We create a cube polywell with following parameters: coil radius 0.15m, coil thickness 0.07m, coil spacing 0.01m, current in coils 200,000 amperes. Coils are kept at potential 10,000V. We surround the system with a faraday cage like construction - kept at ground (0V) potential.
We calculate the electric field resulting from the static structures using this method.
We inject 500 electrons into the system (injection points marked as blue crosses on the images). We let the particles run and sample their positions and speeds at random intervals (particles do not interact with each-other). We get 100,000 samples. Then we map those 100,000 samples into 48 sectors using inherent symmetries and so get 4,800,000 samples.
The sampled particle positions and velocity vectors are used to calculate magnetic and electric fields using these methods and some averaging (somewhat dodgy algorithm, I have to admit). The resulting fields are amplified so that the total charge for magnetic field is -3e-2C, but the amplification for e-field is divided by 5e5 from that so net electric charge is -6e-8C.
The calculated fields are applied on the system and a new set of electrons are injected and sampled.
Note: field levels/colors on different images have not been synced so should not be compared.
| Simulated electron samples mapped into 48 sectors |
Electric potential |
Magnetic field |
Magnetic field, logarithmic |
Magnetic field, field lines |
Electric field |
Electric field, logarithmic |
Electric field, field lines |
Magnetic field generated by the particles during the last step |
Magnetic field generated by the particles during the last step, logarithmic |
Magnetic field generated by the particles during the last step, field lines |
Electric field generated by the particles during the last step |
Electric field generated by the particles during the last step, logarithmic |
Electric field generated by the particles during the last step, field lines |
Charge distribution on coils |
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This is not a true wiffleball simulation but rather an attempt to see whether diamagnetism works and how it scales. I think the field within the ball should be close to 0, in that sense this simulation here is not true. I think this is also the reason for why we don't see that much added confinement here. My field calculation techniques are not perfect either (I'm not strictly speaking using PIC here but my own home-grown algorithm).
A few more technical details: for particle simulations (and visualizations) fields were calculated using tri-cubic interpolation (with 48-symmetry reduction), with cell side 0.0075m. Except the coil generated magnetic field where bicubic interpolation was used instead. Also at calculating input for the tricubic interpolation at greater distances the charges and speeds were aggregated into cells (again 0.0075m cells) and in case the field position was more than 5 cell sides away the aggregated charges and speeds were used (direct particles' positions otherwise). During the simulations electrons' energy peaked at ~9500 eV range which is close to 0.2c.