present. If not already preselected, make the following adjustments inside the dialog box on the Potentials tab: Change the emitting potential to "cathode_pot" and the reference potential to "anode_pot". Click the OK button to confirm your changes. The particle source should now look like this:

Note:¶

The red triangular mesh shows the discretization of the cathode surface, while the blue points visualize the start positions of the particles for the simulation. In this case, the emission model Space charge requires the start positions to be shifted a little bit away from the cathode surface. This shifting is done automatically depending on the mesh close to the cathode.

1. We have finished the particle source definition and can now leave the Define Particle Area Source dialog box by clicking the OK button again.
2. Since some solids are currently hidden, we have to unhide them to see the whole structure again. Select View: Visibility Show (dropdown list) Show All. It is often helpful to hide some solids in order to select faces inside a structure.

The particle source is now defined and ready for emission. Before you continue, have a look at the QuickStart Guide to see the next steps.

The point “Set boundary conditions” has already been set to finished as the boundaries were defined by the Particle Gun template. Nevertheless, the boundary conditions will be discussed in the next section to illustrate the basics of the boundary condition setup.

Define Boundary Conditions¶

The simulation will be performed only within the bounding box of the structure, the socalled computational domain. You can specify certain boundary conditions for each plane (Xmin, Xmax, Ymin, Ymax, Zmin, Zmax) of the computational domain. These boundary conditions reflect the appropriate behavior of the surrounding world.

The boundary conditions are specified in a dialog box which can be opened by choosing Simulation: Settings Boundaries .

While the boundary dialog box is open, the boundary conditions are visualized in the structure view as shown in the next picture.

You can change boundary conditions from within the dialog box or interactively in the view. Select a boundary by double-clicking on the boundary symbol within the view and select the appropriate type from the context menu.

The following table gives an overview of the available boundary conditions and their effect on the tangential and normal component of the electric and magnetic fields:

In our case, we want to use open boundaries in all directions. As we use the Particle Dynamics template, the default boundaries are already set to open.

Furthermore, some extra space is added between the structure and the open boundaries. Click the button Open Boundary to check this setting.

The size of this extra space is the length of the bounding box diagonal times the user defined factor, in our case 0.1. This value is also defined in the Particle Dynamics template. Click Cancel to leave this setting unchanged. Click Cancel again to leave the Boundary Conditions dialog box.

Note: There are two ways to create some space (background material) between structure and boundaries. The first way is described above. Alternatively, some extra space can be defined in the Background Properties dialog box. You can have a look in the paragraph Define the Background Material.

Start the Simulation¶

After having defined all necessary parameters, you are ready to perform your first simulation. The simulation is started from within the particle tracking solver control dialog box: Simulation: Solver Setup Solver .

In this dialog box you can specify the settings of the Particle Tracking Solver and start the simulation process. If multiple particle sources are defined, you can choose between a simulation where all sources emit particles and a simulation where only a single source is active. Enable the Enable gun iteration option to activate the iterative gun solver algorithm, set the Relative accuracy to be -20 dB and the Max. number of iterations to 20. Thus, the Particle Tracking Solver does not just track the particles once through the computational domain. Instead, the solver iteratively repeats an electrostatic calculation and then tracks the particles until the desired accuracy of the space charge deviation between two successive iterations is reached.

The Considered fields box lists all electromagnetic fields that are available for the Particle Tracking Solver. In order to consider a specific field type for the tracking process, check the respective Active checkbox, in our case for the E- and the M-Static fields.

Now you can start the simulation procedure by clicking the Start button in the particle tracking dialog box. A few progress bars will appear to keep you up to date with the solver’s progress.

As you can see in the next paragraph, the complete solving procedure consists of three to four parts, depending upon the selected post processing steps. In this example, part two (electrostatic solver) and part three (particle tracking) are repeated iteratively until the relative accuracy condition specified in the gun iteration section is reached.

1. Magnetostatic Solver¶

1.1. Checking model: During this step, your input model is checked for errors such as invalid overlapping materials, etc.
1.2. Calculating matrices: During these steps, the system of equations, which will subsequently be solved, is set up.
1.3. Magnetostatic solver is running: During this stage, a linear equation solver calculates the field distribution inside the structure.

2. Electrostatic Solver¶

2.1. Calculating matrices: During these steps the system of equations, which will subsequently be solved, are set up.
2.2. Electrostatic solver is running: During this stage, a linear equation solver calculates the field distribution inside the structure.

3. Particle Tracking¶

3.1. Initializing Tracking Solver: The data structure for the collision detection of particles with solids is constructed.
3.2. Tracking Solver is running: The particles are emitted and tracked through the computational domain.

4. Post Processing¶

4.1. From the field distribution, additional results like the inductance matrix or the energy within the computational domain can be calculated.

After a few repetitions of steps two and three, the desired accuracy of -20 dB of the gun iteration is reached, i.e. the relative difference of the space charge distribution between two consecutive solver runs is less than -20 dB. The following diagram explains the algorithm of the iterative gun solver and its convergence condition:

graph TD
  START["START"] --> A["Calculate magnetostatic field distribution"]
  A --> B["Calculate electrostatic field distribution"]
  B --> C["Track particles and monitor space-charge"]
  C --> D{"Converged?"}
  D -->|no| E["Update space charge"]
  E --> B
  D -->|yes| END["END"]

Analyze the Results¶

In tracking applications, users are often interested in the particle beam behavior. To get an overview of the particle movement, a 3D visualization of the trajectories is available in the navigation tree NT: 2D/3D Results Trajectories. The trajectories should now look like in the following picture:

Colors indicate the particle energy. There are lots of options to modify this plot using the Particle Plot properties dialog box 2D/3D Plot: Plot Properties Properties .

Open the dialog box and change some settings, for example the Display type. Click the Start/Stop button on the Animation tab to see the movement of the particles. Detailed explanations can be obtained from the online help. Click the Help button to open the online help. If you like to close this dialog box, click the Cancel button.

Field plots are also available in the navigation tree. To obtain the current density of the particle beam select NT: 2D/3D Results Particle Current Density in the navigation tree. To enable logarithmic scaling check the respective box at 2D/3D Plot Color Ramp Log.

Further plot settings can be changed in the 3D Vector Plot dialog box. This can be opened as usual via 2D/3D Plot: Plot Properties Properties .

To create the field plot above, the Density slider on the Arrows/Bubbles tab was shifted to the right. Try to change some settings. Click the OK button to leave this dialog box.

In the case of gun simulations with space charge limited emission, the emitted current is an important parameter. The 1D result plot emitted current versus gun iteration NT: 1D Results Particle Sources Current vs. Iteration particle1 is available in the navigation tree:

This 1D result offers you the possibility to control the emission process. Thus, it is very helpful that this plot is already available during the gun iteration.

Another plot is also available during the gun iteration, the gun code accuracy. If the user defined accuracy is reached, the iterative gun solver stops. To get this 1D result plot select the folder NT: 1D Results Convergence Gun Iteration Charge Accuracy in the navigation tree:

Apart from this 1D graph, the development of the emitted charge and the perveance during the gun iteration process are also available via NT: 1D Results Particle Sources Charge vs. Iteration particle1 and NT: 1D Results Particle Sources Perveance vs. Iteration particle1.

The collision information under NT: 1D Results Total Collision Information can also be very interesting, because these graphs contain e.g. information about the power that is absorbed by a solid. Precise numbers can easily be read from these graphs via the entry Show Axis Marker from the context menu:

In this case the background consists of vacuum, thus all particles are absorbed by the boundary of our calculation domain.

Parameterization of the Model¶

The previous steps demonstrated how to enter and analyze a simple structure. However, structures are usually analyzed to improve their performance. This procedure may be called “design” in contrast to the “analysis” done before.

After you get some information on how to improve the structure, you will learn how to optimize the structure’s parameters. This could be done by modifying each parameter manually, but this of course is not the best solution. CST Studio Suite offers various options to describe the structure parametrically in order to change the parameters easily.

Let us assume you are interested in the dependency of the emitted current on the cathode's potential. To obtain this dependency, first of all the potential has to be parameterized. Thus, double click on the potential NT: Potentials cathode_pot in the navigation tree.

The Edit Potential dialog box opens and the potential can be edited. Instead of a number type the string "phi" in the Potential value field.

If you click the OK button, you will be asked to delete the current results. Just click the OK button to delete the results. Then the dialog box New Parameter opens to define the value of your parameter "phi".

Enter a value of -3e4 and click the OK button. You have successfully defined your first parameter. The values of your parameters can be edited and checked in the Parameter List window that is usually located in the lower left part of the main window:

Since we did not change the value of the cathode's potential, the results of the simulation would be the same. We will now change the setup to run a so called Parameter Sweep to get the emitted current for potentials in the range from -32 kV to -28 kV. To do this, open the Particle Tracking solver dialog box Simulation: Solver Setup Solver .

To save some time during the parameter sweep disable the checkbox Enable gun iteration. The tracking solver will now run only one calculation and will not operate in the iterative mode.

Click the button Par. Sweep to open the dialog box Parameter Sweep and to configure the parameter range and also the expected results of the parameter sweep.

In this dialog box you can specify calculation sequences that consist of various parameter combinations. To add such a sequence, click the New Seq. button now. Then click the New Par button to add a parameter variation to the sequence:

In the resulting dialog box you can select the name of the parameter to vary in the Name field. Then you can specify different sweep types to define the sampling of the parameter space (Linear sweep, Logarithmic sweep, Arbitrary points). Depending on this selection the sampling can be defined further, e.g. the linear sweep option allows us to define the lower (From) and upper (To) bounds for the parameter variation as well as the definition of either the number of samples or the step width.

In this example you should perform a linear sweep from -32 kV to -28 kV in 5 steps. Click the OK button to confirm your changes. The definition of the sequence is finished but we still need to configure the expected result, the emitted current. The parameter sweep dialog box should look as follows:

After a successful simulation run, many simulation results are already generated automatically under NT: 1D Results and saved in the parametric storage. For more detailed investigations and customized evaluations, Template Based Post-Processing is available. Often, the parametric results are already sufficient to analyze the results.

However, the general procedure of defining and handling Result Templates is outlined below.

In order to evaluate a particular quantity of interest during the parameter sweep, it needs to be defined in advance. Here, the current emitted from the particle source should be monitored.

As can be seen above, this quantity is available as a plot versus gun iteration number under NT: 1D Results Particle Sources Current vs. Iteration particle1. For finding the final value obtained during the gun iteration, we have to extract the value that corresponds to the rightmost point in the plot. Note that this approach is also valid if Gun iteration is deactivated, as we did above, since then the plot only contains a single point.

In order to define the results of interest, click on the button Result Template. The Template Based Post-Processing dialog box opens. Templates are separated into several Template Groups.

Choose the template 0D or 1D Result from 1D Result (Rescale Derivation, etc) in the General 1D group. This very powerful template is intended for post processing or extracting data from any 1D plot. Once you choose this template, a dialog box opens where the data source and the operation have to be entered.

Under Specify Action select y at x-Maximum. Under 1D(C) Results, the data source has to be selected – in our case Particle Sources\Current vs. Iteration\particle1. Leave the dialog by pressing OK.

The Template Based Post-Processing dialog box should be still open and contain the following row:

The Result name can be changed by clicking onto the respective cell. You should change it to something more recognizable since this will become the result plot title, choose, “Emitted Current”:

Click the Close button to return to the parameter sweep. Now start the parameter sweep by clicking Start. After confirming the request to delete existing results with OK, the calculation may take a few minutes. The navigation tree contains a new item called Tables from which you can select the item NT: Tables 0D Results Emitted Current. The 1D result plot should look like in the picture below and gives you the relation between input voltage and emitted current of the electron gun:

Automatic Optimization of the Structure¶

Let us assume that you wish to adjust the emitted current to a value of -0.22 A (which can be achieved within the parameter range of -32 kV to -30 kV according to the parameter sweep). Figuring out the proper parameter can be a lengthy task, but it can also be performed automatically.

CST Studio Suite offers a very powerful built-in optimizer feature for such parametric optimizations.

To use the optimizer, open the tracking solver control dialog box Simulation: Solver Setup Solver in the same way as before, or directly via Simulation: Solver Optimizer . Click the Optimizer button to open the optimizer control dialog box.

First, activate the desired parameter(s) for the optimization in the Settings Tab of the optimization dialog box, here the parameter "phi" should be checked. Second, specify the minimum and maximum values for this parameter during the optimization. From the parameter sweep, we already know that the searched potential is greater than -32 kV and lower than -30 kV. Therefore, you can enter a parameter range between -32 kV and -30 kV. Deactivate Use current as initial value and set the initial start value for the optimization, e.g. to -31.5 kV.

For this simple example, the other settings can be kept as default. Refer to the online documentation for more information on these settings. You can specify a list of goals you wish to achieve during the optimization. In this example, the objective is to find a parameter value for which the emitted current becomes -0.22 A. The next step is to specify this optimization goal. Switch to the Goals Tab and click Add New Goal.

Now you can define the goal for the emitted current. Since you would like to find a value of -0.22 A, you should select the equal operator in the conditions frame. Then set the Target to -0.22. After you click OK, the optimizer dialog box should look as follows:

Note: The optimizer is capable of optimizing multiple parameters at once. Detailed information can be obtained from the online help.

Up to now, you have specified which parameters to optimize and set the goal that you want to achieve. The next step is to start the optimization procedure by clicking the Start button. As shown in the next picture, the optimizer will display its progress in an output window in the Info tab, which is activated automatically. After the whole process has finished, the optimizer output window contains the best parameter values in order to achieve the desired goal.

Note that, due to sophisticated optimization technology, only five solver runs are necessary to find the optimal solution with very high accuracy.

Click the Close button to leave the dialog box. Now look at the final result of the emitted current for the optimal parameter setting phi = -30405.6 V by clicking NT: 1D Results Particle Sources Current vs. Iteration. You should obtain the following result:

As you can see, the final emitted current for the optimized voltage parameter is -0.22 A as it was previously defined by the setting of the optimization goal.

Additional Information: More settings for the Particle Tracking Solver¶

The Particle Tracking and the Particle Tracking Specials dialog boxes offer many more options to change the solver properties. The latter is available by selecting Simulation: Solver Setup Solver and clicking the Specials button.

The Particle dynamics frame offers the possibility to change specific settings of the particle tracking algorithm. The setting Max. timesteps defines the maximum number of simulated steps performed by the tracking algorithm. The Min. pushes per cell value determines the spatial sampling rate of the particle trajectories. The Timestep dynamic parameter specifies the variation of the time step between two pushes and introduces a dynamic adaptation of the time step to the highest particle velocity. Activating the checkbox Monitor charge and current results in monitoring the space charge and current density generated by the particles. This is automatically activated for gun iteration simulations.

In the Gun iteration frame, in addition to the desired Relative accuracy, the maximum number of iterations of consecutive electrostatic simulations and particle tracking computations is defined. The Relaxation parameter describes the influence of the last obtained space charge distribution to the overall charge distribution, which is considered in the next electrostatic computation. By checking Consider self-magnetic field, the magnetic field generated by the particles can be included in the gun iteration.

In order to save disk space, the trajectory data is usually not written for every time step. Instead, a subsampling is performed. The sampling method and its parameters can be set in the Trajectory sampling section of the Particle Tracking Specials dialog.

Additional Information: Treating PEC as Normal Material for Magnetostatic¶

Computations¶

Simulation Setups used for Particle Tracking or PIC simulations often consist of a metallic beam pipe or similar enclosing structure. If these structures are modeled using PEC material, they effectively cannot be penetrated by magnetic fields, which is physically correct within the simulation model but usually not desired.

This is why it is possible to treat PEC as a normal material for the Magnetostatic Solver via a setting in its Specials dialog.

The option Consider PEC as Normal is default only when a Particle Tracking or PIC project template is used - otherwise this checkbox is disabled by default. If you want to change or check this setting, open the Special Settings dialog box of the Magnetostatic Solver Parameters via Home: Simulation Setup Solver (dropdown list) M-Static Solver, Home: Simulation Setup Solver Specials.

If the checkbox Consider PEC as Normal is enabled, PEC materials are considered like normal materials with a permeability µ which can be defined in the material properties of the PEC material. In case the solver is started from problem class “Tracking”, this setting is activated automatically.

Please note that in stand-alone magnetostatic simulations using the Problem Type “Low Frequency”, different results compared to Problem Type “Particle” are obtained despite otherwise identical settings due to the different defaults regarding the consideration of PEC type materials.

Additional Information: Using tetrahedral meshes in the Tracking Solver¶

Especially for models with curved surfaces in the vicinity of the particle beam, a representation of the structure by a hexahedral mesh may require a large number of cells. In these cases, it can be helpful to use a tetrahedral mesh that will model the structure’s surfaces more naturally and thus can yield more accurate surface fields.

You can either switch to the tetrahedral mesh type by selecting Simulation: Mesh Global Properties (dropdown list) Tetrahedral and pressing OK in the appearing Mesh Properties dialog or alternatively via the option in the solver setup dialog Simulation: Solver Setup Solver Mesh Tetrahedral.

When changing the mesh, you will be informed that any existing results have to be deleted. Confirm the deletion of the results by clicking OK.

Before starting a new simulation based on a tetrahedral mesh, a few settings in the model setup have to be changed, part of which can be seen as general recommendations for using the tetrahedral tracking solver:

Open boundaries are not supported. They are automatically replaced by magnetic boundaries (Ht = 0) upon solver start.
In many cases, the automatically generated mesh will be a good starting point for performing your simulations. However, in order to obtain a mesh well adapted to the simulation type, some settings should be changed.

o For modifying the global mesh resolution, you can set the mesh properties via Mesh Global Properties . In the mesh properties dialog, enter 10 under Cells per max model box edge for Model and 15 for Background.

o As the particles only interact with the electromagnetic fields in the vacuum regions, a mesh refinement of the permanent magnets is not of the highest priority. Therefore, you may disable the checkbox Consider material properties for refinement in the Specials dialog. Moreover, the value in the edit field Smooth mesh with equilibrate ratio should be set to 1.3 in order to avoid generating a too large number of tetrahedrons for this example.

Due to using the project template for setting up the simulation project, most of these settings have already been applied automatically.

The mesh can be visualized by entering the mesh view Home: Mesh Mesh View and then pressing Mesh: Mesh Update to invoke the tetrahedral mesher. In case you do not trigger the mesh generation manually, the mesh is automatically constructed upon solver start. After a few seconds, the mesh appears. For the structure in this example, it looks as follows:

The right image has been generated using Mesh: Visibility Background and Mesh: Sectional View Cutting Plane . It includes a visualization of the background mesh cells, i.e., the free-space region where the particle trajectories will be computed. Naturally, the mesh quality in the beam region is important for achieving accurate results.

Please note that particle tracking simulations that are using a tetrahedral mesh will in general be slower than simulations with the same number of hexahedral cells. However, since tetrahedral meshes yield a more precise surface representation, a considerably smaller number of cells will often be sufficient for getting accurate results.

Press Update in the Mesh Properties dialog. This requests the tetrahedral mesher to update the mesh representation. The total number of tetrahedrons is close to 55,000 now, as can be seen in the status bar:

As in the hexahedral case, a local control of the mesh resolution can be reached via the local mesh properties of the respective component.

After leaving the mesh inspection mode via Mesh: Close Close Mesh View , you could start the simulation as before using the particle tracking solver control dialog box: Simulation: Solver Setup Solver Start. However, due to some restrictions that apply to the tracking solver when used with tetrahedral meshes, the following preparations have to be performed (if you omit these steps, the solver will emit respective messages to guide you towards solving possible issues):

While being relative to the mesh dimensions in the hexahedral case, the emission distance for the space charge limited emission model has to be an absolute value when using a tetrahedral mesh. In general, it is a good idea to review all settings of the particle source after switching the mesh type.

In order to do so, right-click onto the particle source in the navigation tree NT: Particle Sources particle1 and select Edit Properties… from the context menu.

This will open the Edit Particle Area Source dialog again. Here you should increase the Number of emission points to a value around 400 again by setting the Scale Factor to 10 and adjusting the slider appropriately.

Furthermore, open the settings of the emission model using the Edit button in the Tracking emission model frame, check the settings and press OK twice to close both dialogs.

Finally, you can now run the particle tracking solver with a tetrahedral mesh via its solver control dialog box: Simulation: Solver Setup Solver Start.

The results should look similar to the ones obtained using a hexahedral mesh for the workflow example described earlier in this section (here for phi = -30 kV and active gun iteration again):

Summary¶

This example gave you a basic overview of the key concepts of the Tracking Solver of CST Studio Suite. You should now have a good idea of how to do the following:

1. Create a structure using the solid modeler
2. Specify the solver parameters, check and modify the mesh and start the tracking simulation
3. Visualize the electromagnetic field distributions and the particles trajectories
4. Define a structure using parameters
5. Use the parameter sweep tool for parameter studies
6. Perform automatic optimizations

If you are familiar with all these topics, you have a very good starting point for further improving your usage of CST Studio Suite.

For more information on a particular topic, we recommend that you look at the contents page of the online help manual, which can be opened via File: Help Help Contents – Get Help using CST Studio Suite . If you have any further questions or remarks, do not hesitate to contact our technical support team. We also strongly recommend that you participate in one of our special training classes held regularly at a location near you. Please ask us for details.

Simulation Workflow: Electromagnetic Particle-in-Cell¶

The basic procedure of running the electromagnetic (EM) particle-in-cell (PIC) solver is very similar to the one demonstrated in the tracking simulation workflow. In contrast to the tracking solver, particles and electromagnetic fields are computed in a selfconsistent way using a time integration scheme. For more information on the physics that can be modelled with the EM PIC solver, an overview is provided in Chapter 3 – Solver Overview: Particle-in-Cell Solver.

The following example demonstrates how to perform a PIC calculation for a simple output cavity of a klystron. Studying this example carefully will allow you to become familiar with many standard operations that are necessary to perform a PIC simulation within CST Studio Suite.

Go through the following explanations carefully even if you are not planning to use the software for PIC simulations. Only a small portion of the example is specific to this particular application type since most of the considerations are general to all solvers and application domains.

The following explanations always describe the menu-based way to open a particular dialog box or to launch a command. Whenever available, the corresponding toolbar item is displayed next to the command description. Due to the limited space in this manual, the shortest way to activate a particular command (i.e. by pressing a shortcut key or activating the command from the context menu) is omitted. You should regularly open the context menu to check available commands for the currently active mode.

The Structure¶

This workflow example demonstrates how to build up the output cavity of a klystron for a PIC simulation. A klystron is a device to amplify microwave and/or radio frequency signals. The output resonator is the last stage (cavity) of a klystron. The amplified signal can be extracted using waveguide ports.

Since only the output resonator as a part of the klystron is simulated, a Gaussian emission model is used to define an already bunched particle beam.

CST Studio Suite allows you to define the properties of the background material. Background material is considered for the space in which no shape is defined. For this structure, it is sufficient to use vacuum for the klystron cavity and perfect electrical conductor (PEC) for the surrounding background space.

Create a New Project¶

After launching the CST Studio Suite you will enter the start screen showing you a list of recently opened projects and allowing you to select the application that best suits your requirements. The easiest way to get started is to configure a project template, which defines the basic settings that are important for your typical application. Therefore, click on the New Template button in the New Project from Template section within the New and Recent tab.

Next, you should choose the application area, Particle Dynamics for the example in this tutorial, and then select the workflow by double-clicking on the corresponding entry.

graph LR
  A["Microwaves & RF/OPTAL"] --> B["EDA/ELECTRONICS"]
  B --> C["EMC/EMI"]
  C --> D["Particle Dynamics"]
  D --> E["Static/Low Frequency"]
  E --> F["Precipitation"]
  F --> G["Space Applications"]
  G --> H["Vacuum Electronic Devices"]
  H --> I["Accelerator Components"]
  I --> J["Beam Optics"]

Please then select the following workflow: Vacuum Electronic Devices Klystron Hot Test Particle in Cell .

You are then requested to select the units that fit your application best. For this example, please select the dimensions as follows:

For the specific application in this tutorial, the other settings can be left unchanged. After clicking the Next button, you can give the project template a name and review a summary of your initial settings:

Finally, click the Finish button to save the project template and to create a new project with the appropriate settings. CST Studio Suite for Particle Dynamics Simulation will be launched automatically due to the choice of this specific project template within the application area Particle Dynamics. Save the newly created “Untitled” project on your hard disk using a name of your choice.

Please note: When you click again on the File: New and Recent you will see that the recently defined template appears below the Project Templates section. For further projects in the same application area, you can simply click on this template entry to launch CST Studio Suite for Particle Dynamics Simulation with useful basic settings. It is not necessary to define a new template each time. You are now able to start the software with reasonable initial settings quickly with just one click on the corresponding template.

Please note: All settings made for a project template can be modified later on during the construction of your model. For example, the units can be modified in the units dialog box (Home: Settings Units ) and the solver type can be selected in the Home: Simulation Setup Solver drop-down list.

Open the PIC QuickStart Guide¶

An interesting feature of the online help system is the QuickStart Guide, an electronic assistant that will guide you through your simulation. If it does not show up automatically, you can open this assistant by selecting QuickStart Guide from the Help button in the upper right corner.

The following dialog box should then be visible at the upper right corner of the main view:

As the project template has already set the solver type, units, boundary conditions and background material, the PIC Analysis is preselected and some entries are marked as done. The blue arrow always indicates the next step necessary for your problem definition. You do not have to follow the steps in this order, but we recommend you follow this guide at the beginning to ensure that all necessary steps have been completed.

Look at the dialog box as you follow the various steps in this example. You may close the assistant at any time. Even if you re-open the window later, it will always indicate the next required step.

If you are unsure of how to access a certain operation, click on the corresponding line. The QuickStart Guide will then either run an animation showing the location of the related menu entry or open the corresponding help page.

Define the Units¶

The Klystron Hot-Test template has already made some settings for you. The defaults for this structure type are geometrical values in mm and times in ns. You can change these settings by entering the desired settings in the units dialog box (Home: Settings Units ) but for this example you should just leave the settings as specified by the template. Additionally, the used units are also displayed in the status bar:

Define the Background Material¶

As discussed above in the Structure section, the klystron cavity is surrounded by perfect electrical conductor (PEC). The material type PEC is already set as default background material in the Klystron Hot-Test template. You may change the background material in the corresponding dialog box (Simulation: Settings Background ). For this example, no change of the background material is needed.

Model the Structure¶

Having defined the initial general settings, the 3D view window is now visible and the working plane is shown therein. The working plane can be turned off (and on) by clicking on View: Visibility Working Plane .

Then, you can start building the 3D structure. First, create a vacuum cylinder along the z-axis of the coordinate system using the following steps:

1. Select the cylinder creation tool Modeling: Shapes Cylinder .
2. Press the ESC key to open the dialog box. Do not click a point in the working plane.
3. Enter "cavity" as name.

1. Enter the parameters "Rcav" as outer radius and "Lcav" as Zmax. Set the Material to "Vacuum". Click the OK button to confirm the changes.
2. The New Parameter dialog box appears. Enter 38.8 as value for Rcav. Press the Return key to confirm. It is also possible to add a description of the parameter.

1. Another New Parameter dialog box appears. Enter 22 as value for Lcav. Press the Return key to confirm. The defined parameters are shown in the Parameter List window of the CST Studio Suite. To view the newly created shape, click on View: Change View Reset view .

graph LR
  A["Static / Low Frequency"] --> B["Microwaves & RF / Optical"]
  B --> C["EDA / Electronics"]
  C --> D["EMC / EMI"]
  D --> E["Particle Dynamics"]
  E --> F["Static / Low Frequency"]

graph LR
  A["Components"] --> B["ParticleBeam1"]
  C["Groups"] --> B
  D["Materials"] --> B
  E["Faces"] --> B
  F["Curves"] --> B
  G["WCS"] --> B
  H["Anchor Points"] --> B
  I["Wires"] --> B
  J["Voxel Data"] --> B
  K["Dimensions"] --> B
  L["Coils"] --> B
  M["Lumped Elements"] --> B
  N["Particle Beams"] --> B
  O["Ports"] --> B
  P["Excitation Signals"] --> B
  Q["Field Monitors"] --> B
  R["Voltage and Current Monitors"] --> B
  S["Probes"] --> B
  T["Mesh"] --> B
  U["1D Results"] --> B
  V["2D/3D Results"] --> B
  W["Tables"] --> B
  X["Wavefield"] -.-> Y["Coordinate System"]
  Z["x"] -.-> Y
  AA["y"] -.-> Y
  AB["z"] -.-> Y

graph TD
  A["1D Results"] --> B["Energy"]
  B --> C["Particle Beams"]
  C --> D["ParticleBeam1"]
  D --> E["Wake integration infos"]
  E --> F["Wake impedance"]
  F --> G["Wake potential"]
  G --> H["Reference Pulse"]
  H --> I["X"]
  H --> J["Y"]
  H --> K["Z"]

graph TD
  A["1D Results"] --> B["Energy"]
  A --> C["Particle Beams"]
  C --> D["ParticleBeam1"]
  D --> E["Wake integration infos"]
  E --> F["Wake impedance"]
  F --> G["Wake potential"]
  G --> H["Charge distribution (distance)"]
  H --> I["Charge distribution (time)"]
  I --> J["Charge distribution spectrum"]
  J --> K["Current"]
  K --> L[""Wake impedance [WakeSpectrum"]"]
  L --> M["Z"]
  L --> N["Y"]
  L --> O["X"]