Detailed Description

TokaMaker G-S solver class.

Public Member Functions
	__del__ (self)
	Free Fortran-side objects by calling `reset()` before object is deleted or GC'd.

	__init__ (self, OFT_env)
	Initialize TokaMaker object.

	abspsi_to_normalized (self, psi_in)
	Convert unnormalized $ \psi $ values to normalized $ \hat{\psi} $ values.

	alam (self)
	F*F' normalization value.

	area_integral (self, field, reg_mask=-1)
	Compute area integral of field over a specified region.

	c_ptr (self)

	calc_delstar_curr (self, psi)
	Get toroidal current density from $ \psi $ through $ \Delta^{*} $ operator.

	calc_jtor_plasma (self)
	Get plasma toroidal current density for current equilibrium.

	calc_loopvoltage (self)
	Get plasma loop voltage.

	coil_dict2vec (self, coil_dict=None, keep_virtual=False, default_value=0.0)
	Create coil vector from dictionary of values.

	coil_reg_term (self, coffs, target=0.0, weight=1.0)
	Define coil current regularization term for the form $ target = \Sigma_i \alpha_i I_i $ to be used in set_coil_reg.

	coil_vec2dict (self, coil_vec, always_virtual=False)
	Create coil value dictionary of from vector values.

	compute_area_integral (self, field, reg_mask=-1)
	Compute area integral of field over a specified region.

	compute_flux_integral (self, psi_vals, field_vals)
	Compute area integral of flux function over the plasma.

	copy_eq (self, skip_targets=False, skip_constraints=False)
	Create a copy of the current equilibrium object.

	diverted (self)
	Diverted flag (limited if `False`)

	eig_td (self, omega=-1.E4, neigs=4, include_bounds=True, pm=False, damping_scale=-1.0)
	Compute eigenvalues for the linearized time-dependent system.

	eig_wall (self, neigs=4, pm=False)
	Compute eigenvalues ( $ 1 / \tau_{L/R} $) for conducting structures.

	ffp_scale (self)
	F*F' scale value.

	ffp_scale (self, value)

	flux_integral (self, psi_vals, field_vals)
	Compute area integral of flux function over the plasma.

	get_coil_currents (self)
	Get currents in each coil [A] and coil region [A-turns].

	get_coil_Lmat (self)
	Get mutual inductance matrix between coils.

	get_conductor_currents (self, psi, cell_centered=False, include_Vcoils=False)
	Get toroidal current density in conducting regions for a given $ \psi $.

	get_conductor_source (self, dpsi_dt)
	Get toroidal current density in conducting regions for a $ d \psi / dt $ source.

	get_delstar_curr (self, psi)
	Get toroidal current density from $ \psi $ through $ \Delta^{*} $ operator.

	get_field_eval (self, field_type)
	Create field interpolator for vector potential.

	get_globals (self)
	Get global plasma parameters.

	get_jtor_plasma (self)
	Get plasma toroidal current density for current equilibrium.

	get_profiles (self, psi=None, psi_pad=1.E-8, npsi=50)
	Get G-S source profiles.

	get_psi (self, normalized=True)
	Get poloidal flux values on node points.

	get_q (self, psi=None, psi_pad=0.02, npsi=50, compute_geo=False)
	Get q-profile at specified or uniformly spaced points.

	get_stats (self, lcfs_pad=None, axis_pad=0.02, li_normalization='std', geom_type='max', beta_Ip=None)
	Get information (Ip, q, kappa, etc.) about current G-S equilbirium.

	get_targets (self)
	Get global target values.

	get_vfixed (self)
	Get required vacuum flux values to balance fixed boundary equilibrium.

	get_xpoints (self)
	Get X-points.

	init_psi (self, r0=-1.0, z0=0.0, a=0.0, kappa=0.0, delta=0.0, curr_source=None)
	Initialize $\psi$ using uniform current distributions.

	lim_point (self)
	Limiting point (limter or active X-point) [2].

	load_profiles (self, f_file='none', foffset=None, p_file='none', eta_file='none', f_NI_file='none')
	Load flux function profiles ( $F*F'$ and $P'$) from files.

	o_point (self)
	Location of O-point (magnetic axis) [2].

	p_scale (self)
	Pressure scale value.

	p_scale (self, value)

	plot_constraints (self, fig, ax, equilibrium=None, isoflux_color='tab:red', isoflux_marker='+', saddle_color='tab:green', saddle_marker='x')
	Plot geometry constraints.

	plot_eddy (self, fig, ax, psi=None, equilibrium=None, dpsi_dt=None, nlevels=40, colormap='jet', clabel=r ' $J_w$[$A/m^2$]', symmap=False, include_Vcoils=False)
	Plot contours of $\hat{\psi}$.

	plot_machine (self, fig, ax, equilibrium=None, vacuum_color='whitesmoke', cond_color='gray', limiter_color='k', coil_color='gray', coil_colormap=None, coil_symmap=False, coil_scale=1.0, coil_clabel=r ' $I_C$[A]', colorbar=None)
	Plot machine geometry.

	plot_psi (self, fig, ax, equilibrium=None, psi=None, normalized=True, plasma_color=None, plasma_nlevels=8, plasma_levels=None, plasma_colormap=None, plasma_linestyles=None, vacuum_color='darkgray', vacuum_nlevels=8, vacuum_levels=None, vacuum_colormap=None, vacuum_linestyles=None, xpoint_color='k', xpoint_marker='x', xpoint_inactive_alpha=0.5, opoint_color='k', opoint_marker=' *')
	Plot contours of $\hat{\psi}$.

	pnorm (self)
	Pressure normalization value.

	print_info (self, lcfs_pad=None, axis_pad=0.02, li_normalization='std', geom_type='max', beta_Ip=None)
	Print information (Ip, q, etc.) about current G-S equilbirium.

	psi_bounds (self)
	Bounding values for $\psi$ ( $\psi_a$, $\psi_0$) [2].

	psinorm_to_absolute (self, psi_in)
	Convert normalized $ \hat{\psi} $ values to unnormalized values $ \psi $.

	reset (self)
	Reset G-S object to enable loading a new mesh and coil configuration.

	sauter_fc (self, psi=None, psi_pad=0.02, npsi=50)
	Evaluate Sauter trapped particle fractions at specified or uniformly spaced points.

	save_eqdsk (self, filename, nr=65, nz=65, rbounds=None, zbounds=None, run_info='', lcfs_pad=0.01, rcentr=None, truncate_eq=True, limiter_file='', lcfs_pressure=0.0, cocos=7)
	Save current equilibrium to gEQDSK format.

	save_ifile (self, filename, npsi=65, ntheta=65, lcfs_pad=0.01, lcfs_pressure=0.0, pack_lcfs=True, single_precision=False)
	Save current equilibrium to iFile format.

	save_mug (self, filename)
	Save current equilibrium to MUG transfer format.

	set_coil_bounds (self, coil_bounds=None)
	Set hard constraints on coil currents.

	set_coil_current_dist (self, coil_name, curr_dist=None, normalize=False)
	Overwrite coil with non-uniform current distribution.

	set_coil_currents (self, currents=None)
	Set coil currents.

	set_coil_reg (self, reg_mat=None, reg_targets=None, reg_weights=None, reg_terms=None)
	Set regularization matrix for coil currents when isoflux and/or saddle constraints are used.

	set_coil_vsc (self, coil_gains)
	Define a vertical stability coil set from one or more coils.

	set_dipole_a (self, a_exp=None)
	Update anisotropy exponent `a` when dipole mode is used, calling with no argument will disable pressure anisotropy.

	set_flux (self, locations, targets, weights=None)
	Set explicit flux constraint points $ \psi(x_i) $ [Wb/rad].

	set_flux_constraints (self, locations, targets, weights=None)
	Set explicit flux constraint points $ \psi(x_i) $ [Wb].

	set_isoflux (self, isoflux, weights=None, grad_wt_lim=-1.0, ref_points=None)
	Set isoflux constraint points (all points lie on a flux surface)

	set_isoflux_constraints (self, isoflux, weights=None, grad_wt_lim=-1.0, ref_points=None)
	Set isoflux constraint points (all points lie on a flux surface)

	set_mirror_slosh (self, n_exp=None, b_turn=None, z_throat=None)
	Update anisotropy exponent `a` when dipole mode is used, calling with no arguments will disable pressure anisotropy.

	set_profiles (self, ffp_prof=None, foffset=None, pp_prof=None, ffp_NI_prof=None, keep_files=False)
	Set flux function profiles ( $F*F'$ and $P'$) using a piecewise linear definition.

	set_psi (self, psi, update_bounds=False)
	Set poloidal flux values on node points.

	set_psi_constraints (self, locations, targets, weights=None)
	Set explicit flux constraint points $ \psi(x_i) $ [Wb/rad].

	set_psi_dt (self, psi0, dt, coil_currents=None, coil_voltages=None)
	Set reference poloidal flux and time step for eddy currents in .solve()

	set_resistivity (self, eta_prof=None)
	Set flux function profile $\eta$ using a piecewise linear definition.

	set_saddle_constraints (self, saddles, weights=None)
	Set saddle constraint points (poloidal field should vanish at each point)

	set_saddles (self, saddles, weights=None)
	Set saddle constraint points (poloidal field should vanish at each point)

	set_targets (self, Ip=None, Ip_ratio=None, pax=None, estore=None, R0=None, V0=None, Z0=None, retain_previous=False)
	Set global target values.

	set_vcoils (self, coil_resistances)
	Set or unset one or more coils as Vcoils by defining their lumped resistances.

	setup (self, order=2, F0=0.0, full_domain=False)
	Setup G-S solver.

	setup_mesh (self, r=None, lc=None, reg=None, mesh_file=None)
	Setup mesh for static and time-dependent G-S calculations.

	setup_regions (self, cond_dict={}, coil_dict={})
	Define mesh regions (coils and conductors)

	setup_td (self, dt, lin_tol, nl_tol, pre_plasma=False)
	Setup the time-dependent G-S solver.

	solve (self, vacuum=False)
	Solve G-S equation with specified constraints, profiles, etc.

	step_td (self, time, dt, coil_currents=None, coil_voltages=None)
	Advance time-dependent solution by one time step.

	trace_surf (self, psi)
	Trace surface for a given poloidal flux.

	update_settings (self)
	Update settings after changes to values in python.

	vac_solve (self, psi=None, rhs_source=None)
	Solve for vacuum solution (no plasma), with present coil currents and optional other currents.

Public Attributes
	coil_set_names
	Coil set names in order of id number.

	coil_sets
	Coil set definitions, including sub-coils.

	dist_coils
	Distribution coils, only (currently) saved for plotting utility.

	lc
	Mesh triangles [nc,3].

	Lcoils
	Coil self-inductance matrix [ncoils].

	lim_contour
	Limiting contour.

	lim_contours
	Limiting contours (if multiple)

	nc
	Number of cells in mesh.

	ncoils
	Number of coils in mesh.

	np
	Number of points in mesh.

	nregs
	Number of regions in mesh.

	nvac
	Number of vacuum regions in mesh.

	psi_convention
	Normalized flux convention (0 -> tokamak, 1 -> spheromak)

	r
	Mesh vertices [np,3] (last column should be all zeros)

	reg
	Mesh regions [nc].

	settings
	General settings object.

Protected Attributes
	_coil_dict
	Coil definition dictionary.

	_cond_dict
	Conductor definition dictionary.

	_F0
	Vacuum F value.

	_mesh_ptr
	Internal mesh object.

	_oft_env

	_tMaker_equil
	Internal Grad-Shafranov object (gs_equil)

	_tMaker_ptr
	Internal Grad-Shafranov object (gs_factory)

	_vac_dict
	Vacuum definition dictionary.

	_vcoils
	Voltage coils dictionary.

	_virtual_coils
	Virtual coils, if present (currently only ‘’#VSC'`)

Constructor & Destructor Documentation

◆ init()

__init__	(	self,
		OFT_env
	)

Initialize TokaMaker object.

Parameters

OFT_env OFT runtime environment object (See OFT_env)

◆ del()

__del__ ( self )

Free Fortran-side objects by calling reset() before object is deleted or GC'd.

Member Function Documentation

◆ abspsi_to_normalized()

abspsi_to_normalized	(	self,
		psi_in
	)

Convert unnormalized $ \psi $ values to normalized $ \hat{\psi} $ values.

Parameters

psi_in Input $ \psi $ values

Returns: Normalized $ \hat{\psi} $ values

◆ alam()

alam ( self )

F*F' normalization value.

Deprecated:: Use ffp_scale property instead.

◆ area_integral()

area_integral	(	self,
		field,
		reg_mask = `-1`
	)

Compute area integral of field over a specified region.

Deprecated:: Use compute_area_integral instead.

Parameters

field	Field to integrate [np]
reg_mask	ID of region for integration (negative for whole mesh)

Returns: $ \int f dA $

◆ c_ptr()

c_ptr ( self )

C pointer to Fortran-side TokaMaker object

◆ calc_delstar_curr()

calc_delstar_curr	(	self,
		psi
	)

Get toroidal current density from $ \psi $ through $ \Delta^{*} $ operator.

Parameters

psi	$ \psi $ corresponding to desired current density

Returns: $ J_{\phi} = \textrm{M}^{-1} \Delta^{*} \psi $ [A/m^2]

◆ calc_jtor_plasma()

calc_jtor_plasma ( self )

Get plasma toroidal current density for current equilibrium.

Returns: $ J_{\phi} $ by evalutating RHS source terms

◆ calc_loopvoltage()

calc_loopvoltage ( self )

Get plasma loop voltage.

Returns: Vloop [Volts]

◆ coil_dict2vec()

coil_dict2vec	(	self,
		coil_dict = `None`,
		keep_virtual = `False`,
		default_value = `0.0`
	)

Create coil vector from dictionary of values.

Parameters

coil_dict	Input dictionary
keep_virtual	Keep virtual coils in vector instead of mapping to component coils
default_value	Fill value for unspecified entries

Returns: Ouput vector

◆ coil_reg_term()

coil_reg_term	(	self,
		coffs,
		target = `0.0`,
		weight = `1.0`
	)

Define coil current regularization term for the form $ target = \Sigma_i \alpha_i I_i $ to be used in set_coil_reg.

Parameters

coffs	Dictionary of coefficients $ \alpha $ (zero for unspecified coils)
target	Regularization target (default: 0.0)
weight	Weight for regularization term (default: 1.0)

◆ coil_vec2dict()

coil_vec2dict	(	self,
		coil_vec,
		always_virtual = `False`
	)

Create coil value dictionary of from vector values.

Parameters

coil_vec	Input vector
always_virtual	Always include virtual coils even if not present in vector

Returns: Ouput dictionary

◆ compute_area_integral()

compute_area_integral	(	self,
		field,
		reg_mask = `-1`
	)

Compute area integral of field over a specified region.

Parameters

field	Field to integrate [np,]
reg_mask	ID of region for integration (negative for whole mesh)

Returns: $ \int f dA $

◆ compute_flux_integral()

compute_flux_integral	(	self,
		psi_vals,
		field_vals
	)

Compute area integral of flux function over the plasma.

Parameters

psi_vals	$ \hat{\psi} $ values defining flux function [:]
field_vals	Flux function values at each $ \hat{\psi} $ value [:]

Returns: $ \int f dA $

◆ copy_eq()

copy_eq	(	self,
		skip_targets = `False`,
		skip_constraints = `False`
	)

Create a copy of the current equilibrium object.

Parameters

skip_targets	When copying, skip copying target values
skip_constraints	When copying, skip copying constraint values

Returns: New TokaMaker_equilibrium object with copied values

◆ diverted()

diverted ( self )

Diverted flag (limited if False)

◆ eig_td()

eig_td	(	self,
		omega = `-1.E4`,
		neigs = `4`,
		include_bounds = `True`,
		pm = `False`,
		damping_scale = `-1.0`
	)

Compute eigenvalues for the linearized time-dependent system.

Parameters

omega	Growth rate localization point (eigenvalues closest to this value will be found)
neigs	Number of eigenvalues to compute
include_bounds	Include bounding flux terms for constant normalized profiles?
pm	Print solver statistics and raw eigenvalues?
damping_scale	Scale factor for damping term to artificially limit growth rate (negative to disable)?

Returns: eigenvalues[neigs], eigenvectors[neigs,:]

◆ eig_wall()

eig_wall	(	self,
		neigs = `4`,
		pm = `False`
	)

Compute eigenvalues ( $ 1 / \tau_{L/R} $) for conducting structures.

Parameters

neigs	Number of eigenvalues to compute
pm	Print solver statistics and raw eigenvalues?

Returns: eigenvalues[neigs], eigenvectors[neigs,:]

◆ ffp_scale() [1/2]

ffp_scale ( self )

F*F' scale value.

◆ ffp_scale() [2/2]

ffp_scale	(	self,
		value
	)

◆ flux_integral()

flux_integral	(	self,
		psi_vals,
		field_vals
	)

Compute area integral of flux function over the plasma.

Deprecated:: Use compute_flux_integral instead.

Parameters

psi_vals	$ \hat{\psi} $ values defining flux function [:]
field_vals	Flux function values at each $ \hat{\psi} $ value [:]

Returns: $ \int f dA $

◆ get_coil_currents()

get_coil_currents ( self )

Get currents in each coil [A] and coil region [A-turns].

Returns: Coil currents [ncoils], Coil currents by region [nregs]

◆ get_coil_Lmat()

get_coil_Lmat ( self )

Get mutual inductance matrix between coils.

Note: This is the inductance in terms of A-turns. To get in terms of current in a single of the $n$ windings you must multiply by $n_i*n_j$.

Returns: L[ncoils+1,ncoils+1]

◆ get_conductor_currents()

get_conductor_currents	(	self,
		psi,
		cell_centered = `False`,
		include_Vcoils = `False`
	)

Get toroidal current density in conducting regions for a given $ \psi $.

Parameters

psi	Psi corresponding to field with conductor currents (eg. from time-dependent simulation)
cell_centered	Get currents at cell centers
include_Vcoils	Include voltage coils in the calculation?

◆ get_conductor_source()

get_conductor_source	(	self,
		dpsi_dt
	)

Get toroidal current density in conducting regions for a $ d \psi / dt $ source.

Parameters

dpsi_dt dPsi/dt source eddy currents (eg. from linear stability)

◆ get_delstar_curr()

get_delstar_curr	(	self,
		psi
	)

Get toroidal current density from $ \psi $ through $ \Delta^{*} $ operator.

Deprecated:: Use calc_delstar_curr instead.

Parameters

psi	$ \psi $ corresponding to desired current density

Returns: $ J_{\phi} = \textrm{M}^{-1} \Delta^{*} \psi $ [A/m^2]

◆ get_field_eval()

get_field_eval	(	self,
		field_type
	)

Create field interpolator for vector potential.

Parameters

field_type Field to interpolate, must be one of ("B", "psi", "F", "P", "dPSI", "dBr", "dBt", or "dBz")

Returns: Field interpolation object

◆ get_globals()

get_globals ( self )

Get global plasma parameters.

Returns: Ip, [R_Ip, Z_Ip], $\int dV$, $\int P dV$, diamagnetic flux, enclosed toroidal flux

◆ get_jtor_plasma()

get_jtor_plasma ( self )

Get plasma toroidal current density for current equilibrium.

Deprecated:: Use calc_jtor_plasma instead.

Returns: $ J_{\phi} $ by evalutating RHS source terms

◆ get_profiles()

get_profiles	(	self,
		psi = `None`,
		psi_pad = `1.E-8`,
		npsi = `50`
	)

Get G-S source profiles.

Parameters

psi	Explicit sampling locations in $\hat{\psi}$
psi_pad	End padding (axis and edge) for uniform sampling (ignored if `psi` is not None)
npsi	Number of points for uniform sampling (ignored if `psi` is not None)

Returns: $\hat{\psi}$, $F(\hat{\psi})$, $F'(\hat{\psi})$, $P(\hat{\psi})$, $P'(\hat{\psi})$

◆ get_psi()

get_psi	(	self,
		normalized = `True`
	)

Get poloidal flux values on node points.

Parameters

normalized Normalize (and offset) poloidal flux

Returns: $\hat{\psi} = \frac{\psi-\psi_0}{\psi_a-\psi_0} $ or $\psi$

◆ get_q()

get_q	(	self,
		psi = `None`,
		psi_pad = `0.02`,
		npsi = `50`,
		compute_geo = `False`
	)

Get q-profile at specified or uniformly spaced points.

Parameters

psi	Explicit sampling locations in $\hat{\psi}$
psi_pad	End padding (axis and edge) for uniform sampling (ignored if `psi` is not None)
npsi	Number of points for uniform sampling (ignored if `psi` is not None)
compute_geo	Compute geometric values for LCFS

Returns: $\hat{\psi}$, $q(\hat{\psi})$, $[<R>,<1/R>,dV/dPsi]$, length of last surface, [r(R_min),r(R_max)], [r(z_min),r(z_max)]

◆ get_stats()

get_stats	(	self,
		lcfs_pad = `None`,
		axis_pad = `0.02`,
		li_normalization = `'std'`,
		geom_type = `'max'`,
		beta_Ip = `None`
	)

Get information (Ip, q, kappa, etc.) about current G-S equilbirium.

See eq. 1 for ‘li_normalization='std’and eq 2. forli_normalization='iter'` in Jackson et al.

Parameters

lcfs_pad	Padding at LCFS for boundary calculations (default: 1.0 for limited; 0.99 for diverted)
li_normalization	Form of normalized $ l_i $ ('std', 'ITER')
geom_type	Method for computing geometric major/minor radius ('max': Use LCFS extrema, 'mid': Use axis plane extrema)
beta_Ip	Override $ I_p $ used for beta calculations

Returns: Dictionary of equilibrium parameters

◆ get_targets()

get_targets ( self )

Get global target values.

Returns: Dictionary of global target values

◆ get_vfixed()

get_vfixed ( self )

Get required vacuum flux values to balance fixed boundary equilibrium.

Returns: sampling points [:,2], flux values [:]

◆ get_xpoints()

get_xpoints ( self )

Get X-points.

Returns: X-points, is diverted?

◆ init_psi()

init_psi	(	self,
		r0 = `-1.0`,
		z0 = `0.0`,
		a = `0.0`,
		kappa = `0.0`,
		delta = `0.0`,
		curr_source = `None`
	)

Initialize $\psi$ using uniform current distributions.

If r0>0 then a uniform current density inside a surface bounded by a curve of the form defined in oftpy.create_isoflux is used. If r0<0 then a uniform current density over the entire plasma region is used.

Parameters

r0	Major radial position for flux surface-based approach
z0	Vertical position for flux surface-based approach
a	Minor radius for flux surface-based approach
kappa	Elongation for flux surface-based approach
delta	Triangularity for flux surface-based approach
curr_source	Current source for arbitrary current distribution

◆ lim_point()

lim_point ( self )

Limiting point (limter or active X-point) [2].

◆ load_profiles()

load_profiles	(	self,
		f_file = `'none'`,
		foffset = `None`,
		p_file = `'none'`,
		eta_file = `'none'`,
		f_NI_file = `'none'`
	)

Load flux function profiles ( $F*F'$ and $P'$) from files.

Parameters

f_file	File containing $F*F'$ (or $F'$ if `mode=0`) definition
foffset	Value of $F0=R0*B0$
p_file	File containing $P'$ definition
eta_file	File containing $\eta$ definition
f_NI_file	File containing non-inductive $F*F'$ definition

◆ o_point()

o_point ( self )

Location of O-point (magnetic axis) [2].

◆ p_scale() [1/2]

p_scale ( self )

Pressure scale value.

◆ p_scale() [2/2]

p_scale	(	self,
		value
	)

◆ plot_constraints()

plot_constraints	(	self,
		fig,
		ax,
		equilibrium = `None`,
		isoflux_color = `'tab:red'`,
		isoflux_marker = `'+'`,
		saddle_color = `'tab:green'`,
		saddle_marker = `'x'`
	)

Plot geometry constraints.

Parameters

fig	Figure to add to
ax	Axis to add to
equilibrium	Equilibrium object (if `None`, current equilibrium is used)
isoflux_color	Color of isoflux points (`None` to disable)
saddle_color	Color of saddle points (`None` to disable)

◆ plot_eddy()

plot_eddy	(	self,
		fig,
		ax,
		psi = `None`,
		equilibrium = `None`,
		dpsi_dt = `None`,
		nlevels = `40`,
		colormap = `'jet'`,
		clabel = `r'$J_w$ [$A/m^2$]'`,
		symmap = `False`,
		include_Vcoils = `False`
	)

Plot contours of $\hat{\psi}$.

Parameters

fig	Figure to add to
ax	Axis to add to
psi	Psi corresponding to eddy currents (eg. from time-dependent simulation)
equilibrium	Equilibrium object (if `equilibrium=None`, `psi=None` and `dpsi_dt=None`, current equilibrium is used)
dpsi_dt	dPsi/dt source eddy currents (eg. from linear stability)
nlevels	Number contour lines used for shading (with "psi" only)
colormap	Colormap to use for shadings
clabel	Label for colorbar (`None` to disable colorbar)
symmap	Make colorscale symmetric around zero (only applies if `colormap` is specified)
include_Vcoils	Include V-coil regions when plotting eddy currents? (only applies if `dpsi_dt=None` is specified)

Returns: Colorbar object

◆ plot_machine()

plot_machine	(	self,
		fig,
		ax,
		equilibrium = `None`,
		vacuum_color = `'whitesmoke'`,
		cond_color = `'gray'`,
		limiter_color = `'k'`,
		coil_color = `'gray'`,
		coil_colormap = `None`,
		coil_symmap = `False`,
		coil_scale = `1.0`,
		coil_clabel = `r'$I_C$ [A]'`,
		colorbar = `None`
	)

Plot machine geometry.

Parameters

fig	Figure to add to
ax	Axis to add to
equilibrium	Equilibrium object (if `None`, current equilibrium is used)
vacuum_color	Color to shade vacuum region (`None` to disable)
cond_color	Color for conducting regions (`None` to disable)
limiter_color	Color for limiter contour (`None` to disable)
coil_color	Color for coil regions (`None` to disable)
coil_colormap	Colormap for coil current values
coil_symmap	Make coil current colorscale symmetric
coil_scale	Scale for coil currents when plotting
coil_clabel	Label for coil current colorbar (`None` to disable colorbar)
colorbar	Colorbar instance to overwrite (`None` to add)

Returns: Colorbar instance for coil colors or None

◆ plot_psi()

plot_psi	(	self,
		fig,
		ax,
		equilibrium = `None`,
		psi = `None`,
		normalized = `True`,
		plasma_color = `None`,
		plasma_nlevels = `8`,
		plasma_levels = `None`,
		plasma_colormap = `None`,
		plasma_linestyles = `None`,
		vacuum_color = `'darkgray'`,
		vacuum_nlevels = `8`,
		vacuum_levels = `None`,
		vacuum_colormap = `None`,
		vacuum_linestyles = `None`,
		xpoint_color = `'k'`,
		xpoint_marker = `'x'`,
		xpoint_inactive_alpha = `0.5`,
		opoint_color = `'k'`,
		opoint_marker = `'*'`
	)

Plot contours of $\hat{\psi}$.

Parameters

fig	Figure to add to
ax	Axis to add to
equilibrium	Equilibrium object (if `None`, current equilibrium is used)
psi	Flux values to plot (otherwise `equilibrium.get_psi()` is called)
normalized	Retreive normalized flux, or assume normalized psi if passed as argument
plasma_color	Color for plasma contours
plasma_nlevels	Number of plasma contours
plasma_levels	Explicit levels for plasma contours
plasma_colormap	Colormap for plasma contours (cannot be specified with `plasma_color`)
plasma_linestyles	Linestyle for plasma contours
vacuum_color	Color for vacuum contours
vacuum_nlevels	Number of vacuum contours
vacuum_levels	Explicit levels for vacuum contours (cannot be specified with `vacuum_color`)
vacuum_colormap	Colormap for vacuum contours
vacuum_linestyles	Linestyle for vacuum contours
xpoint_color	Color for X-point markers (`None` to disable)
xpoint_marker	Marker style for X-points
xpoint_inactive_alpha	Alpha value for inactive X-points
opoint_color	Color for O-point markers (`None` to disable)
opoint_marker	Marker style for O-points

◆ pnorm()

pnorm ( self )

Pressure normalization value.

Deprecated:: Use p_scale property instead.

◆ print_info()

print_info	(	self,
		lcfs_pad = `None`,
		axis_pad = `0.02`,
		li_normalization = `'std'`,
		geom_type = `'max'`,
		beta_Ip = `None`
	)

Print information (Ip, q, etc.) about current G-S equilbirium.

Parameters

lcfs_pad	Padding at LCFS for boundary calculations (default: 1.0 for limited; 0.99 for diverted)
li_normalization	Form of normalized $ l_i $ ('std', 'ITER')
geom_type	Method for computing geometric major/minor radius ('max': Use LCFS extrema, 'mid': Use axis plane extrema)
beta_Ip	Override $ I_p $ used for beta calculations

◆ psi_bounds()

psi_bounds ( self )

Bounding values for $\psi$ ( $\psi_a$, $\psi_0$) [2].

◆ psinorm_to_absolute()

psinorm_to_absolute	(	self,
		psi_in
	)

Convert normalized $ \hat{\psi} $ values to unnormalized values $ \psi $.

Parameters

psi_in Input $ \hat{\psi} $ values

Returns: Unnormalized $ \psi $ values

◆ reset()

reset ( self )

Reset G-S object to enable loading a new mesh and coil configuration.

◆ sauter_fc()

sauter_fc	(	self,
		psi = `None`,
		psi_pad = `0.02`,
		npsi = `50`
	)

Evaluate Sauter trapped particle fractions at specified or uniformly spaced points.

Parameters

psi	Explicit sampling locations in $\hat{\psi}$
psi_pad	End padding (axis and edge) for uniform sampling (ignored if `psi` is not None)
npsi	Number of points for uniform sampling (ignored if `psi` is not None)

Returns: $ f_c $, [ $<R>,<1/R>,<a>$], [ $<|B|>,<|B|^2>$]

◆ save_eqdsk()

save_eqdsk	(	self,
		filename,
		nr = `65`,
		nz = `65`,
		rbounds = `None`,
		zbounds = `None`,
		run_info = `''`,
		lcfs_pad = `0.01`,
		rcentr = `None`,
		truncate_eq = `True`,
		limiter_file = `''`,
		lcfs_pressure = `0.0`,
		cocos = `7`
	)

Save current equilibrium to gEQDSK format.

Parameters

filename	Filename to save equilibrium to
nr	Number of radial sampling points
nz	Number of vertical sampling points
rbounds	Extents of grid in R
zbounds	Extents of grid in Z
run_info	Run information for gEQDSK file (maximum of 40 characters)
lcfs_pad	Padding in normalized flux at LCFS
rcentr	`RCENTR` value for gEQDSK file (if `None`, geometric axis is used)
truncate_eq	Truncate equilibrium at `lcfs_pad`, if `False` $ q(\hat{\psi} > 1-pad) = q(1-pad) $
limiter_file	File containing limiter contour to use instead of TokaMaker limiter
lcfs_pressure	Plasma pressure on the LCFS (zero by default)
cocos	COCOS version. (Only 2 or 7 supported. `cocos=7` is the default.)

◆ save_ifile()

save_ifile	(	self,
		filename,
		npsi = `65`,
		ntheta = `65`,
		lcfs_pad = `0.01`,
		lcfs_pressure = `0.0`,
		pack_lcfs = `True`,
		single_precision = `False`
	)

Save current equilibrium to iFile format.

Parameters

filename	Filename to save equilibrium to
npsi	Number of radial sampling points
ntheta	Number of vertical sampling points
lcfs_pad	Padding in normalized flux at LCFS
lcfs_pressure	Plasma pressure on the LCFS (zero by default)
pack_lcfs	Pack toward LCFS with quadraturic sampling?
single_precision	Save single precision file? (default: double precision)

◆ save_mug()

save_mug	(	self,
		filename
	)

Save current equilibrium to MUG transfer format.

Parameters

filename Filename to save equilibrium to

◆ set_coil_bounds()

set_coil_bounds	(	self,
		coil_bounds = `None`
	)

Set hard constraints on coil currents.

Can be used with or without regularization terms (see set_coil_reg).

Parameters

coil_bounds Minimum and maximum allowable coil currents (dictionary of form {coil_name: coil_bound[2]})

◆ set_coil_current_dist()

set_coil_current_dist	(	self,
		coil_name,
		curr_dist = `None`,
		normalize = `False`
	)

Overwrite coil with non-uniform current distribution.

Parameters

coil_name	Name of coil to modify
curr_dist	Relative current density [self.np] (None to disable non-uniform distribution and return to uniform current)
normalize	Normalize distribution to have unit current?

◆ set_coil_currents()

set_coil_currents	(	self,
		currents = `None`
	)

Set coil currents.

Parameters

currents Current in each coil [A]

◆ set_coil_reg()

set_coil_reg	(	self,
		reg_mat = `None`,
		reg_targets = `None`,
		reg_weights = `None`,
		reg_terms = `None`
	)

Set regularization matrix for coil currents when isoflux and/or saddle constraints are used.

Can be used to enforce "soft" constraints on coil currents. For hard constraints see set_coil_bounds.

Parameters

reg_mat	Regularization matrix [nregularize,ncoils+1]
reg_targets	Regularization targets [nregularize] (default: 0)
reg_weights	Weights for regularization terms [nregularize] (default: 1)
reg_terms	List of regularization terms created with coil_reg_term

◆ set_coil_vsc()

set_coil_vsc	(	self,
		coil_gains
	)

Define a vertical stability coil set from one or more coils.

Parameters

coil_gains Gains for each coil (absolute scale is arbitrary)

◆ set_dipole_a()

set_dipole_a	(	self,
		a_exp = `None`
	)

Update anisotropy exponent a when dipole mode is used, calling with no argument will disable pressure anisotropy.

Parameters

a_exp New value for a exponent

◆ set_flux()

set_flux	(	self,
		locations,
		targets,
		weights = `None`
	)

Set explicit flux constraint points $ \psi(x_i) $ [Wb/rad].

Deprecated:: Use set_psi_constraints or set_flux_constraints instead.

Parameters

locations	List of points defining constraints [:,2]
targets	Target $ \psi $ value in Wb/rad at each point [:]
weights	Weight to be applied to each constraint point [:] (default: 1)

◆ set_flux_constraints()

set_flux_constraints	(	self,
		locations,
		targets,
		weights = `None`
	)

Set explicit flux constraint points $ \psi(x_i) $ [Wb].

Parameters

locations	List of points defining constraints [:,2]
targets	Target $ \psi $ value in Wb at each point [:]
weights	Weight to be applied to each constraint point [:] (default: 1)

◆ set_isoflux()

set_isoflux	(	self,
		isoflux,
		weights = `None`,
		grad_wt_lim = `-1.0`,
		ref_points = `None`
	)

Set isoflux constraint points (all points lie on a flux surface)

To constraint points more uniformly in space additional weighting based on the gradient of $\psi$ at each point can also be included by setting grad_wt_lim>0. When set the actual weight will be $w_i * min(grad_wt_lim,|\nabla \psi|_{max} / |\nabla \psi|_i)$

Deprecated:: Use set_isoflux_constraints instead.

Parameters

isoflux	List of points defining constraints [:,2]
weights	Weight to be applied to each constraint point [:] (default: 1)
grad_wt_lim	Limit on gradient-based weighting (negative to disable)
ref_points	Reference points for each isoflux point [:,2] (default: `isoflux[0,:]` is used for all points)

◆ set_isoflux_constraints()

set_isoflux_constraints	(	self,
		isoflux,
		weights = `None`,
		grad_wt_lim = `-1.0`,
		ref_points = `None`
	)

Set isoflux constraint points (all points lie on a flux surface)

To constraint points more uniformly in space additional weighting based on the gradient of $\psi$ at each point can also be included by setting grad_wt_lim>0. When set the actual weight will be $w_i * min(grad_wt_lim,|\nabla \psi|_{max} / |\nabla \psi|_i)$

Parameters

isoflux	List of points defining constraints [:,2]
weights	Weight to be applied to each constraint point [:] (default: 1)
grad_wt_lim	Limit on gradient-based weighting (negative to disable)
ref_points	Reference points for each isoflux point [:,2] (default: `isoflux[0,:]` is used for all points)

◆ set_mirror_slosh()

set_mirror_slosh	(	self,
		n_exp = `None`,
		b_turn = `None`,
		z_throat = `None`
	)

Update anisotropy exponent a when dipole mode is used, calling with no arguments will disable pressure anisotropy.

Parameters

n_exp	New value for `n` exponent
b_turn	Relative B-field at ion turning point (b_turn = B/B_0)
z_throat	Location of mirror throat

◆ set_profiles()

set_profiles	(	self,
		ffp_prof = `None`,
		foffset = `None`,
		pp_prof = `None`,
		ffp_NI_prof = `None`,
		keep_files = `False`
	)

Set flux function profiles ( $F*F'$ and $P'$) using a piecewise linear definition.

Parameters

ffp_prof	Dictionary object containing FF' profile ['y'] and sampled locations in normalized Psi ['x']
foffset	Value of $F0=R0*B0$
pp_prof	Dictionary object containing P' profile ['y'] and sampled locations in normalized Psi ['x']
ffp_NI_prof	Dictionary object containing non-inductive FF' profile ['y'] and sampled locations in normalized Psi ['x']
keep_files	Retain temporary profile files

◆ set_psi()

set_psi	(	self,
		psi,
		update_bounds = `False`
	)

Set poloidal flux values on node points.

Parameters

psi	Poloidal flux values (should not be normalized!)
update_bounds	Update plasma bounds by determining new limiting points

◆ set_psi_constraints()

set_psi_constraints	(	self,
		locations,
		targets,
		weights = `None`
	)

Set explicit flux constraint points $ \psi(x_i) $ [Wb/rad].

Parameters

locations	List of points defining constraints [:,2]
targets	Target $ \psi $ value in Wb/rad at each point [:]
weights	Weight to be applied to each constraint point [:] (default: 1)

◆ set_psi_dt()

set_psi_dt	(	self,
		psi0,
		dt,
		coil_currents = `None`,
		coil_voltages = `None`
	)

Set reference poloidal flux and time step for eddy currents in .solve()

Parameters

psi0	Reference poloidal flux at t-dt (unnormalized)
dt	Time since reference poloidal flux
coil_currents	Currents for Vcoils [A] (dictionary of form `{coil_name: coil_curr}`, defaults to current solution)
coil_voltages	Voltages for Vcoils [V] (dictionary of form `{coil_name: coil_volt}`)

◆ set_resistivity()

set_resistivity	(	self,
		eta_prof = `None`
	)

Set flux function profile $\eta$ using a piecewise linear definition.

Arrays should have the form array[i,:] = ( $\hat{\psi}_i$, $f(\hat{\psi}_i)$) and span $\hat{\psi}_i = [0,1]$.

Parameters

eta_prof Values defining $\eta$ [:,2]

◆ set_saddle_constraints()

set_saddle_constraints	(	self,
		saddles,
		weights = `None`
	)

Set saddle constraint points (poloidal field should vanish at each point)

Parameters

saddles	List of points defining constraints [:,2]
weights	Weight to be applied to each constraint point [:] (default: 1)

◆ set_saddles()

set_saddles	(	self,
		saddles,
		weights = `None`
	)

Set saddle constraint points (poloidal field should vanish at each point)

Deprecated:: Use set_saddle_constraints instead.

Parameters

saddles	List of points defining constraints [:,2]
weights	Weight to be applied to each constraint point [:] (default: 1)

◆ set_targets()

set_targets	(	self,
		Ip = `None`,
		Ip_ratio = `None`,
		pax = `None`,
		estore = `None`,
		R0 = `None`,
		V0 = `None`,
		Z0 = `None`,
		retain_previous = `False`
	)

Set global target values.

Note: Values that are not specified are reset to their defaults on each call unless retain_previous=True.

Parameters

Ip	Target plasma current [A]
Ip_ratio	Amplitude of net plasma current contribution from FF' compared to P'
pax	Target axis pressure [Pa]
estore	Target sotred energy [J]
R0	Target major radius for magnetic axis
V0	Target vertical position for magnetic axis
Z0	Target vertical position for magnetic axis
retain_previous	Keep previously set targets unless explicitly updated? (default: False)

◆ set_vcoils()

set_vcoils	(	self,
		coil_resistances
	)

Set or unset one or more coils as Vcoils by defining their lumped resistances.

Parameters

coil_resistances Lumped coil resistances for Vcoils [Ohms] (dictionary of form {coil_name: coil_res})

◆ setup()

setup	(	self,
		order = `2`,
		F0 = `0.0`,
		full_domain = `False`
	)

Setup G-S solver.

Parameters

order	Order of FE representation to use
F0	Vacuum $F(\psi)$ value (B0*R0)

◆ setup_mesh()

setup_mesh	(	self,
		r = `None`,
		lc = `None`,
		reg = `None`,
		mesh_file = `None`
	)

Setup mesh for static and time-dependent G-S calculations.

A mesh should be specified by passing "r", "lc", and optionally "reg" or using a "mesh_file". When a region is specified the following ordering should apply:

1: Plasma region
2: Vacuum/air regions
3+: Conducting regions and coils

Parameters

r	Mesh point list [np,2]
lc	Mesh cell list [nc,3] (base one)
reg	Mesh region list [nc] (base one)
mesh_file	Filename containing mesh to load (native format only)

◆ setup_regions()

setup_regions	(	self,
		cond_dict = `{}`,
		coil_dict = `{}`
	)

Define mesh regions (coils and conductors)

Parameters

cond_dict Dictionary specifying conducting regions

◆ setup_td()

setup_td	(	self,
		dt,
		lin_tol,
		nl_tol,
		pre_plasma = `False`
	)

Setup the time-dependent G-S solver.

Parameters

dt	Starting time step
lin_tol	Tolerance for linear solver
nl_tol	Tolerance for non-linear solver
pre_plasma	Use plasma contributions in preconditioner (default: False)

◆ solve()

solve	(	self,
		vacuum = `False`
	)

Solve G-S equation with specified constraints, profiles, etc.

Parameters

vacuum Perform vacuum solve? Plasma-related targets (eg. Ip) will be ignored.

Returns: Equilibrium object

◆ step_td()

step_td	(	self,
		time,
		dt,
		coil_currents = `None`,
		coil_voltages = `None`
	)

Advance time-dependent solution by one time step.

Parameters

time	Time at the start of the time step [s]
dt	Timestep size [s]
coil_currents	Coil currents at the end of the timestep (if `None`, current coil currents are used)
coil_voltages	Coil voltages to apply over the timestep (if `None`, zero voltages are assumed)

Returns: new time, new dt, # of NL iterations, # of linear iterations, # of retries

◆ trace_surf()

trace_surf	(	self,
		psi
	)

Trace surface for a given poloidal flux.

Parameters

psi	Flux surface to trace $\hat{\psi}$

Returns: $r(\hat{\psi})$

◆ update_settings()

update_settings ( self )

Update settings after changes to values in python.

◆ vac_solve()

vac_solve	(	self,
		psi = `None`,
		rhs_source = `None`
	)

Solve for vacuum solution (no plasma), with present coil currents and optional other currents.

Note: If isoflux, flux, or saddle constraints are desired use solve instead.

Parameters

psi	Boundary values for vacuum solve
rhs_source	Current source [A/m^2] (optional)

Returns: Equilibrium object

Member Data Documentation

◆ _coil_dict

_coil_dict

protected

Coil definition dictionary.

◆ _cond_dict

_cond_dict

protected

Conductor definition dictionary.

◆ _F0

_F0

protected

Vacuum F value.

◆ _mesh_ptr

_mesh_ptr

protected

Internal mesh object.

◆ _oft_env

_oft_env

protected

◆ _tMaker_equil

_tMaker_equil

protected

Internal Grad-Shafranov object (gs_equil)

◆ _tMaker_ptr

_tMaker_ptr

protected

Internal Grad-Shafranov object (gs_factory)

◆ _vac_dict

_vac_dict

protected

Vacuum definition dictionary.

◆ _vcoils

_vcoils

protected

Voltage coils dictionary.

Currently only used for plotting on python side.

◆ _virtual_coils

_virtual_coils

protected

Virtual coils, if present (currently only ‘’#VSC'`)

◆ coil_set_names

coil_set_names

Coil set names in order of id number.

◆ coil_sets

coil_sets

Coil set definitions, including sub-coils.

◆ dist_coils

dist_coils

Distribution coils, only (currently) saved for plotting utility.

◆ lc

lc

Mesh triangles [nc,3].

◆ Lcoils

Lcoils

Coil self-inductance matrix [ncoils].

◆ lim_contour

lim_contour

Limiting contour.

◆ lim_contours

lim_contours

Limiting contours (if multiple)

◆ nc

nc

Number of cells in mesh.

◆ ncoils

ncoils

Number of coils in mesh.

◆ np

np

Number of points in mesh.

◆ nregs

nregs

Number of regions in mesh.

◆ nvac

nvac

Number of vacuum regions in mesh.

◆ psi_convention

psi_convention

Normalized flux convention (0 -> tokamak, 1 -> spheromak)

◆ r

r

Mesh vertices [np,3] (last column should be all zeros)

◆ reg

reg

Mesh regions [nc].

◆ settings

settings

General settings object.

The documentation for this class was generated from the following file:

python/OpenFUSIONToolkit/TokaMaker/_core.py

coffs	Dictionary of coefficients \( \alpha \) (zero for unspecified coils)
target	Regularization target (default: 0.0)
weight	Weight for regularization term (default: 1.0)

psi_vals	\( \hat{\psi} \) values defining flux function [:]
field_vals	Flux function values at each \( \hat{\psi} \) value [:]

psi	Explicit sampling locations in \(\hat{\psi}\)
psi_pad	End padding (axis and edge) for uniform sampling (ignored if `psi` is not None)
npsi	Number of points for uniform sampling (ignored if `psi` is not None)

f_file	File containing \(F*F'\) (or \(F'\) if `mode=0`) definition
foffset	Value of \(F0=R0*B0\)
p_file	File containing \(P'\) definition
eta_file	File containing $\eta$ definition
f_NI_file	File containing non-inductive \(F*F'\) definition

order	Order of FE representation to use
F0	Vacuum \(F(\psi)\) value (B0*R0)

Detailed Description

Public Member Functions

Public Attributes

Protected Attributes

Constructor & Destructor Documentation

◆ __init__()

◆ __del__()

Member Function Documentation

◆ abspsi_to_normalized()

◆ alam()

◆ area_integral()

◆ c_ptr()

◆ calc_delstar_curr()

◆ calc_jtor_plasma()

◆ calc_loopvoltage()

◆ coil_dict2vec()

◆ coil_reg_term()

◆ coil_vec2dict()

◆ compute_area_integral()

◆ compute_flux_integral()

◆ copy_eq()

◆ diverted()

◆ eig_td()

◆ eig_wall()

◆ ffp_scale() [1/2]

◆ ffp_scale() [2/2]

◆ flux_integral()

◆ get_coil_currents()

◆ get_coil_Lmat()

◆ get_conductor_currents()

◆ get_conductor_source()

◆ get_delstar_curr()

◆ get_field_eval()

◆ get_globals()

◆ get_jtor_plasma()

◆ get_profiles()

◆ get_psi()

◆ get_q()

◆ get_stats()

◆ get_targets()

◆ get_vfixed()

◆ get_xpoints()

◆ init_psi()

◆ lim_point()

◆ load_profiles()

◆ o_point()

◆ p_scale() [1/2]

◆ p_scale() [2/2]

◆ plot_constraints()

◆ plot_eddy()

◆ plot_machine()

◆ plot_psi()

◆ pnorm()

◆ print_info()

◆ psi_bounds()

◆ psinorm_to_absolute()

◆ reset()

◆ sauter_fc()

◆ save_eqdsk()

◆ save_ifile()

◆ save_mug()

◆ set_coil_bounds()

◆ set_coil_current_dist()

◆ set_coil_currents()

◆ set_coil_reg()

◆ set_coil_vsc()

◆ set_dipole_a()

◆ set_flux()

◆ set_flux_constraints()

◆ set_isoflux()

◆ set_isoflux_constraints()

◆ set_mirror_slosh()

◆ set_profiles()

◆ set_psi()

◆ set_psi_constraints()

◆ set_psi_dt()

◆ set_resistivity()

◆ set_saddle_constraints()

◆ set_saddles()

◆ set_targets()

◆ init()

◆ del()