essos.fields

Classes

MagneticField
BiotSavart
BiotSavart_from_gamma
Vmec	VMEC equilibrium from a wout file.
near_axis
CombinedField	Sum of several magnetic fields, traced as one.

Functions

d_dtheta_fft(f_theta)
d2_dtheta2_fft(f_theta)
gamma_dash_from_gamma(gamma)
gamma_dashdash_from_gamma(gamma)
_radial_interp(s, grid, table, xm[, covariant_s, ...])	Interpolate every Fourier mode of a wout table at s.

Module Contents

class essos.fields.MagneticField

abstractmethod sqrtg(points)

abstractmethod B(points)

B_covariant(points)

B_contravariant(points)

AbsB(points)

dB_by_dX(points)

dAbsB_by_dX(points)

grad_B_covariant(points)

curl_B(points)

curl_b(points)

kappa(points)

gc_quantities(points)

Field quantities of the guiding-center equations at one point.

Returns (B_covariant, B_contravariant, |B|, grad|B|, curl b, kappa, sqrtg). This generic version calls the individual methods; fields that can form all of them from one evaluation of B and its gradient (see BiotSavart) override it.

abstractmethod to_xyz(points)

class essos.fields.BiotSavart(coils)

Bases: MagneticField

coils

_r_axis = None

_z_axis = None

property dofs

sqrtg(points)

gc_quantities(points)

Guiding-center field quantities from one pass over the coils.

The separate methods each rebuild B and its Jacobian (kappa even recomputes curl_b). Here a single forward-mode Jacobian yields B and dB/dX together, and in Cartesian coordinates (sqrtg = 1) grad|B| = (dB/dX)^T b, curl b = curl B/|B| + B x grad|B|/|B|^2 and kappa = -B x curl b / |B| follow algebraically.

B(points)

b_cyl(R, phi, Z)

Return (B_R, B_phi, B_Z) on broadcast cylindrical arrays.

This field-provider interface lets VMEC/NESTOR evaluate ESSOS coils directly on a changing plasma boundary without writing an mgrid file. It uses the same traceable Biot–Savart graph as B(), so coil shape and current derivatives are retained.

property r_axis

property z_axis

to_xyz(points)

_tree_flatten()

classmethod _tree_unflatten(aux_data, children)

essos.fields.d_dtheta_fft(f_theta)

essos.fields.d2_dtheta2_fft(f_theta)

essos.fields.gamma_dash_from_gamma(gamma)

essos.fields.gamma_dashdash_from_gamma(gamma)

class essos.fields.BiotSavart_from_gamma(gamma, gamma_dash=None, gamma_dashdash=None, currents=None)

Bases: MagneticField

currents = None

gamma

_gamma_dash = None

_gamma_dashdash = None

_coils_length = None

_coils_curvature = None

_r_axis = None

_z_axis = None

property gamma_dash

property gamma_dashdash

property coils_length

property coils_curvature

property r_axis

property z_axis

sqrtg(points)

B(points)

to_xyz(points)

essos.fields._radial_interp(s, grid, table, xm, covariant_s=False, half_grid=False, axis_m1=None)

Interpolate every Fourier mode of a wout table at s.

table is on the full grid, or on the half grid with VMEC’s unused first row (half_grid=True); both grids are uniform. Near the magnetic axis the modes of a regular scalar vanish as s**(m/2), and those of B_s (covariant_s=True) one power of sqrt(s) lower. Each mode is therefore divided by s**p, interpolated linearly and multiplied back, with p = min(m, 2 + m % 2) / 2 (less 1 for B_s, at least -1/2; 0 for m = 0). For m > 0 the axis row of a full-grid table is replaced by the extrapolation of the next two rows, or, for m = 1, by axis_m1 when it is given. Interpolating the modes themselves leaves the m > 0 terms finite on the axis, where |B| then depends on theta.

class essos.fields.Vmec(wout_filename, ntheta=50, nphi=50, close=True, range_torus='full torus', mode_tolerance=0.0)

VMEC equilibrium from a wout file.

mode_tolerance drops a Fourier mode when, in every table of its set, its largest amplitude over the radial grid is below that fraction of the table’s largest: R and Z for the geometry modes, and |B|, sqrt(g) and the B components for the Nyquist modes. Evaluation cost scales with the number of modes kept.

wout_filename

nc

nfp

bmnc

xm

xn

rmnc

zmns

bsubsmns

bsubumnc

bsubvmnc

bsupumnc

bsupvmnc

gmnc

xm_nyq

xn_nyq

len_xm_nyq

ns

s_full_grid = None

ds

s_half_grid

r_axis

z_axis

mpol

ntor

range_torus = 'full torus'

_surface

Aminor_p

_drop_small_modes(tolerance)

property surface

_bsubs_axis_m1()

Axis limit of sqrt(s) B_s for the m = 1 modes, from B_theta.

Near the axis the leading m = 1 parts of B_s and B_theta are the gradient of sqrt(s) Psi(theta, phi), so sqrt(s) B_s tends to B_theta / (2 sqrt(s)) and their contributions to the toroidal current cancel. VMEC’s B_s next to the axis misses that limit (by about 10% on an HSX wout), and extrapolating it gave curl B a toroidal component that grew as 1/sqrt(s) on the axis.

_NYQUIST

_nyquist_series(points)

Each Nyquist table’s Fourier sum at points and its (s, theta, phi) gradient.

One set of angles, cosines, sines and radial weights serves every table and the gradients are analytic, so |B|, sqrt(g), the B components and their derivatives cost one evaluation between them when traced together, and curl b and the curvature need no automatic differentiation.

B_covariant(points)

B_contravariant(points)

sqrtg(points)

B(points)

AbsB(points)

dB_by_dX(points)

dAbsB_by_dX(points)

grad_B_covariant(points)

curl_B(points)

curl_b(points)

kappa(points)

to_xyz(points)

class essos.fields.near_axis(*args, **kwargs)

class essos.fields.CombinedField(*fields)

Bases: MagneticField

Sum of several magnetic fields, traced as one.

The usual case is a coil field plus a plasma contribution: B and B_contravariant add over the fields, while the geometry helpers sqrtg and to_xyz come from the first field, which is the one that carries the coordinate system.

fields = ()

B(points)

B_contravariant(points)

sqrtg(points)

to_xyz(points)

_tree_flatten()

classmethod _tree_unflatten(aux_data, children)