Paraxial field of a solenoid
solenoid-pedge.biot |
BiotSavart version 4.0.14 introduced sophisticated paraxial calculations from the paper by R.H. Jackson. To validate the implementation in the case of a solenoid we use the example provided by Jackson and calculate the magnetic field along the inner edge.
R.H. Jackson, "Off-axis expansion solution of Laplace's equation: Application to accurate and rapid calculation of coil magnetic fields", IEEE Transactions on Electron Devices 46 (1999) 1050.
The specifications of the coil from the article are
Coil inner radius | 4 cm |
Coil outer radius | 6 cm |
Coil length | 20 cm |
Current density | 100 A/cm^2 |
Current | 4000 A |
The coil (cutaway view) and probes:
Results
The calculated magnetic field is accurate right up to the inner surface of the solenoid. At r=4cm and z=0cm we have the following comparison between paraxial solenoid field and field obtained by discretizing with indicated resolution and using non-paraxial loop field as integration kernel:
Paraxial field | 22.853 mT |
Discrete (1mm resolution) | 22.801 mT |
Discrete (0.5mm resolution) | 22.827 mT |
For paraxial calculation the exported field is found in file export-field.txt which has the following contents:
4.000000e-02 0.000000e+00 -7.500000e-01 -1.256201e-06 0.000000e+00 1.538942e-05 1.544061e-05 4.000000e-02 0.000000e+00 -7.400000e-01 -1.326900e-06 0.000000e+00 1.603011e-05 1.608494e-05 4.000000e-02 0.000000e+00 -7.300000e-01 -1.402661e-06 0.000000e+00 1.670698e-05 1.676576e-05 4.000000e-02 0.000000e+00 -7.200000e-01 -1.483929e-06 0.000000e+00 1.742261e-05 1.748569e-05 4.000000e-02 0.000000e+00 -7.100000e-01 -1.571192e-06 0.000000e+00 1.817984e-05 1.824761e-05 4.000000e-02 0.000000e+00 -7.000000e-01 -1.664990e-06 0.000000e+00 1.898173e-05 1.905461e-05 4.000000e-02 0.000000e+00 -6.900000e-01 -1.765924e-06 0.000000e+00 1.983165e-05 1.991012e-05 4.000000e-02 0.000000e+00 -6.800000e-01 -1.874656e-06 0.000000e+00 2.073325e-05 2.081782e-05 4.000000e-02 0.000000e+00 -6.700000e-01 -1.991923e-06 0.000000e+00 2.169053e-05 2.178180e-05 4.000000e-02 0.000000e+00 -6.600000e-01 -2.118547e-06 0.000000e+00 2.270787e-05 2.280648e-05 4.000000e-02 0.000000e+00 -6.500000e-01 -2.255440e-06 0.000000e+00 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