cfsem 5.1.0

Quasi-steady electromagnetics including filamentized approximations, Biot-Savart, and Grad-Shafranov.
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# cfsem python examples

## Field Explorer

In this interactive example, examine the B-field and A-field of cfsem's finite-length-finite-thickness filament calcs
and compare to point-source calculations, section discretizations, and $B = \nabla \times A$ equivalence tests.

The full example can be run like `uv run --group dev examples/field_explorer.py`; the plot shown below is only an excerpt.

<figure markdown="span">
  <iframe
    class="plotly-embed"
    loading="lazy"
    src="../example_outputs/field_explorer.html"
    title="Field explorer example"
  ></iframe>
  <figcaption>
    B-field of an arrangement of finite-length, finite-thickness filaments.
  </figcaption>
</figure>

## Helmholtz Coil Pair

This example uses [cfsem.flux_density_circular_filament][] to map the B-field of
a [Helmholtz coil pair](https://en.wikipedia.org/wiki/Helmholtz_coil),
an arrangement of two circular coils which produces a region of
nearly uniform magnetic field.

<figure markdown="span">
  ![Helmholtz coil example](example_outputs/helmholtz.png)
  <figcaption>
    B-field of a Helmholtz coil, calculated with cfsem.
    On the left, the red dashes outline where the B-field magnitude is within 1% of its value at (r=0, z=0), and the black dots show where the coils intersect the r-z plane.
  </figcaption>
</figure>

``` py title="examples/helmholtz.py"
--8<-- "examples/helmholtz.py"
```

## High-aspect-ratio Coil Inductance

Estimate the (low-frequency) self- and mutual- inductance of a pair of air-core solenoids,
comparing results from modeling as either collections of axisymmetric loops or
as thin helical filaments.

``` py title="examples/inductance.py"
--8<-- "examples/inductance.py"
```

## Loop Inductance

Estimate the (low-frequency) self-inductance of a finite-radius wire loop by different methods.

<figure markdown="span">
  ![Helmholtz coil example](example_outputs/loop_inductance.png)
  <figcaption>
    Inductance of a wire loop by different integration methods.
  </figcaption>
</figure>