Nils Berglund | Cherenkov radiation of an even faster particle @NilsBerglund | Uploaded May 2024 | Updated October 2024, 2 hours ago.
In this third simulation of Cherenkov radiation, the speed of light in the medium has been reduced by a factor 1.5, compared to the one used in the video youtu.be/BpkKYLuwRlc . As a result, the shock wave created when the local speed of light becomes smaller than the speed of the particle occurs earlier. I don't have a good explanation for the envelope of the created wave, but I think it is due a combination of the space-dependent speed of light and interference of waves emitted at different times. If anyone has a more precise explanation, feel free to comment.
Update: I finally found the origin of this "singularity", which is, sadly, a mistake in the way I initialized the refractive index of the medium. Instead of decreasing linearly while remaining positive, the wave speed in the medium decreases linearly, then reaches zero, and then increases linearly again. The singularity happens where the wave speed vanishes. A corrected version will be released in a couple of days.
Cherenkov radiation is produced when a fast moving particle enters a medium in which the speed of light is smaller than the speed of the particle. This does not contradict special relativity, because only the speed of light in a vacuum cannot be reached by a massive particle, while the speed of light in a medium is in general smaller than in a vacuum.
In this simulation, a particle moves at constant speed from left to right, emitting pulses at regular time intervals. The speed of light decreases linearly, reaches zero and increases linearly again. The ratio of the indices between the left to the right boundary of the simulation rectangle is 2.78. When the speed of light in the medium becomes smaller than the speed of a particle, a shock wave appears, which is the origin of Cherenkov radiation.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 1:12
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.
There are absorbing boundary conditions on the borders of the simulated rectangle. The display at the bottom shows the signal along a horizontal line, slightly below the path of the particle.
Render time: 22 minutes 48 seconds
Compression: crf 23
Color scheme: Part 1 - Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firing
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap
Music: "Meditation" by Silent Partner
See also https://images.math.cnrs.fr/Des-ondes-dans-mon-billard-partie-I.html 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 #Cherenkov #shock_wave
In this third simulation of Cherenkov radiation, the speed of light in the medium has been reduced by a factor 1.5, compared to the one used in the video youtu.be/BpkKYLuwRlc . As a result, the shock wave created when the local speed of light becomes smaller than the speed of the particle occurs earlier. I don't have a good explanation for the envelope of the created wave, but I think it is due a combination of the space-dependent speed of light and interference of waves emitted at different times. If anyone has a more precise explanation, feel free to comment.
Update: I finally found the origin of this "singularity", which is, sadly, a mistake in the way I initialized the refractive index of the medium. Instead of decreasing linearly while remaining positive, the wave speed in the medium decreases linearly, then reaches zero, and then increases linearly again. The singularity happens where the wave speed vanishes. A corrected version will be released in a couple of days.
Cherenkov radiation is produced when a fast moving particle enters a medium in which the speed of light is smaller than the speed of the particle. This does not contradict special relativity, because only the speed of light in a vacuum cannot be reached by a massive particle, while the speed of light in a medium is in general smaller than in a vacuum.
In this simulation, a particle moves at constant speed from left to right, emitting pulses at regular time intervals. The speed of light decreases linearly, reaches zero and increases linearly again. The ratio of the indices between the left to the right boundary of the simulation rectangle is 2.78. When the speed of light in the medium becomes smaller than the speed of a particle, a shock wave appears, which is the origin of Cherenkov radiation.
This video has two parts, showing the same evolution with two different color gradients:
Wave height: 0:00
Averaged wave energy: 1:12
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.
There are absorbing boundary conditions on the borders of the simulated rectangle. The display at the bottom shows the signal along a horizontal line, slightly below the path of the particle.
Render time: 22 minutes 48 seconds
Compression: crf 23
Color scheme: Part 1 - Viridis by Nathaniel J. Smith, Stefan van der Walt and Eric Firing
Part 2 - Inferno by Nathaniel J. Smith and Stefan van der Walt
github.com/BIDS/colormap
Music: "Meditation" by Silent Partner
See also https://images.math.cnrs.fr/Des-ondes-dans-mon-billard-partie-I.html 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 #Cherenkov #shock_wave
