OpenFUSIONToolkit.TokaMaker.bootstrap Namespace Reference

Detailed Description

Solvers and helper functions for TokaMaker bootstrap current functionality.

Authors

Daniel Burgess

Date

January 2026

Functions
	analyze_bootstrap_edge_spike (psi_N, j_bootstrap, diagnostic_plots=False)
	Analyze bootstrap edge spike location, width, and height.
	calculate_ln_lambda (Te, Ti, ne, ni, Zeff=1.0, electron_lnLambda_model='sauter', ion_lnLambda_model='unity')
	Calculate Coulomb logarithm for electrons and ions.
	find_optimal_scale (mygs, psi_N, pressure, ffp_prof, pp_prof, j_inductive, Ip_target, psi_pad, spike_prof=None, find_j0=True, scale_j0=1.0, tolerance=0.01, max_iter=5, diagnostic_plots=False, verbose=True)
	Optimize scaling to match input/output \(j_0\) or \(I_p\).
	Hmode_profiles (edge=0.08, ped=0.4, core=2.5, rgrid=201, expin=1.5, expout=1.5, widthp=0.04, xphalf=None)
	This function generates H-mode density and temperature profiles evenly spaced in your favorite radial coordinate.
	parameterize_edge_jBS (psi, amp, center, width, offset, sk, y_sep=0.0, blend_width=0.03, tail_alpha=1.5)
	Generate parameterized edge bootstrap current profile with tunable concave fall-off.
	redl_bootstrap (psi_N=None, Te=None, Ti=None, ne=None, ni=None, pe=None, pi=None, Zeff=None, R=None, q=None, eps=None, fT=None, I_psi=None, dT_e_dpsi=None, dT_i_dpsi=None, dn_e_dpsi=None, dn_i_dpsi=None, dp_dpsi=None, ln_lambda_e=17.0, ln_lambda_ii=17.0, use_legacy_L34=False, use_sign_q=False, ion_collisionality_model='Zeff', formula_form='jB', Zeff_override=None, nu_e_star_override=None, nu_i_star_override=None)
	Bootstrap current via Redl et al., Phys.
	solve_jphi (mygs, ffp_prof, pp_prof, Ip_target, pax_target)
	Solve Grad-Shafranov equilibrium for given profiles.
	solve_with_bootstrap (mygs, ne, Te, ni, Ti, Zeff, Ip_target, inductive_jphi=None, Zis=None, scale_jBS=1.0, isolate_edge_jBS=False, psi_pad=1e-3, iterations=3, diagnostic_plots=False, parameterize_jBS=False, use_OMFIT_sauter=False, verbose=True)
	Self-consistently compute bootstrap current from H-mode profiles.

Function Documentation

analyze_bootstrap_edge_spike()

analyze_bootstrap_edge_spike	(		psi_N,
			j_bootstrap,
			diagnostic_plots = False
	)

Analyze bootstrap edge spike location, width, and height.

Parameters

psi_N	Normalized poloidal flux profile \(\hat{\psi}\)
j_bootstrap	Bootstrap current profile \(j_{BS}(\hat{\psi})\)
diagnostic_plots	If True, plot diagnostic figures

Returns

Dictionary with spike properties and parameterized spike model

calculate_ln_lambda()

calculate_ln_lambda	(		Te,
			Ti,
			ne,
			ni,
			Zeff = 1.0,
			electron_lnLambda_model = 'sauter',
			ion_lnLambda_model = 'unity'
	)

Calculate Coulomb logarithm for electrons and ions.

Parameters

Te	Electron temperature profile \(T_e\) [eV]
Ti	Ion temperature profile \(T_i\) [eV]
ne	Electron density profile \(n_e\) [m$^{-3}$]
ni	Ion density profile \(n_i\) [m$^{-3}$]
Zeff	Effective charge \(Z_{eff}\)
electron_lnLambda_model	Model for electron Coulomb log ('sauter', 'NRL')
ion_lnLambda_model	Model for ion Coulomb log ('unity', 'Zavg')

Returns

Tuple ( \(\ln\Lambda_e\), \(\ln\Lambda_{ii}\))

find_optimal_scale()

find_optimal_scale	(		mygs,
			psi_N,
			pressure,
			ffp_prof,
			pp_prof,
			j_inductive,
			Ip_target,
			psi_pad,
			spike_prof = None,
			find_j0 = True,
			scale_j0 = 1.0,
			tolerance = 0.01,
			max_iter = 5,
			diagnostic_plots = False,
			verbose = True
	)

Optimize scaling to match input/output \(j_0\) or \(I_p\).

Parameters

mygs	Grad-Shafranov solver object
psi_N	Normalized poloidal flux profile \(\hat{\psi}\)
pressure	Plasma pressure profile \(p(\hat{\psi})\) [Pa]
ffp_prof	Toroidal current profile ( \(j_\phi(\hat{\psi})\))
pp_prof	Pressure gradient profile (

Hmode_profiles()

Hmode_profiles	(		edge = 0.08,
			ped = 0.4,
			core = 2.5,
			rgrid = 201,
			expin = 1.5,
			expout = 1.5,
			widthp = 0.04,
			xphalf = None
	)

This function generates H-mode density and temperature profiles evenly spaced in your favorite radial coordinate.

Copied from https://omfit.io/_modules/omfit_classes/utils_fusion.html

Parameters

edge	Separatrix height (float)
ped	Pedestal height (float)
core	On-axis profile height (float)
rgrid	Number of radial grid points (int)
expin	Inner core exponent for H-mode pedestal profile (float)
expout	Outer core exponent for H-mode pedestal profile (float)
widthp	Width of pedestal (float)
xphalf	Position of tanh (float, optional)

Returns

H-mode profile array over radial grid

parameterize_edge_jBS()

parameterize_edge_jBS	(		psi,
			amp,
			center,
			width,
			offset,
			sk,
			y_sep = 0.0,
			blend_width = 0.03,
			tail_alpha = 1.5
	)

Generate parameterized edge bootstrap current profile with tunable concave fall-off.

Parameters

psi	Normalized poloidal flux profile \(\hat{\psi}\)
amp	Amplitude of edge skewed Gaussian spike
center	Center location of edge skewed Gaussian spike
width	Width of edge skewed Gaussian spike
offset	Height of core flat profile
sk	Skewness parameter of Gaussian
y_sep	Value at separatrix ( \(\hat{\psi}=1\)) for profile
blend_width	Blending width for smooth transition in \(\hat{\psi}\)
tail_alpha	Controls right-side fall-off shape (1.0 = cosine, >1.0 = concave)

Returns

Parameterized bootstrap current profile as array over \(\hat{\psi}\)

redl_bootstrap()

redl_bootstrap	(		psi_N = None,
			Te = None,
			Ti = None,
			ne = None,
			ni = None,
			pe = None,
			pi = None,
			Zeff = None,
			R = None,
			q = None,
			eps = None,
			fT = None,
			I_psi = None,
			dT_e_dpsi = None,
			dT_i_dpsi = None,
			dn_e_dpsi = None,
			dn_i_dpsi = None,
			dp_dpsi = None,
			ln_lambda_e = 17.0,
			ln_lambda_ii = 17.0,
			use_legacy_L34 = False,
			use_sign_q = False,
			ion_collisionality_model = 'Zeff',
			formula_form = 'jB',
			Zeff_override = None,
			nu_e_star_override = None,
			nu_i_star_override = None
	)

Bootstrap current via Redl et al., Phys.

Plasmas 28, 022502 (2021)

Parameters

psi_N	Normalized poloidal flux profile \(\hat{\psi}\)
Te	Electron temperature profile \(T_e\) [eV]
Ti	Ion temperature profile \(T_i\) [eV]
ne	Electron density profile \(n_e\) [m$^{-3}$]
ni	Ion density profile \(n_i\) [m$^{-3}$]
pe	Electron pressure profile \(p_e\) [Pa]
pi	Ion pressure profile \(p_i\) [Pa]
Zeff	Effective charge \(Z_{eff}\)
R	Major radius \(R\) [m]
q	Safety factor \(q\)
eps	Inverse aspect ratio \(\epsilon\)
fT	Trapped particle fraction \(f_T\)
I_psi	Toroidal current function \(I(\psi)\)
dT_e_dpsi	Derivative of \(T_e\) w.r.t. \(\psi\)
dT_i_dpsi	Derivative of \(T_i\) w.r.t. \(\psi\)
dn_e_dpsi	Derivative of \(n_e\) w.r.t. \(\psi\)
dn_i_dpsi	Derivative of \(n_i\) w.r.t. \(\psi\)
dp_dpsi	Derivative of total pressure w.r.t. \(\psi\)
ln_lambda_e	Electron Coulomb logarithm \(\ln\Lambda_e\)
ln_lambda_ii	Ion Coulomb logarithm \(\ln\Lambda_{ii}\)
use_legacy_L34	Use legacy L34 formula (see Redl Eq. 19)
use_sign_q	Multiply by sign of \(q\)
ion_collisionality_model	Model for ion collisionality ('Zeff', 'Koh', 'unity')
formula_form	Use 'jB' (default) or 'jboot1' equation
Zeff_override	Override \(Z_{eff}\) if set
nu_e_star_override	Override electron collisionality if set
nu_i_star_override	Override ion collisionality if set

Returns

Tuple (bootstrap current profile \(j_{BS}(\hat{\psi})\), coefficient dictionary)

solve_jphi()

solve_jphi	(		mygs,
			ffp_prof,
			pp_prof,
			Ip_target,
			pax_target
	)

Solve Grad-Shafranov equilibrium for given profiles.

Parameters

mygs	Grad-Shafranov solver object
ffp_prof	Toroidal current profile ( \(j_\phi(\hat{\psi})\)), type 'jphi-linterp'
pp_prof	Pressure gradient profile (

solve_with_bootstrap()

solve_with_bootstrap	(		mygs,
			ne,
			Te,
			ni,
			Ti,
			Zeff,
			Ip_target,
			inductive_jphi = None,
			Zis = None,
			scale_jBS = 1.0,
			isolate_edge_jBS = False,
			psi_pad = 1e-3,
			iterations = 3,
			diagnostic_plots = False,
			parameterize_jBS = False,
			use_OMFIT_sauter = False,
			verbose = True
	)

Self-consistently compute bootstrap current from H-mode profiles.

Parameters

mygs	Grad-Shafranov solver object
ne	Electron density profile \(n_e(\hat{\psi})\) [m$^{-3}$]
Te	Electron temperature profile \(T_e(\hat{\psi})\) [eV]
ni	Ion density profile \(n_i(\hat{\psi})\) [m$^{-3}$]
Ti	Ion temperature profile \(T_i(\hat{\psi})\) [eV]
Zeff	Effective charge profile \(Z_{eff}(\hat{\psi})\)
Ip_target	Target plasma current \(I_p\) [A]
inductive_jphi	Inductive toroidal current profile \(j_{ind}(\hat{\psi})\)
Zis	List of impurity atomic numbers (default: [1.0])
scale_jBS	Scaling factor for bootstrap current
isolate_edge_jBS	If True, isolate edge spike in bootstrap current
psi_pad	Padding for flux surface calculations
iterations	Number of solver iterations
diagnostic_plots	If True, plot diagnostic figures
parameterize_jBS	If True, use parameterized edge spike
use_OMFIT_sauter	If True, use OMFIT Sauter model

Returns

Dictionary with total, bootstrap, inductive, and isolated edge current profiles