We create a cube polywell with following parameters: coil radius 0.15m, coil thickness 0.07m, coil spacing 0.01m. Coils
are kept at potential 10000V. We add 8 electron guns at the corners and surround the system with a faraday cage
like construction - both structures kept at ground (0V) potential.
The effective potential well is less than the difference of the potential in the middle and at the coils.
The reason is that at faces the potential does not reach coil levels so ions would be able to escape.
We add a sphere of uniform charge (charge density within the sphere is constant) with radius 0.1m
in the middle of the system. Lets visualize the fields at different charge levels.
The calculation method is "lines of linear charge distribution". Field levels on different pictures can be compared. You can click on pictures to get a better view.
| Configuration |
Potential well |
Electric field magnitude |
Logarithmic field magnitude |
Field lines |
Relative charge distribution |
Coil voltage = 10000.00 V
Space charge = -0.00000e+00 C
Potential in the middle: 9701.34 V
Potential well: 0.00 V
Electron acceleration: 9811.74 V
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Coil voltage = 10000.00 V
Space charge = -1.50000e-08 C
Potential in the middle: 8251.21 V
Potential well: 918.21 V
Electron acceleration: 9700.67 V
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Coil voltage = 10000.00 V
Space charge = -3.00000e-08 C
Potential in the middle: 6801.09 V
Potential well: 2083.02 V
Electron acceleration: 9620.79 V
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Coil voltage = 10000.00 V
Space charge = -4.50000e-08 C
Potential in the middle: 5350.96 V
Potential well: 3310.44 V
Electron acceleration: 9554.86 V
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Coil voltage = 10000.00 V
Space charge = -6.00000e-08 C
Potential in the middle: 3900.84 V
Potential well: 4572.66 V
Electron acceleration: 9497.50 V
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Coil voltage = 10000.00 V
Space charge = -7.50000e-08 C
Potential in the middle: 2450.71 V
Potential well: 5857.98 V
Electron acceleration: 9446.11 V
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Coil voltage = 10000.00 V
Space charge = -9.00000e-08 C
Potential in the middle: 1000.59 V
Potential well: 7160.12 V
Electron acceleration: 9399.22 V
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Coil voltage = 10000.00 V
Space charge = -1.05000e-07 C
Potential in the middle: -449.54 V
Potential well: 8475.22 V
Electron acceleration: 9355.85 V
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Coil voltage = 10000.00 V
Space charge = -1.20000e-07 C
Potential in the middle: -1899.66 V
Potential well: 9800.69 V
Electron acceleration: 9315.34 V
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Coil voltage = 10000.00 V
Space charge = -1.35000e-07 C
Potential in the middle: -3349.79 V
Potential well: 11134.72 V
Electron acceleration: 9277.23 V
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Lets see how the potential well and electron acceleration from the electron gun towards the system relate to the space charge in the middle.
For geometric clarity here's a picture showing where exactly the field is shown (I omited one of the coils for clarity):
