Paraxial calculations

BiotSavart implements the accurate paraxial calculations for loops and solenoids described in

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) 1050-1062.

Paraxial calculation allows fast and accurate computuation of magnetic fields when the probe point is sufficiently close to the axis of the coil. In the case of a solenoid the expansion can be quite accurate right up to the inner radius of the solenoid.

To enable paraxial calculation, go to the Calc tab of the edit window for the particular Loop or Solenoid object. Check the paraxial checkbox, and enter a value for the distance from the axis below which the paraxial calculation will be employed.

Changes to the paraxial checkbox and cutoff distance take effect immediately: if AutoRecompute is enabled, field probes will recalculate right away.

Here is an example showing how to set a solenoid to calculate paraxially for probe points whose distance to the axis of the solenoid is less than 3mm:

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Note that for a solenoid the normal "sum over loops" calculation will differ from the paraxial calculation even on-axis, where the paraxial calculation is exact. Thus the paraxial mode may be used to examine the accuracy obtained for a given subdivision resolution.