desc.magnetic_fields.OmnigenousField

class desc.magnetic_fields.OmnigenousField(L_B=0, M_B=2, L_x=0, M_x=0, N_x=0, NFP=1, helicity=(1, 0), B_lm=None, x_lmn=None)Source

A magnetic field with perfect omnigenity (but is not necessarily analytic).

Uses parameterization from Dudt et. al. [1]

Parameters:

• L_B (int) – Resolution of the radial Chebyshev polynomials for magnetic well parameters.

• M_B (int) – Number of monotonic spline knots per surface of the magnetic well parameters.

• L_x (int) – Resolution of the radial Chebyshev polynomials for the omnigenity parameters.

• M_x (int) – Resolution of the Fourier series in eta for the omnigenity parameters.

• N_x (int) – Resolution of the Fourier series in alpha for the omnigenity parameters.

• NFP (int) – Number of field periods.

• helicity (tuple, optional) – Type of pseudo-symmetry (M, N). Default = toroidal contours (1, 0).

• B_lm (ndarray, optional) – Magnetic well parameters describing ||B||(ρ,η). These values are a flattened 2D array of shape (L_B + 1, M_B), where the rows are Chebyshev coefficients corresponding to the modes in B_basis for the radial variation, and the columns are the values of ||B|| at linearly spaced monotonic spline knots. (The array is flattened in the default row-major or ‘C’-style order.) If not supplied, B_lm defaults to a constant field of 1 T.

• x_lmn (ndarray, optional) – Omnigenity parameters describing h(ρ,η,α). The coefficients correspond to the modes in x_basis. If not supplied, x_lmn defaults to zero for all modes.

Notes

Doesn’t conform to MagneticField API, as it only knows about \(|B|\) in computational coordinates, not vector B in lab coordinates.

References

[1]

Dudt, Daniel W., et al. “Magnetic fields with general omnigenity.” Journal of Plasma Physics (2024) doi:10.1017/S0022377824000151

Methods

change_resolution([L_B, M_B, L_x, M_x, N_x, NFP])	Set the spectral resolution of field parameters.
compute(names[, grid, params, transforms, ...])	Compute the quantity given by name on grid.
copy([deepcopy])	Return a (deep)copy of this object.
equiv(other)	Compare equivalence between DESC objects.
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.
unpack_params(x)	Convert a single array of concatenated parameters into a dictionary.

Attributes

B_basis	Spectral basis for B_lm.
B_lm	Omnigenity magnetic well shape parameters.
L_B	Radial resolution of the magnetic well parameters well_l.
L_x	Radial resolution of x_lmn.
M_B	Number of spline points in the magnetic well parameters well_l.
M_x	Poloidal resolution of x_lmn.
NFP	Number of (toroidal) field periods.
N_x	Toroidal resolution of x_lmn.
dim_x	total number of optimizable parameters.
dimensions	dictionary of integers of sizes of each optimizable parameter.
helicity	Type of omnigenity (M, N).
optimizable_params	string names of parameters that have been declared optimizable.
params_dict	dictionary of arrays of optimizable parameters.
x_basis	Spectral basis for x_lmn.
x_idx	arrays of indices for each parameter in concatenated array.
x_lmn	Omnigenity coordinate mapping parameters.