Klystron Output Resonator - Particle-in-Cell (PIC) Simulation

This article shows the simulation of an RF extraction circuit studied during a collaboration of DESY and Darmstadt University of Technology for developing a new S-Band klystron. The example demonstrates the simulation of moving charged particles in combination with arbitrary time dependent fields. The simulation is performed with the Particle in Cell (PIC) code of CST PARTICLE STUDIO™ (CST PS). The code enables a mutual coupling of the charge movement and the electromagnetic field. Since the PIC code is embedded in the transient solver of CST MICROWAVE STUDIO® (CST MWS), there are already many features as for example waveguide ports, discrete ports, dispersive and gyrotropic materials available.

The output resonator is inversely set up, that means the blue parts are the vacuum filling. On top and bottom there are waveguide ports (red) attached. This automatically records the power coupled into the attached waveguides. The grey cylinder is used as emission body for the charged particles.

The definition of a particle source is similar to the CST PS gun code approach. The emission surface has to be picked and then the particle properties as mass, charge, initial energy etc. can be modified according to the users needs. Figure 2 shows the triangulation of the emission surface and the particle properties. In this example a series of Gaussian bunches is emitted.

Besides the particle emission used in this example, CST PS is also able to handle simulaton results from other CST PS runs, such as particle distributions from previous CST PS GUN simulations.

Static magnetic fields,  can be superimposed to the PIC simulation. These fields can be either homogeneous, cylindrically symmetric with arbitrary longitudinal dependency, or precalculated by an CST EM STUDIO™ simulation of an arbitrary coil geometry. In this case a homogeneous field is used to compensate the bunch divergence due to space charge effects (see figure 3).

Figure 4 shows the particle trajectories of the simulated bunches. The colour  indicates the energy dsitribution of the particles inside the bunch. The time varying amplitude of the bunch current has a Gaussian distribution. The spatial distribution of the charged particles is defined to be uniform over the emission surfaces cross section. The electric field caused by the moving charged particles is shown in figure 5. The time dependent field and particle monitors also show the space charge effect on the bunches.

The output power (wave amplitude) is directly recorded by the waveguide ports (see figure 6). In the beginning there is no output power at all, since no bunch has passed the cavity yet. With increasing number of bunches the signal saturates to the klystron's design value. 

With the template based post processing one can easily perfom a discrete fourier transformation of the time signal. The corresponding frequency spectrum is shown in figure 7. It shows a nice peak around 3GHz which was the design value for this klystron.

This article shows an typical example for the usage of the CST PS PIC solver.  A mutual coupling between particle movement and electromagnetic fields is included. That means all space charge effects are taken into account. Since the PIC solver benefits from the CST MWS enviroment, informations such as output power, time dependent fields can be extracted in a comfortable way.