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Cyclotron simulation
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I'm trying to simulate a Cyclotron, as the attached mp4 video, but have no idea. Please help!
Refer to this link below.
http://hyperphysics.phyast...
Some considerations,
1. time slider is the animation, so particle velocity changes can be shown.
2. Consider the effect of relativistic effects on the mass of the particle.
3. In CAS, I want to get the acceleration as a function of time, but failed.
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Certainly an unexpected solution and without any calculations but assuming that the gap between the two electrodes is 0 (what is not the case).
The (constant) frequency is given by the speed of E. The visual speed increase is obtained by the (ggb) fact that the 11 semicircles (plus 1 segment = 12 elements) are passed each (element) in the same time (with longer way).
I mean: this corresponds exactly to the mode of action of a cyclotron. Of course without taking into account the voltage and the associated acceleration between the electrodes as well as the power of the magnets. This is implicitly given by the larger radius and speedE.
Seems can't upload mp4 file.
here is the link: https://v.qq.com/x/page/s01...
and a snapshot
Certainly an unexpected solution and without any calculations but assuming that the gap between the two electrodes is 0 (what is not the case).
The (constant) frequency is given by the speed of E. The visual speed increase is obtained by the (ggb) fact that the 11 semicircles (plus 1 segment = 12 elements) are passed each (element) in the same time (with longer way).
I mean: this corresponds exactly to the mode of action of a cyclotron. Of course without taking into account the voltage and the associated acceleration between the electrodes as well as the power of the magnets. This is implicitly given by the larger radius and speedE.
Attached my solution.
The two solutions agree (exactly enough).
In my solution the number of cycles are variable and I used your cleaned background image.
In addition, a checkbox lets you project your graphic semitransparently over my solution.

I interpreted your function for the radii as recursive and did not understand it either.
Therefore I have derived the function vRad_n as follows:
If we set all constant variables in the function for the velocity (v) equal to 1, the variable cycle remains.
This results in the function f(x)=sqrt(x) where x corresponds to the cycle. The radii are proportional to this.
The largest radius (maxRad) determines the factor by which f(x) must be multiplied to obtain the radii.
vRad_n(x)=f(x)/f(maxRad)*maxRad.
The first cycle results in an insignificant deviation from your solution, which I did not examine more.
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