desc.magnetic_fields.FourierCurrentPotentialField

class desc.magnetic_fields.FourierCurrentPotentialField(Phi_mn=array([0.]), modes_Phi=array([[0, 0]]), I=0, G=0, sym_Phi=False, M_Phi=None, N_Phi=None, R_lmn=None, Z_lmn=None, modes_R=None, modes_Z=None, NFP=1, sym='auto', M=None, N=None, name='', check_orientation=True)Source

Magnetic field due to a surface current potential on a toroidal surface.

Surface current K is assumed given by

K = n x ∇ Φ

Φ(θ,ζ) = Φₛᵥ(θ,ζ) + Gζ/2π + Iθ/2π

where:

  • n is the winding surface unit normal.

  • Phi is the current potential function, which is a function of theta and zeta, and is given as a secular linear term in theta/zeta and a double Fourier series in theta/zeta.

This function then uses biot-savart to find the B field from this current density K on the surface.

Parameters:

  • Phi_mn (ndarray) – Fourier coefficients of the double FourierSeries part of the current potential.

  • modes_Phi (array-like, shape(k,2)) – Poloidal and Toroidal mode numbers corresponding to passed-in Phi_mn coefficients.

  • I (float) – Net current linking the plasma and the surface toroidally Denoted I in the algorithm

  • G (float) – Net current linking the plasma and the surface poloidally Denoted G in the algorithm NOTE: a negative G will tend to produce a positive toroidal magnetic field B in DESC, as in DESC the poloidal angle is taken to be positive and increasing when going in the clockwise direction, which with the convention n x grad(phi) will result in a toroidal field in the negative toroidal direction.

  • sym_Phi ({False,"cos","sin"}) – whether to enforce a given symmetry for the DoubleFourierSeries part of the current potential.

  • M_Phi (int or None) – Maximum poloidal and toroidal mode numbers for the single valued part of the current potential.

  • N_Phi (int or None) – Maximum poloidal and toroidal mode numbers for the single valued part of the current potential.

  • R_lmn (array-like, shape(k,)) – Fourier coefficients for winding surface R and Z in cylindrical coordinates

  • Z_lmn (array-like, shape(k,)) – Fourier coefficients for winding surface R and Z in cylindrical coordinates

  • modes_R (array-like, shape(k,2)) – poloidal and toroidal mode numbers [m,n] for R_lmn.

  • modes_Z (array-like, shape(k,2)) – mode numbers associated with Z_lmn, defaults to modes_R

  • NFP (int) – number of field periods

  • sym (bool) – whether to enforce stellarator symmetry for the surface geometry. Default is “auto” which enforces if modes are symmetric. If True, non-symmetric modes will be truncated.

  • M (int or None) – Maximum poloidal and toroidal mode numbers. Defaults to maximum from modes_R and modes_Z.

  • N (int or None) – Maximum poloidal and toroidal mode numbers. Defaults to maximum from modes_R and modes_Z.

  • name (str) – name for this field

  • check_orientation (bool) – ensure that this surface has a right handed orientation. Do not set to False unless you are sure the parameterization you have given is right handed (ie, e_theta x e_zeta points outward from the surface).

Methods

change_Phi_resolution([M, N, NFP, sym_Phi])

Change the maximum poloidal and toroidal resolution for Phi.

change_resolution(*args, **kwargs)

Change the maximum poloidal and toroidal 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.

constant_offset_surface(offset[, grid, M, ...])

Create a FourierRZSurface with constant offset from the base surface (self).

copy([deepcopy])

Return a (deep)copy of this object.

equiv(other)

Compare equivalence between DESC objects.

from_input_file(path)

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_surface(surface[, Phi_mn, modes_Phi, ...])

Create FourierCurrentPotentialField using geometry of given surface.

from_values(coords, theta[, zeta, M, N, ...])

Create a surface from given R,Z coordinates in real space.

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.

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(m[, n, R, Z])

Set specific Fourier coefficients.

unpack_params(x)

Convert a single array of concatenated parameters into a dictionary.

Attributes

G

Net current linking the plasma and the surface poloidally.

I

Net current linking the plasma and the surface toroidally.

L

Maximum radial mode number.

M

Maximum poloidal mode number.

M_Phi

Poloidal resolution of periodic part of Phi.

N

Maximum toroidal mode number.

NFP

Number of (toroidal) field periods.

N_Phi

Toroidal resolution of periodic part of Phi.

Phi_basis

Spectral basis for Phi.

Phi_mn

Fourier coefficients describing single-valued part of potential.

R_basis

Spectral basis for R.

R_lmn

Spectral coefficients for R.

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.

sym

Whether or not the surface is stellarator symmetric.

sym_Phi

Type of symmetry of periodic part of Phi (no symmetry if False).

x_idx

arrays of indices for each parameter in concatenated array.