Two-Cavity Monotron Particle in Cell (PIC) Simulation

Microwave tubes in general are devices to convert DC energy into RF energy by means of an electron beam interacting with any kind of structure. A simple form of a microwave tube is a monotron. More complex devices are for examples travelling wave tubes or backward wave oscillators where the beam interacts with a slow wave structure to amplify an RF wave.

In case of the monotron the device is self excited by the beam and the interaction takes place with the TM010 Mode of the cavity. The actual design considerations are described in [1]. The simulations are performed with the 3D Particle in Cell code of CST PARTICLE STUDIO® (CST PS).

In figure 1 the geometry of the monotron is shown. Basically it consists of 2 cavities coupled by a slot which also provides the path for the beam. In red the particle source is shown. The particles are emitted as DC current with 20keV beam voltage and a current of 10A according to [1].

There are several possibilites to analyze the structure. One is to evaluate the electromagntetic field, which can be done with field probes known from CST MWS. The probe monitors the electric/magnetic field versus time of the specified component at a defined point. The position of the field probe used in this case is y=0.8cm and z=2.6cm as shown in figure 2.

The signal monitored by the probe is depicted in figure 3 (left). As can be seen the oscillation builts up for t>400ns and stabilizes for t>750ns which agrees quite well with the predictions made in [1].

Furthermore the frequency spectrum (figure 3, right) of the probe signal shows the peak at 4GHz and higher order harmonics as expected due to the design goal of the monotron.

With a particle monitor the evolution of the beam can be visualized. Figure 4 shows the beam at the beginning of the interaction process (@100ns). Since only a very small electromagnetic field has been created so far, the beam propagates almost unchanged through the cavities. The particles energy stays at the 20keV input energy.

In Figure 5 the particle trajectory in the saturation regime is shown. Obviously the trajectory has changed due to the interaction of the particles to the Eigenmode within the cavity. The plot also illustrates with the colour indication that the beam has lost energy to the created Eigenmode field, since the particles show an energy less than 20keV.

A more quantitative evaluation of the particles' energy is possible with phase space plots, where the energy of every living particle is recorded versus the longitudinal direction. For the example under discussion the phase space plot at 800ns (saturation regime) is shown on the left hand side of figure 6. This plot verifies nicely the particles' loss of energy. At the input (z=0cm) all particles show an energy of 20keV and at the end section (z=3.8cm) the particles energy is below 13.5keV.

The electron population at the end section (z=3.75cm-3.8cm) is shown in more detail on the right hand side of figure 6. When exiting the cavity most electrons have an energy of 4.5keV which agrees again well to the predicitions made in [1].

This article demonstrates that simulations of microwave tubes -in this example a monotron- can be conveniently performed with CST PS. The results of this simulation show good agreement to published results [1]. 

References:

[1]  Joaquim J. Barroso, "Design Study of a Two-Cavity Monotron", Proceedings of the IVEC 2009, Rome, Italy, April 28-30, pp. 433-434, 2009.