Simulation of gyrotrons using the high-order methods
High-power microwave generation is possible by using gyrotron devices that provide millimeter and upper sub-millimeter range radiation. The kinetic energy of an accelerated electron hollow beam is converted into electromagnetic energy by utilizing the electron cyclotron resonance (ECR) instability. Due to the inaccessibility of measurements in the core part of the gyrotron, which is a vacuum tube, simulations can offer significant insight into the relevant physics at nowadays moderate computational costs. Therefore, the Particle-In-Cell (PIC) method, which is accompanied by a long history of development, is a prominent example of kinetic methods that are able to tackle these problems accurately. Here, high-order PIC methods are utilized, which offer different advantages as compared with low-order frameworks.
Advantages of PICLas
The simulation tool PICLas, which is applied here, combines multiples advantages as compared with current state-of-the are codes for the simulation of gyrotron devices. Key features are:
- High physical detail due to advanced numerical modelling by coupling finite-element and finite-volume schemes
- Simulation run on 3456 CPU cores (144 nodes each with 24 cores) due to excellent scalability and adaptive load-balancing techniques
- Non-conforming and curvilinear mesh generation with HOPR
- High-order DG methods for drastically reduced degrees of freedom for the field solver
1 MW 140 GHz Gyrotron for Wendelstein 7-X
A 140 GHz gyrotron operating in a TE28,8 mode has been designed to provide the required power in the MW range for the ECR heating system of the experimental fusion reactor Wendelstein 7-X, which is located in Greifswald, Germany. Simulations of the core part of the gyrotron, the resonant cavity, as well as the adjacent geometry have been conducted by high-order PIC simulations. Therefore, an electron hollow beam in injected into a rotationally symmetric geometry. When the electron beam reaches the resonant cavity, the TE28,8 mode is self-excited, draining the kinetic energy of the electron hollow beam. An image of the gyrotron as well as the region of interest, which is considered in the simulation is shown in the pictures below (Photograph (left) by Z6ehswhha5HGRTd - Own work. Licensed under CC BY-SA 4.0, via Wikimedia Commons).
Simulation results are available in form of particle information and field variables. In the figure, a distinct mode pattern, the TE28,8 mode, is visible within the resonant cavity as indicated by the azimuthal electric field. This mode travels down-stream, is converted into a Gaussian shape by a special set of mirrors and is extracted from the gyrotron device.
The video below shows the gyrotron device in operation, where the electron hollow beam is injected from the left, travels through the geometry and exits on the right. In the center of the device, the resonant cavity, the energy conversion takes place. Here, the 140 GHz TE28,8 mode is excited. No physical assumptions within the utilized PIC model have to be applied in order for the correct mode and frequency to be excited.
More information regarding the applied theory and modelling:
- Copplestone, S. M., Ortwein, P., Munz, C.-D., Avramidis, K. A., Jelonnek, J. (2017). Simulation of gyrotrons using the high-order particle-in-cell code PICLas. EPJ Web Conf., 149, 4019.
- Ortwein, P., Copplestone, S. M., Munz, C.-D., Marek, A., Jelonnek, J., Ortwein, P., … Jelonnek, J. (2017). Benchmarking a high-order particle-in-cell code for the simulation of a gyrotron traveling-wave tube. EPJ Web Conf., 149, 4020.