Coil designs
Geometry. Winding. Field.
Real numerical examples from the CoilGen2 repository, with the calculated fields and their evaluation context.
01 / Current GitHub gallery
Gradient and shim designs.
Four saved examples from the ISMRM 2027 abstract draft: shielded y-gradient, biplanar x-gradient, cylindrical X²−Y² shim and conical Z2 shim.
| Design | ROI radius (mm) | Efficiency | Relative RMS Bz error (%) |
|---|---|---|---|
| Shielded y-gradient | 20 | 1.759mT/(m·A) | 4.432 |
| Biplanar x-gradient | 20 | 1.636mT/(m·A) | 11.766 |
| Cylindrical X²−Y² shim | 20 | 12.635mT/(m²·A) | 4.572 |
| Conical Z2 shim | 50 | 2.442mT/(m²·A) | 10.577 |
Efficiency in physical units: Achieved field coefficient divided by the common current through each coil part: mT/(m·A) for linear gradients and mT/(m²·A) for second-order shims. Coefficients are fitted to the mounted-centerline Bz field over 2,048 independent ROI points. The shim fit includes an offset, all three linear terms and all five second-order harmonic terms. Currents are not added across parts. Gradient calculation ↗ · Shim calculation ↗
Field error: The relative RMS Bz errors use the original fixed-current fields, without fitting gain or offset. The descriptive coefficient fits do not change these errors.
| Shim | Target strength (mT/m²) | Current used (A) |
|---|---|---|
| Cylindrical X²−Y² shim | 25.000 | +1.921 |
| Conical Z2 shim | 4.000 | +1.601 |
Polynomial conventions: X²−Y²: Bz = S(x²−y²). Z2: Bz = S[z²−(x²+y²)/2]. Coordinates are in metres; S is in mT/m² and Bz is in mT. The table gives the target S. Efficiencies use the achieved fitted S; current signs refer to the saved winding direction.
Interpretation: These are numerical designs. The illustrated shim sweep failed configured geometric checks; fabrication qualification and hardware performance are separate.
Stage comparisons, methods & provenance ↗02 / Surface-current examples
See the solution before routing.
A cylindrical Gy and a biplanar Gz example show the relation between optimized current sheets, extracted turns and calculated fields.
These examples use a 10 mT/m target and a 90 mm diameter spherical target volume. A separate untouched 1,472-point holdout is documented in the source. These values describe the contour stage, not connected winding performance.
03 / Field validation
Compare the field, not just the shape.
Evaluate the current sheet and processed contours against the target. Track discretization and processing error before making downstream design decisions.
Example applications
Start from a documented project.
The repository includes conventional three-axis gradients, biplanar systems, Halbach-oriented geometries. These are computational starting points with application-specific assumptions.