Creating field-aligned meshes

FusionSC can used its field line maps to transform meshes between field-aligned coordinates and real-space. This examples shows how to move between the different views.

import fusionsc as fsc
from fusionsc.devices import w7x

import numpy as np
import matplotlib.pyplot as plt

import pyvista as pv
pv.set_jupyter_backend('static')

For this example, we want to use standard configuration and the lower W7-X divertors in modules 1 and 2

geo = w7x.divertor().filter({"moduleNo" : [1, 2], "upper" : 0}).merge()
mapping = w7x.computeMapping(w7x.standard())

geo.asPyvista().plot()

# TODO: Remove after release
fsc.backends.alwaysUseBackend(fsc.backends.localBackend())

Let’s have a look what the divertor looks like in straight-field coordinates. We expand around the divertor bean plane at phi = 0.

fa = geo.triangulate(0.01).toFieldAligned(mapping, r0 = 5.5, phi0 = 0)
fa.asPyvista().plot(cpos = [[6,-10,-0.5],[5.5,6,-0.5],[0,0,1]])

C:\Users\Knieps\Documents\repos\fsc\src\python\fusionsc\_api_markers.py:15: UserWarning: The function fusionsc.geometry.Geometry.toFieldAligned is part of the unstable API. It might change or get removed in the near future. While unlikely, it might also not be compatible across client/server versions.
  warnings.warn(f"The function {f.__module__}.{f.__qualname__} is part of the unstable API. It might change or get removed in the near future. While unlikely, it might also not be compatible across client/server versions.")

It appears that the divertor is indeed fairly straight when viewed in field-aligned coordinates. However, it can also be seen that the next divertor appears quite deformed in that perspective (which makes sense, as it should be covering a different flux tube).

fa.asPyvista().plot(cpos = [[3,25,0],[5.5,40,0],[0,0,1]])

On the other hand, if we were to try to design our own divertor structure, it helps a lot to create these in field aligned coordinates. In this case, we show that by just setting up two quads in field-aligned space. To do this, we use the “quadMesh” function that creates quad meshes from N by M grids in 2D space. For the fun of it, we will also give the parts a 1 degree pitch angle against the magnetic field.

z1 = -0.5
z2 = 0.5

quad1 = [
    [[5.5, 5.7], [5.5, 5.7]], # X values of corners on 2x2 grid
    [[-10, -10], [10, 10]], # Y values of cornerss on 2x2 grid
    [[z1, z1], [z1, z1]] # Z values of cornerss on 2x2 grid
]

quad2 = [
    [[5.5, 5.7], [5.5, 5.7]],
    [[-10, -10], [10, 10]],
    [[z2, z2], [z2, z2]]
]

geo1 = fsc.geometry.Geometry.quadMesh(quad1)
geo2 = fsc.geometry.Geometry.quadMesh(quad2)

pitchAngle = np.radians(1) # Pitch angle of 5 degrees
# Note: rotate can also rotate around non-origin centers, but we just
# want to rotate around [0,0,0] so we omit the "center" argument
geo1 = geo1.rotate(-pitchAngle, axis = [1,0,0])
geo2 = geo2.rotate(pitchAngle, axis = [1,0,0])

geoIn = geo1 + geo2
geoIn.asPyvista().plot(jupyter_backend="static")

To make sure we follow the curve of the field in the geometry, we first upsample the quads to 1cm edge length, then transform from field space into real-space.

newGeo = geoIn.triangulate(0.01).fromFieldAligned(mapping, 5.5, 0)
newGeo.asPyvista().plot()

C:\Users\Knieps\Documents\repos\fsc\src\python\fusionsc\_api_markers.py:15: UserWarning: The function fusionsc.geometry.Geometry.fromFieldAligned is part of the unstable API. It might change or get removed in the near future. While unlikely, it might also not be compatible across client/server versions.
  warnings.warn(f"The function {f.__module__}.{f.__qualname__} is part of the unstable API. It might change or get removed in the near future. While unlikely, it might also not be compatible across client/server versions.")