OpenFUSIONToolkit.TokaMaker.util Namespace Reference

Detailed Description

General utility and supporting functions for TokaMaker.

Authors

Chris Hansen

Date

April 2024

Functions
	_inner_arc (r_x, z_x, r_inner_mid, z_inner_mid, zeta, n)
	Generate an inverted-INTOR inner arc from X-point to inner midplane.
	_intor_arc (r0, z0_arc, a, kappa_eff, theta_x, r_x, zeta, n, endpoint=False, sign=1)
	Generate one half of the INTOR outer arc.
	compute_forces_components (tMaker_obj, psi, cell_centered=False)
	Compute terms needed for evaluating forces in passively conducting regions.
	create_isoflux (npts, r0, z0, a, kappa, delta, kappaL=None, deltaL=None)
	Create isoflux points using simple analytic form.
	create_isoflux_xpts (npts, r0, z0, a, kappa_upper, delta_upper, kappa_lower=None, delta_lower=None, r_inner_mid=None, zeta_outer_upper=0.0, zeta_outer_lower=0.0, zeta_inner_upper=0.0, zeta_inner_lower=0.0)
	Create isoflux boundary points for single-null configurations with X-points.
	create_power_flux_fun (npts, alpha, gamma)
	Build power law flux function of the form \( (1-\hat{\psi}^{\alpha})^{\gamma} \).
	create_spline_flux_fun (npts, x, y, axis_bc=[1, 0.0], edge_bc=[1, 0.0], normalize=True)
	Build cubic spline flux function.
	eval_green (x, xc)
	Evaluate Green's function for a toroidal filament.
	get_jphi_from_GS (ffprime, pprime, R_avg, one_over_R_avg)
	Calculate j_phi profile from Grad-Shafranov equation.
	read_eqdsk (filename)
	Read gEQDSK file.
	read_ifile (filename)
	Read i-file inverse equilibrium file.
	read_kfile (path, machine_dict, e_coil_names=None, f_coil_names=None)
	read_mhdin (path, e_coil_names=None, f_coil_names=None)
	xpoints_from_moments (r0, z0, a, kappa_upper, delta_upper, kappa_lower=None, delta_lower=None)
	Compute X-point locations from Miller shaping moments.

Function Documentation

_inner_arc()

_inner_arc ( r_x, z_x, r_inner_mid, z_inner_mid, zeta, n )

protected

Generate an inverted-INTOR inner arc from X-point to inner midplane.

Uses \(R(\alpha) = r_x - a_\mathrm{in}\cos(\alpha - \zeta\sin 2\alpha)\), \(Z(\alpha) = z_\mathrm{mid} + a_\mathrm{in}\kappa_\mathrm{in}\sin(\alpha + \zeta\sin 2\alpha)\) with \(\alpha\) from \(\pi/2\) (X-point) to 0 (midplane, excluded). The tangent is vertical at the midplane, so joining upper and lower halves is kink-free.

Parameters

r_x	R coordinate of the X-point
z_x	Z coordinate of the X-point
r_inner_mid	R at the inner midplane
z_inner_mid	Z at the inner midplane
zeta	INTOR squareness parameter
n	Number of points (midplane endpoint excluded)

Returns

r, z arrays for the arc segment

_intor_arc()

_intor_arc ( r0, z0_arc, a, kappa_eff, theta_x, r_x, zeta, n, endpoint = False, sign = 1 )

protected

Generate one half of the INTOR outer arc.

Arc spans \(\theta\) from 0 (outboard midplane) to \(\mathrm{sign}\cdot\theta_x\) (X-point). sign=+1 gives the upper half (Z > z0_arc); sign=-1 gives the lower half. delta_eff is solved so the arc passes exactly through r_x at theta_x.

Parameters

r0	Major radial position for magnetic axis
z0_arc	Vertical center for this arc half (typically the magnetic axis Z)
a	Minor radius
kappa_eff	Elongation for this half
theta_x	Poloidal angle at the X-point
r_x	R coordinate of the X-point
zeta	INTOR squareness parameter
n	Number of points to generate
endpoint	Whether to include the final endpoint (default: False)
sign	+1 for upper half, -1 for lower half (default: +1)

Returns

r, z arrays for the arc segment

compute_forces_components()

compute_forces_components	(		tMaker_obj,
			psi,
			cell_centered = False )

Compute terms needed for evaluating forces in passively conducting regions.

Parameters

tMaker_obj	TokaMaker equilibrium object
psi	\( \psi \) corresponding to desired currents
cell_centered	Evaluate at cell centers instead of node points?

Returns

J_cond, B_cond, mask, R

create_isoflux()

create_isoflux	(		npts,
			r0,
			z0,
			a,
			kappa,
			delta,
			kappaL = None,
			deltaL = None )

Create isoflux points using simple analytic form.

Parameters

npts	Number of points to sample (evenly spaced in \(\theta\))
r0	Major radial position for magnetic axis
z0	Vertical position for magnetic axis
a	Minor radius
kappa	Elongation (upper only if kappaL is set)
delta	Triangularity (upper only if deltaL is set)
kappaL	Lower elongation (default: kappa)
deltaL	Lower triangularity (default: delta)

Returns

Point list [npts,2]

create_isoflux_xpts()

create_isoflux_xpts	(		npts,
			r0,
			z0,
			a,
			kappa_upper,
			delta_upper,
			kappa_lower = None,
			delta_lower = None,
			r_inner_mid = None,
			zeta_outer_upper = 0.0,
			zeta_outer_lower = 0.0,
			zeta_inner_upper = 0.0,
			zeta_inner_lower = 0.0 )

Create isoflux boundary points for single-null configurations with X-points.

Generates a closed boundary contour suitable for use with set_isoflux_constraints() and set_saddle_constraints(). The outer (low-field-side) arc uses the INTOR analytic formula centered on the magnetic axis; the inner arcs use an inverted-INTOR formula that gives a smooth vertical tangent at the inner midplane. Supports non-up-down-symmetric equilibria via independent upper and lower shaping moments and squareness values.

Use xpoints_from_moments() with the same kappa/delta arguments to obtain the matching saddle-constraint array.

Parameters

npts	Total number of boundary points
r0	Major radial position for magnetic axis
z0	Vertical position for magnetic axis
a	Minor radius
kappa_upper	Upper elongation (sets X-point height and outer arc shape)
delta_upper	Upper triangularity
kappa_lower	Lower elongation (default: kappa_upper)
delta_lower	Lower triangularity (default: delta_upper)
r_inner_mid	R at the inner midplane (default: r0 - a)
zeta_outer_upper	INTOR squareness of the upper outer corner (default: 0)
zeta_outer_lower	INTOR squareness of the lower outer corner (default: 0)
zeta_inner_upper	INTOR squareness of the upper inner corner (default: 0)
zeta_inner_lower	INTOR squareness of the lower inner corner (default: 0)

Returns

Point list [npts, 2]

create_power_flux_fun()

create_power_flux_fun	(		npts,
			alpha,
			gamma )

Build power law flux function of the form \( (1-\hat{\psi}^{\alpha})^{\gamma} \).

Parameters

npts	Number of points for definition
alpha	Inner exponent
gamma	Outer exponent

Returns

Flux function definition dictionary

create_spline_flux_fun()

create_spline_flux_fun	(		npts,
			x,
			y,
			axis_bc = [1,0.0],
			edge_bc = [1,0.0],
			normalize = True )

Build cubic spline flux function.

Parameters

npts	Number of points for definition
x	Location of spline "knots" in normalized flux
y	Value of flux function at spline "knots"
axis_bc	SciPy BC specification on axis ( \( \hat{\psi} = 0 \))
edge_bc	SciPy BC specification on LCFS ( \( \hat{\psi} = 1 \))

Returns

Flux function definition dictionary

eval_green()

eval_green	(		x,
			xc )

Evaluate Green's function for a toroidal filament.

Parameters

x	Observation point [2]
xc	Coil location [:,2]

Returns

\(\psi(x)\) due to a coil with unit current [A] at xc

get_jphi_from_GS()

get_jphi_from_GS	(		ffprime,
			pprime,
			R_avg,
			one_over_R_avg )

Calculate j_phi profile from Grad-Shafranov equation.

Parameters

ffprime	FF'(psi_N) profile
pprime	P'(psi_N) profile
R_avg	<R>(psi_N) profile
one_over_R_avg	<1/R>(psi_N) profile Returns: j_phi(\psi_N) profile

read_eqdsk()

read_eqdsk

(

filename

)

Read gEQDSK file.

Parameters

filename

Path to gEQDSK file

Returns

Dictionary containing gEQDSK information

read_ifile()

read_ifile

(

filename

)

Read i-file inverse equilibrium file.

Parameters

filename

Path to file

Returns

Dictionary containing i-file information

read_kfile()

read_kfile	(		path,
			machine_dict,
			e_coil_names = None,
			f_coil_names = None )

Read k-file.

@param path Path to file
@param e_coil_names Names of E coils (hardcoded, generates indexed names if None)
@param f_coil_names Names of F coils (hardcoded, generates indexed names if None)
@param machine_dict Result from read_mhdin (contents of mhdin.dat file)
@result probes_dict Dictionary containing probe values and weights (0 if not selected).
@result loops_dict Dictionary containing loop values and weights (0 if not selected).
@result e_coil_dict Dictionary containing E copil values and weights (0 if not selected).
@result f_coil_dict Dictionary containing F coil values and weights (0 if not selected).
@result raw Dictionary containing all other data from k-file.

read_mhdin()

read_mhdin	(		path,
			e_coil_names = None,
			f_coil_names = None )

Read mhdin.dat file.

@param path Path to file
@param e_coil_names Names of E coils (hardcoded, generates indexed names if None)
@param f_coil_names Names of F coils (hardcoded, generates indexed names if None)
@result machine_dict Dictionary containing coil coordinates and turns, loop names, and probe names and angles.
@result raw Dictionary containing all other data from mhdin.dat

xpoints_from_moments()

xpoints_from_moments	(		r0,
			z0,
			a,
			kappa_upper,
			delta_upper,
			kappa_lower = None,
			delta_lower = None )

Compute X-point locations from Miller shaping moments.

Upper: \((r_0 - a\,\delta_U,\; z_0 + a\,\kappa_U)\). Lower: \((r_0 - a\,\delta_L,\; z_0 - a\,\kappa_L)\).

Parameters

r0	Major radial position for magnetic axis
z0	Vertical position for magnetic axis
a	Minor radius
kappa_upper	Upper elongation
delta_upper	Upper triangularity
kappa_lower	Lower elongation (default: kappa_upper)
delta_lower	Lower triangularity (default: delta_upper)

Returns

X-point array, shape (2, 2): [[R_upper, Z_upper], [R_lower, Z_lower]]