Interesting! This is similar to the work by Carl Størmer on particles in Earth's inner magnetosphere. There there are regions with long-term trapped particle trajectories which makes up the radiation belts. They were initially thought to be empty - since no particles ought to enter them - but were later found to be filled with rather high-energy electrons and protons. The reason is that the variability of the solar wind that allows particles to fill these trajectories, then the particles remains there and some fraction of them pick up energy. The relation between scale size of the electrical potential and the gyro-radius is obviously "slightly different" than in this simulation...
The time step was probably a bit too large in this simulation. The next sim in this series will use a smaller time step, which fixes the problem to some extent.
If the particle falls in the electrical potential its potential energy decreases and its kinetic energy increases. As long as the particles doesn't collide the total energy around the drifting gyro-orbit should be conserved, but its kinetic energy should vary around the orbit as it is moving up and down the electrical potential. Perhaps this shift of the gyro-centre is the reason for the systematic shift in kinetic energy.
It is indeed the case that the kinetic energy depends on the y coordinate as long as the particles do not hit the obstacle. The kinetic energy varies in fact periodically over time. Hitting the obstacle changes the y coordinate of the gyro-centre, which I agree accounts for part of the variation in kinetic energy. However, the particle circling the obstacle several times also seems to pick up some kinetic energy, which I think is due to round-off errors (though the time step is already much smaller than the what the plotted trajectory may suggest).
I'm using an implicit method adapted from a thermostat (but at zero temperature here, where it should conserve energy), which is quite similar to Størmer-Verlet. So it should perform better than Euler.
Interesting! This is similar to the work by Carl Størmer on particles in Earth's inner magnetosphere. There there are regions with long-term trapped particle trajectories which makes up the radiation belts. They were initially thought to be empty - since no particles ought to enter them - but were later found to be filled with rather high-energy electrons and protons. The reason is that the variability of the solar wind that allows particles to fill these trajectories, then the particles remains there and some fraction of them pick up energy. The relation between scale size of the electrical potential and the gyro-radius is obviously "slightly different" than in this simulation...
Interesting, thanks!
everyone loves a slinky, you're gonna get a slinky. Slinky, slinky, go slinky go!
The right circle for the leaving particle is bigger. This means the particle is faster. Where did that energy come from.
The time step was probably a bit too large in this simulation. The next sim in this series will use a smaller time step, which fixes the problem to some extent.
If the particle falls in the electrical potential its potential energy decreases and its kinetic energy increases. As long as the particles doesn't collide the total energy around the drifting gyro-orbit should be conserved, but its kinetic energy should vary around the orbit as it is moving up and down the electrical potential. Perhaps this shift of the gyro-centre is the reason for the systematic shift in kinetic energy.
It is indeed the case that the kinetic energy depends on the y coordinate as long as the particles do not hit the obstacle. The kinetic energy varies in fact periodically over time. Hitting the obstacle changes the y coordinate of the gyro-centre, which I agree accounts for part of the variation in kinetic energy. However, the particle circling the obstacle several times also seems to pick up some kinetic energy, which I think is due to round-off errors (though the time step is already much smaller than the what the plotted trajectory may suggest).
@@NilsBerglund Are you using a 1'st order method or a fancy higher order energy conserving method?
I'm using an implicit method adapted from a thermostat (but at zero temperature here, where it should conserve energy), which is quite similar to Størmer-Verlet. So it should perform better than Euler.
Though I always think of electrons as non local repulsive/divergent clouds, which feed the convergent localized proton/mass.
What happens if you use a softer potential (such as inverse square) for the obstacle?
I'm not aware that this has been studied, but I could imagine a similar behavior for appropriate parameter values.
@@NilsBerglundMy question was really more of an experimental proposal than a question about the literature. 🙂
What kind of circus act is this
Try reading the description of the video.
@@bjornfeuerbacher5514 I did
Salto electromagnetico?