desc.magnetic_fields.SourceFreeField

class desc.magnetic_fields.SourceFreeField(surface, M, N, NFP=None, sym=None, B0=None, I=0.0, Y=0.0)Source

Compute source free magnetic fields.

Implements the Neumann formulation in multiply connected geometry described in [1].

Let 𝒳 be an open set with continuously differentiable closed boundary ∂𝒳. This class solves the following partial differential equation for the globally defined harmonic remainder ϕ, represented in the solver by Phi_tilde. The physical harmonic field carrying the prescribed periods is B0.

• ∆φ(x) = 0 x ∈ 𝒳

• (B - ∇φ - B₀)(x) = 0 x ∈ 𝒳

• n dot (∇φ + B₀)(x) = 0 x ∈ ∂𝒳

• n dot B(x) = 0 x ∈ ∂𝒳

• curl (B - B₀)(x) = 0 x ∈ 𝒳

• div B(x) = 0 ∀x

Parameters:

• surface (Surface) – Geometry defining ∂𝒳.

• M (int) – Poloidal Fourier resolution to interpolate potential on ∂𝒳.

• N (int) – Toroidal Fourier resolution to interpolate potential on ∂𝒳.

• NFP (int) – Field periodicity of potential on ∂𝒳. Default is surface.NFP which is correct only if the globally defined part of B0 produces an NFP periodic field.

• sym (str) – Symmetry for the Fourier basis interpolating the globally defined potential remainder. Default is sin when the surface is stellarator symmetric and False otherwise. Pass False explicitly when the boundary data do not share the surface symmetry.

• B0 (_MagneticField) – Magnetic field due to sources other than the selected I and Y harmonic representatives. The complete auxiliary field is exposed as B0; the field supplied here is exposed as B0_base.

• I (float) – Net toroidal current. Its physical harmonic representative is the field of a unit-period toroidal filament on an axis inferred from surface. The filament lies inside the surface and is therefore intended for an exterior source-free domain. Default is zero.

• Y (float) – Net poloidal current. Its physical harmonic representative is Y * grad(phi), implemented as a toroidal magnetic field with magnitude Y / R. Default is zero.

References

[1]

Unalmis et al. New high-order accurate free surface stellarator equilibria optimization and boundary integral methods in DESC.

Methods

change_resolution(*args, **kwargs)	Change the maximum poloidal and toroidal resolution.
compute(names, grid[, params, transforms, ...])	Compute the quantity given by name on grid.
constant_offset_surface(offset[, grid, M, ...])	Create a new FourierRZToroidalSurface with constant offset from self.
copy([deepcopy])	Return a (deep)copy of this object.
equiv(other)	Compare equivalence between DESC objects.
from_input_file(path, **kwargs)	Create a surface from Fourier coefficients in a DESC or VMEC input file.
from_qp_model([major_radius, aspect_ratio, ...])	Create a surface from a near-axis model for quasi-poloidal symmetry.
from_shape_parameters([major_radius, ...])	Create a surface using a generalized Miller parameterization.
from_values(coords, theta[, zeta, M, N, ...])	Create a surface from given R,Z coordinates in real space.
get_axis()	Get the axis of the surface.
get_coeffs(m[, 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.
save(file_name[, file_format, file_mode])	Save the object.
set_coeffs(m[, n, R, Z])	Set specific Fourier coefficients.
unpack_params(x)	Convert a single array of concatenated parameters into a dictionary.

Attributes

B0	Complete auxiliary field, including the I and Y periods.
B0_base	User-supplied field excluding the built period fields.
I	Net toroidal-current period in T m.
L	Maximum radial mode number.
M	Maximum poloidal mode number.
M_Phi_tilde	Poloidal resolution of the potential remainder.
N	Maximum toroidal mode number.
NFP	Number of (toroidal) field periods.
N_Phi_tilde	Toroidal resolution of the potential remainder.
Phi_tilde_basis	Basis for the globally defined potential remainder.
R_basis	Spectral basis for R.
R_lmn	Spectral coefficients for R.
Y	Net poloidal-current period in T m.
Z_basis	Spectral basis for Z.
Z_lmn	Spectral coefficients for Z.
dim_x	total number of optimizable parameters.
dimensions	dictionary of integers of sizes of each optimizable parameter.
name	Name of the surface.
optimizable_params	string names of parameters that have been declared optimizable.
params_dict	dictionary of arrays of optimizable parameters.
rho	Flux surface label.
surface	Surface geometry defining boundary.
sym	Whether the surface is stellarator symmetric.
sym_Phi_tilde	Symmetry of the potential remainder (no symmetry if False).
x_idx	arrays of indices for each parameter in concatenated array.