Nils Berglund | Non-coherent waves in a magnetron-shaped resonator @NilsBerglund | Uploaded August 2024 | Updated October 2024, 3 minutes ago.
In this simulation of waves in a magnetron-shaped resonator, I followed a suggestion in comments to use sources with different frequencies and phases. There are ten wave sources, which start all slightly out of phase, and have slightly different frequencies. This can be seen as a way to model the random aspects of electron emission in a real magnetron, though this simulation remains a simplified model of that.
Magnetrons were used in early radars, and are still used in microwave ovens, as sources of the microwaves. Cavity magnetrons use a resonating cavity with several chambers, together with a magnetic field. In this simulation, there is no magnetic field, and waves are produced as pulses near the center of the device, so it does not represent a real magnetron. However, I still found it interesting to look at the effect of the resonating cavities on the output.
Since this simulation is in 2D, I added a channel at one side to act as an outlet for the waves. In 3D, my understanding is that the outlet would rather be along the axis of the device.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 1:48
In the first part, the color hue depends on the height of the wave. In the second part, it depends on the energy of the wave, averaged over a sliding time window. The contrast has been enhanced by a shading procedure, similar to the one I have used in videos of reaction-diffusion equations. The process is to compute the normal vector to a surface in 3D that would be obtained by using the third dimension to represent the field, and then to make the luminosity depend on the angle between the normal vector and a fixed direction.
There are absorbing boundary conditions on the borders of the simulated rectangle. The graph at the right shows a slightly time-averaged version of the signal.
Render time: 44 minutes 2 seconds
Compression: crf 23
Color scheme: Part 1 - Twilight by Bastian Bechtold
github.com/bastibe/twilight
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap
Music: "Some Other Place" by South London Hifi@discobiscuit1320
See also
https://images.math.cnrs.fr/des-ondes-dans-mon-billard-partie-i/ for more explanations (in French) on a few previous simulations of wave equations.
The simulation solves the wave equation by discretization. The algorithm is adapted from the paper hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf
C code: github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!
#wave #resonator #magnetron
In this simulation of waves in a magnetron-shaped resonator, I followed a suggestion in comments to use sources with different frequencies and phases. There are ten wave sources, which start all slightly out of phase, and have slightly different frequencies. This can be seen as a way to model the random aspects of electron emission in a real magnetron, though this simulation remains a simplified model of that.
Magnetrons were used in early radars, and are still used in microwave ovens, as sources of the microwaves. Cavity magnetrons use a resonating cavity with several chambers, together with a magnetic field. In this simulation, there is no magnetic field, and waves are produced as pulses near the center of the device, so it does not represent a real magnetron. However, I still found it interesting to look at the effect of the resonating cavities on the output.
Since this simulation is in 2D, I added a channel at one side to act as an outlet for the waves. In 3D, my understanding is that the outlet would rather be along the axis of the device.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 1:48
In the first part, the color hue depends on the height of the wave. In the second part, it depends on the energy of the wave, averaged over a sliding time window. The contrast has been enhanced by a shading procedure, similar to the one I have used in videos of reaction-diffusion equations. The process is to compute the normal vector to a surface in 3D that would be obtained by using the third dimension to represent the field, and then to make the luminosity depend on the angle between the normal vector and a fixed direction.
There are absorbing boundary conditions on the borders of the simulated rectangle. The graph at the right shows a slightly time-averaged version of the signal.
Render time: 44 minutes 2 seconds
Compression: crf 23
Color scheme: Part 1 - Twilight by Bastian Bechtold
github.com/bastibe/twilight
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap
Music: "Some Other Place" by South London Hifi@discobiscuit1320
See also
https://images.math.cnrs.fr/des-ondes-dans-mon-billard-partie-i/ for more explanations (in French) on a few previous simulations of wave equations.
The simulation solves the wave equation by discretization. The algorithm is adapted from the paper hplgit.github.io/fdm-book/doc/pub/wave/pdf/wave-4print.pdf
C code: github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html
Many thanks to Marco Mancini and Julian Kauth for helping me to accelerate my code!
#wave #resonator #magnetron
