desc.coils.FourierPlanarCoil

class desc.coils.FourierPlanarCoil(current=1, center=[10, 0, 0], normal=[0, 1, 0], r_n=2, modes=None, basis='xyz', name='')Source 

Coil that lies in a plane.

Parameterized by a point (the center of the coil), a vector (normal to the plane), and a Fourier series defining the radius from the center as a function of the polar angle theta.

Parameters:

current (float) – Current through the coil, in Amperes.
center (array-like, shape(3,)) – Coordinates of center of curve, in system determined by basis.
normal (array-like, shape(3,)) – Components of normal vector to planar surface, in system determined by basis.
r_n (array-like) – Fourier coefficients for radius from center as function of polar angle
modes (array-like) – mode numbers associated with r_n
basis ({'xyz', 'rpz'}) – Coordinate system for center and normal vectors. Default = ‘xyz’.
name (str) – Name for this coil

Examples

from desc.coils import FourierPlanarCoil
from desc.grid import LinearGrid
import numpy as np

I = 10
mu0 = 4 * np.pi * 1e-7
R_coil = 10
# circular coil given by center at (0,0,0)
# and normal vector in Z direction (0,0,1) and radius 10
coil = FourierPlanarCoil(
    current=I,
    center=[0, 0, 0],
    normal=[0, 0, 1],
    r_n=R_coil,
    modes=[0],
)
z0 = 10
field_evaluated = coil.compute_magnetic_field(
    np.array([[0, 0, 0], [0, 0, z0]]), basis="rpz"
)
np.testing.assert_allclose(
    field_evaluated[0, :], np.array([0, 0, mu0 * I / 2 / R_coil]), atol=1e-8
)
np.testing.assert_allclose(
    field_evaluated[1, :],
    np.array([0, 0, mu0 * I / 2 * R_coil**2 / (R_coil**2 + z0**2) ** (3 / 2)]),
    atol=1e-8,
)

Methods

`change_resolution`([N])	Change the maximum angular resolution.
`compute`(names[, grid, params, transforms, ...])	Compute the quantity given by name on grid.
`compute_Bnormal`(surface[, eval_grid, ...])	Compute Bnormal from self on the given surface.
`compute_magnetic_field`(coords[, params, ...])	Compute magnetic field at a set of points.
`compute_magnetic_vector_potential`(coords[, ...])	Compute magnetic vector potential at a set of points.
`copy`([deepcopy])	Return a (deep)copy of this object.
`equiv`(other)	Compare equivalence between DESC objects.
`flip`([normal])	Flip the curve about the plane with specified normal in X,Y,Z coordinates.
`from_values`(current, coords[, N, basis, name])	Fit coordinates to FourierPlanarCoil representation.
`get_coeffs`(n)	Get Fourier coefficients for given mode number(s).
`load`(load_from[, file_format])	Initialize from file.
`pack_params`(p)	Convert a dictionary of parameters into a single array.
`rotate`([axis, angle])	Rotate the curve by a fixed angle about axis in X,Y,Z coordinates.
`save`(file_name[, file_format, file_mode])	Save the object.
`save_BNORM_file`(surface, fname[, basis_M, ...])	Create BNORM-style .txt file containing Bnormal Fourier coefficients.
`save_mgrid`(path, Rmin, Rmax, Zmin, Zmax[, ...])	Save the magnetic field to an mgrid NetCDF file in "raw" format.
`set_coeffs`(n[, r])	Set specific Fourier coefficients.
`to_FourierPlanar`([N, grid, basis, name])	Convert Coil to FourierPlanarCoil representation.
`to_FourierRZ`([N, grid, NFP, sym, name])	Convert Coil to FourierRZCoil representation.
`to_FourierXY`([N, grid, s, basis, name])	Convert Coil to FourierXYCoil representation.
`to_FourierXYZ`([N, grid, s, name])	Convert coil to FourierXYZCoil representation.
`to_SplineXYZ`([knots, grid, method, name])	Convert coil to SplineXYZCoil.
`translate`([displacement])	Translate the curve by a rigid displacement in X,Y,Z coordinates.
`unpack_params`(x)	Convert a single array of concatenated parameters into a dictionary.

Attributes

`N`	Maximum mode number.
`basis`	Coordinate system for center and normal vectors.
`center`	Center of planar curve polar coordinates.
`current`	Current passing through the coil, in Amperes.
`dim_x`	total number of optimizable parameters.
`dimensions`	dictionary of integers of sizes of each optimizable parameter.
`name`	Name of the curve.
`normal`	Normal vector to plane.
`num_coils`	Number of coils.
`optimizable_params`	string names of parameters that have been declared optimizable.
`params_dict`	dictionary of arrays of optimizable parameters.
`r_basis`	Spectral basis for Fourier series.
`r_n`	Spectral coefficients for r.
`rotmat`	Rotation matrix of curve in X, Y, Z.
`shift`	Displacement of curve in X, Y, Z.
`x_idx`	arrays of indices for each parameter in concatenated array.