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CST – Computer Simulation Technology

Electron Gun for a 6-18GHz, 20W Helix-TWT Amplifier

Electron guns are the starting point of every charged particle application. There, the DC energy is translated into an extracted beam, which later on interacts with all kinds of EM structures. The basic principle of an electron tube is shown in figure 1.



Figure 1: Schematic of an electron tube

The electron gun has to provide the slow wave structure with a beam, which then interacts with the electromagnetic wave existing in the structure and finally is collected in the collector. In order to enable the interaction, the particles' velocity has to match the EM-wave's velocity on the circuit. This velocity can a priori be found out via a dispersion analysis, explained in the article "Periodic Eigenmode Simulation of a Traveling Wave Tube". The necessary velocity determines the voltage to be applied. The electron gun then has to be designed in a way, that the emitted current is maximized....



Figure 2: Structure of the electron gun, cut through view (left) full model (right)

The structure of the electron gun discussed in this article is shown in figure 2. The relevant parts for the Electrostatic (Es) simulation are the cathode, focusing electrode and anode (left). Important for the Magnetostatic (Ms) simulation are the iron yoke and permanent magnets. The potentials and permanent magnets serve as sources for the Es and Ms solver of CST EM STUDIO® (here run from CST PARTICLE STUDIO®) respectively. They are shown in more detail in figure 3. The iron yoke is considered as non-linear material, where the working point is obtained by a non-linear iteration scheme in the Ms solver.



Figure 3: Sources of the Electrostatic (left) and Magnetostatic (right) simulation

The potentials applied to the metal bodies result in the electric potential distribution (isolines) and the electrostatic field (arrows) shown in figure 4. This electric field serves for accelerating the particles to the desired velocity. During the emission process the electron cloud in front of the cathode is taken into account by means of a space charge limited emission. Furthermore the beam's space charge throughout the calculation domain is considered via a gun iteration available in the tracking code of CST PARTICLE STUDIO (CST PS).



Figure 4: Electrostatic potential (isolines) and field (arrows)

In order to keep the beam focused a periodic permanent magnet (PPM) stackup is applied as explained above. The resulting magnetic field is shown in figure 5 (left). Additionally a 1D description of the longitudinal field vs. longitudinal axis is depicted on the right.



Figure 5: 2D view of the B-field (left) and 1D description of Bx vs. x (right)

After introducing the particles, CST PS will give the resulting trajectory as shown in figure 6 (left). The colour indicates quite nicely the increase in velocity during the particles' propagation through the Es-field. When entering the PPM region, the focusing starts which leads to the undulated trajectories. Since the Ms field cannot accelerate or decelerate the particles, the velocity in this area and therefore the trajectory's colour is unchanged.

The convergence of the emitted current is shown in figure 6 (right). The resulting current matches quite well to the design value of 41mA.



Figure 6: Particle trajectory (left) and emitted source current (right)

This article shows the workflow and typical settings of an electron gun simulation. Such a simulation can be performed within the tracking code of CST PS, which is using the electrostatic and magnetostatic solvers of CST EM STUDIO. The space charge can be easily included with a so called "gun iteration". Current and trajectory are directly given and can be further postprocessed within the CST STUDIO SUITE®.

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