Particle dynamics applications

Accelerator components

Accelerator components such as cavities or beam position monitors are typically designed with the Eigenmode, Transient or Frequency Domain solvers. However, when it comes to inclusion of the beam, the Wakefield solver is an incredibly versatile tool (read more about CST Studio Suite solvers here).

If you consider the 9-Tesla cavity accelerator shown here, the goal is to maintain the electron beam accelerated during the whole propagation along the accelerator axis. The induced EM-Field established in the Tesla cavities when the electrons are passing through needs to keep the right phase to maintain the particle acceleration. Therefore, one can see that the cavity oscillations and the generation of higher order modes could limit or interrupt the acceleration process. The simulation and the use of the Wakefield solver allows accurate design of the accelerator components.   

Thermal effects

Thermal effects can be included in a coupled simulation where low frequency (LF) losses are imported into the thermal solver.

If the LF solver is used, the eddy currents can be found (diagram on the left). With the losses of the material, these eddy currents represent a loss density evaluated automatically by the LF solver. This can be loaded into the thermal solver, which then shows the weak temperature behavior in the diagram on the right. This loop can be automized with our System Assembly and Modelling Approach, which allows a parametric coupling of the different physics.

Magnet Design

Particle beams in the accelerator have to be guided and focused. That is possible via potentially complex magnet designs. Opera 2D or 3D is a market-leading software for this application. Depending on the user preference, this can also be simulated within CST Studio Suite.

Vacuum Electron Devices such as Traveling Wave Tubes (TWT) are used mainly for satellite communication because of their reliability, but also thanks to their performances. For instance, in the frequency range between 1-60 GHz, the amplified signal can reach an output power up to 500W with an efficiency over 50% (for space TWTs).

In contrast to their solid state counterparts, they show higher efficiency, higher reliability, better thermal performance and a slightly better linearity. However, they are more expensive to build. Thus, TWTs are used when reliability is a must, such as for high powers and on satellites. Simulation is very attractive in these design processes as it reduces the need for multiple costly prototypes.

The design of a TWT can be completely performed using the PIC solver to characterize the Slow Wave Structure (SWS) which corresponds to the interaction region between the electron beam and the RF-signal sustained by the helical structure.

An RF-signal is introduced from an input coupler. During the propagation of the electrons along the SWS, the kinetic energy of the electrons is transferred to the traveling wave. Along the tube, the electron beam starts to be bunched and the electrons lose their kinetic energy which is globally transferred to the traveling wave. The traveling wave is then amplified with a maximum power extracted in the output coupler.  

Plasma applications typically have large time scales and the plasma can be described by its space charge interaction between the electrons and the ions. The Electrostatic Particle-In-Cell (ES-PIC) technology computes space charge versus time, taking into account the electrostatic effect only. This means that compared to a pure PIC approach, there is no current and H-Field induced but it is very well suited for these plasma applications. It also stays valid for plasma applications where the phenomenon can be described by the space charge dynamics and collisions at relatively low pressure, neglecting the temperature gradients of the ions and the convection effects which would require another numerical approach.

Plasma for Fusion

Plasmas for fusion are very hot plasmas are created in tokamaks and provide a new source of energy production. This is one of the sustainable energy under investigation nowadays to answer the energetic problems the world is facing with. The energy of the future must come from clean, safe and controlled fusion.

In the main operating principle, the plasma needs to be maintained confined. This is the role of the very complex magnetic coils design surrounding the tokamak. Then, the plasma needs to be sufficiently hot to maintain the thermonuclear reactions. This is the role of the Gyrotron Devices which can be fully designed and simulated with the PIC solver.

Gyrotrons are high power vacuum electron devices capable of generating output powers in the order of hundreds of kW with operating frequencies up to several hundreds of GHz. Gyrotrons are very well suited for plasma heating process because the microwave frequency generated can excite one of the plasma proper frequencies. The waves transfer their energy to the plasma leading to the heating process.