List of Variables

The table below contains a list of variables that are used in the code and that are available for plotting / analysis.

• Name : Name of the variable as it appears in the code. Pass a string with this name to any of the plotting functions to plot, or to the relevant .compute() method to return the calculated quantity.

• Label : TeX label for the variable.

• Units : Physical units for the variable.

• Description : Description of the variable.

• Aliases : Alternative names of the variable that are equivalent to the primary name.

• kwargs : Optional keyword arguments that can be supplied when computing the variable. See the bottom of this page for detailed descriptions and default values of each argument. The only keyword argument that is valid for all variables is ‘basis’ (see explanation below).

All vector quantities are computed in toroidal coordinates \((R,\phi,Z)\) by default. The keyword argument basis='xyz' can be used to convert the variables into Cartesian coordinates \((X,Y,Z)\). basis must be one of {'rpz', 'xyz'}.

desc.equilibrium.equilibrium.Equilibrium

List of Variables: desc.equilibrium.equilibrium.Equilibrium

Name	Label	Units	Description	Aliases	kwargs
((B*grad)B)_rho	\(((\mathbf{B} \cdot \nabla) \mathbf{B})_{\rho}\)	Tesla squared	Covariant radial component of magnetic tension
((B*grad)B)_theta	\(((\mathbf{B} \cdot \nabla) \mathbf{B})_{\theta}\)	Tesla squared	Covariant poloidal component of magnetic tension
((B*grad)B)_zeta	\(((\mathbf{B} \cdot \nabla) \mathbf{B})_{\zeta}\)	Tesla squared	Covariant toroidal component of magnetic tension
(B*grad(|B|))_r	\(\partial_{\theta} (\mathbf{B} \cdot \nabla B)\)	Tesla squared / meters
(B*grad(|B|))_t	\(\partial_{\theta} (\mathbf{B} \cdot \nabla B)\)	Tesla squared / meters
(B*grad(|B|))_z	\(\partial_{\zeta} (\mathbf{B} \cdot \nabla B)\)	Tesla squared / meters
(B*grad)B	\((\mathbf{B} \cdot \nabla) \mathbf{B}\)	Tesla squared / meters	Magnetic tension
(J*sqrt(g))_r	\(\partial_{\rho} (\mathbf{J} \sqrt{g})\)	Ampere meters	Plasma current density weighted by 3-D volume Jacobian, radial derivative
(curl(B)xB)_rho	\(((\nabla \times \mathbf{B}) \times \mathbf{B})_{\rho}\)	Tesla squared	Covariant radial component of Lorentz force
(curl(B)xB)_theta	\(((\nabla \times \mathbf{B}) \times \mathbf{B})_{\theta}\)	Tesla squared	Covariant poloidal component of Lorentz force
(curl(B)xB)_zeta	\(((\nabla \times \mathbf{B}) \times \mathbf{B})_{\zeta}\)	Tesla squared	Covariant toroidal component of Lorentz force
0	\(0\)	None	Zeros
<1/|B|>	\(\langle 1/|B| \rangle\)	1 / Tesla	Flux surface averaged inverse field strength
<J*B>	\(\langle \mathbf{J} \cdot \mathbf{B} \rangle\)	Newtons / cubic meter	Flux surface average of current density dotted into magnetic field (note units are not Amperes)
<J*B> Redl	\(\langle\mathbf{J}\cdot\mathbf{B}\rangle_{Redl}\)	Tesla Ampere / meter^2	Bootstrap current profile, Redl model for quasisymmetry		helicity
<beta>_vol	\(\langle \beta \rangle_{vol}\)	None	Normalized plasma pressure
<beta_pol>_vol	\(\langle \beta_{pol} \rangle_{vol}\)	None	Normalized poloidal plasma pressure
<beta_tor>_vol	\(\langle \beta_{tor} \rangle_{vol}\)	None	Normalized toroidal plasma pressure
<|(B*grad)B|>_vol	\(\langle |(\mathbf{B} \cdot \nabla) \mathbf{B}| \rangle_{vol}\)	Tesla squared / meters	Volume average magnetic tension magnitude
<|B|>	\(\langle |B| \rangle\)	Tesla	Flux surface average magnetic field
<|B|>_rms	\(\langle |B| \rangle_{rms}\)	Tesla	Volume average magnetic field, root mean square
<|B|>_vol	\(\langle |B| \rangle_{vol}\)	Tesla	Volume average magnetic field
<|B|^2>	\(\langle |B|^2 \rangle\)	Tesla squared	Flux surface average magnetic field squared
<|B|^2>_r	\(\partial_{\rho} \langle |B|^2 \rangle\)	Tesla squared	Flux surface average magnetic field squared, radial derivative
<|F|>_vol	\(\langle |\mathbf{J} \times \mathbf{B} - \nabla p| \rangle_{vol}\)	Newtons / cubic meter	Volume average of magnitude of force balance error
<|grad(p)|>_vol	\(\langle |\nabla p| \rangle_{vol}\)	Newtons per cubic meter	Volume average of magnitude of pressure gradient
<|grad(|B|^2)|/2mu0>_vol	\(\langle |\nabla |B|^{2}/(2\mu_0)| \rangle_{vol}\)	Newtons per cubic meter	Volume average of magnitude of magnetic pressure gradient
A	\(A\)	square meters	Average cross-sectional area
A(r)	\(A(\rho)\)	square meters	Average cross-sectional area enclosed by flux surfaces
A(z)	\(A(\zeta)\)	square meters	Cross-sectional area as function of zeta
B	\(\mathbf{B}\)	Tesla	Magnetic field
B modes	\(\mathrm{Boozer~modes}\)	None	Boozer harmonics		M_booz, N_booz
B*grad(|B|)	\(\mathbf{B} \cdot \nabla B\)	Tesla squared / meters
B0	\(\psi' / \sqrt{g}\)	Tesla / meter
B0_r	\(\partial_{\rho} (\psi' / \sqrt{g})\)	Tesla / meter
B0_rr	\(\partial_{\rho \rho} (\psi' / \sqrt{g})\)	Tesla / meters
B0_rt	\(\partial_{\rho\theta} (\psi' / \sqrt{g})\)	Tesla / meters		B0_tr
B0_rz	\(\partial_{\rho\zeta} (\psi' / \sqrt{g})\)	Tesla / meters		B0_zr
B0_t	\(\partial_{\theta} (\psi' / \sqrt{g})\)	Tesla / meter
B0_tt	\(\partial_{\theta \theta} (\psi' / \sqrt{g})\)	Tesla / meter
B0_tz	\(\partial_{\theta\zeta} (\psi' / \sqrt{g})\)	Tesla / meter		B0_zt
B0_z	\(\partial_{\zeta} (\psi' / \sqrt{g})\)	Tesla / meter
B0_zz	\(\partial_{\zeta \zeta} (\psi' / \sqrt{g})\)	Tesla / meter
B^rho	\(B^{\rho}\)	Tesla / meter	Contravariant radial component of magnetic field
B^theta	\(B^{\theta}\)	Tesla / meter	Contravariant poloidal component of magnetic field
B^theta_r	\(\partial_{\rho} B^{\theta}\)	Tesla / meter	Contravariant poloidal component of magnetic field, derivative wrt radial coordinate
B^theta_rr	\(\partial_{\rho\rho} B^{\theta}\)	Tesla / meter	Contravariant poloidal component of magnetic field, second derivative wrt radial and radial coordinates
B^theta_rt	\(\partial_{\rho\theta} B^{\theta}\)	Tesla / meter	Contravariant poloidal component of magnetic field, second derivative wrt radial and poloidal coordinates	B^theta_tr
B^theta_rz	\(\partial_{\rho\zeta} B^{\theta}\)	Tesla / meter	Contravariant poloidal component of magnetic field, second derivative wrt radial and toroidal coordinates	B^theta_zr
B^theta_t	\(\partial_{\theta} B^{\theta}\)	Tesla / meter	Contravariant poloidal component of magnetic field, derivative wrt poloidal coordinate
B^theta_tt	\(\partial_{\theta\theta} B^{\theta}\)	Tesla / meter	Contravariant poloidal component of magnetic field, second derivative wrt poloidal and poloidal coordinates
B^theta_tz	\(\partial_{\theta\zeta} B^{\theta}\)	Tesla / meter	Contravariant poloidal component of magnetic field, second derivative wrt poloidal and toroidal coordinates	B^theta_zt
B^theta_z	\(\partial_{\zeta} B^{\theta}\)	Tesla / meter	Contravariant poloidal component of magnetic field, derivative wrt toroidal coordinate
B^theta_zz	\(\partial_{\zeta\zeta} B^{\theta}\)	Tesla / meter	Contravariant poloidal component of magnetic field, second derivative wrt toroidal and toroidal coordinates
B^zeta	\(B^{\zeta}\)	Tesla / meter	Contravariant toroidal component of magnetic field
B^zeta_r	\(\partial_{\rho} B^{\zeta}\)	Tesla / meter	Contravariant toroidal component of magnetic field, derivative wrt radial coordinate
B^zeta_rr	\(\partial_{\rho\rho} B^{\zeta}\)	Tesla / meter	Contravariant toroidal component of magnetic field, second derivative wrt radial and radial coordinates
B^zeta_rt	\(\partial_{\rho\theta} B^{\zeta}\)	Tesla / meter	Contravariant toroidal component of magnetic field, second derivative wrt radial and poloidal coordinates	B^zeta_tr
B^zeta_rz	\(\partial_{\rho\zeta} B^{\zeta}\)	Tesla / meter	Contravariant toroidal component of magnetic field, second derivative wrt radial and toroidal coordinates	B^zeta_zr
B^zeta_t	\(\partial_{\theta} B^{\zeta}\)	Tesla / meter	Contravariant toroidal component of magnetic field, derivative wrt poloidal coordinate
B^zeta_tt	\(\partial_{\theta\theta} B^{\zeta}\)	Tesla / meter	Contravariant toroidal component of magnetic field, second derivative wrt poloidal and poloidal coordinates
B^zeta_tz	\(\partial_{\theta\zeta} B^{\zeta}\)	Tesla / meter	Contravariant toroidal component of magnetic field, second derivative wrt poloidal and toroidal coordinates	B^zeta_zt
B^zeta_z	\(\partial_{\zeta} B^{\zeta}\)	Tesla / meter	Contravariant toroidal component of magnetic field, derivative wrt toroidal coordinate
B^zeta_zz	\(\partial_{\zeta\zeta} B^{\zeta}\)	Tesla / meter	Contravariant toroidal component of magnetic field, second derivative wrt toroidal and toroidal coordinates
B_R	\(B_{R}\)	Tesla	Radial component of magnetic field in lab frame
B_Z	\(B_{Z}\)	Tesla	Vertical component of magnetic field in lab frame
B_phi	\(B_{\phi}\)	Tesla	Toroidal component of magnetic field in lab frame
B_r	\(\partial_{\rho} \mathbf{B}\)	Tesla	Magnetic field, derivative wrt radial coordinate
B_rho	\(B_{\rho}\)	Tesla * meters	Covariant radial component of magnetic field
B_rho_r	\(\partial_{\rho} B_{\rho}\)	Tesla * meters	Covariant radial component of magnetic field, derivative wrt radial coordinate
B_rho_rr	\(\partial_{\rho\rho} B_{\rho}\)	Tesla * meters	Covariant radial component of magnetic field, second derivative wrt radial coordinate
B_rho_rt	\(\partial_{\rho\theta} B_{\rho}\)	Tesla * meters	Covariant radial component of magnetic field, second derivative wrt radial coordinate and poloidal angle	B_rho_tr
B_rho_rz	\(\partial_{\rho\zeta} B_{\rho}\)	Tesla * meters	Covariant radial component of magnetic field, second derivative wrt radial coordinate and toroidal angle	B_rho_zr
B_rho_t	\(\partial_{\theta} B_{\rho}\)	Tesla * meters	Covariant radial component of magnetic field, derivative wrt poloidal angle
B_rho_tt	\(\partial_{\theta\theta} B_{\rho}\)	Tesla * meters	Covariant radial component of magnetic field, second derivative wrt poloidal angle
B_rho_tz	\(\partial_{\theta\zeta} B_{\rho}\)	Tesla * meters	Covariant radial component of magnetic field, second derivative wrt poloidal and toroidal angles	B_rho_zt
B_rho_z	\(\partial_{\zeta} B_{\rho}\)	Tesla * meters	Covariant radial component of magnetic field, derivative wrt toroidal angle
B_rho_zz	\(\partial_{\zeta\zeta} B_{\rho}\)	Tesla * meters	Covariant radial component of magnetic field, second derivative wrt toroidal angle
B_rr	\(\partial_{\rho\rho} \mathbf{B}\)	Tesla	Magnetic field, second derivative wrt radial coordinate
B_rt	\(\partial_{\rho\theta} \mathbf{B}\)	Tesla	Magnetic field, second derivative wrt radial coordinate and poloidal angle	B_tr
B_rz	\(\partial_{\rho\zeta} \mathbf{B}\)	Tesla	Magnetic field, second derivative wrt radial coordinate and toroidal angle	B_zr
B_t	\(\partial_{\theta} \mathbf{B}\)	Tesla	Magnetic field, derivative wrt poloidal angle
B_theta	\(B_{\theta}\)	Tesla * meters	Covariant poloidal component of magnetic field
B_theta_mn	\(B_{\theta, m, n}\)	Tesla * meters	Fourier coefficients for covariant poloidal component of magnetic field		M_booz, N_booz
B_theta_r	\(\partial_{\rho} B_{\theta}\)	Tesla * meters	Covariant poloidal component of magnetic field, derivative wrt radial coordinate
B_theta_rr	\(\partial_{\rho\rho} B_{\theta}\)	Tesla * meters	Covariant poloidal component of magnetic field, second derivative wrt radial coordinate
B_theta_rt	\(\partial_{\rho\theta} B_{\theta}\)	Tesla * meters	Covariant poloidal component of magnetic field, second derivative wrt radial coordinate and poloidal angle	B_theta_tr
B_theta_rz	\(\partial_{\rho\zeta} B_{\theta}\)	Tesla * meters	Covariant poloidal component of magnetic field, second derivative wrt radial coordinate and toroidal angle	B_theta_zr
B_theta_t	\(\partial_{\theta} B_{\theta}\)	Tesla * meters	Covariant poloidal component of magnetic field, derivative wrt poloidal angle
B_theta_tt	\(\partial_{\theta\theta} B_{\theta}\)	Tesla * meters	Covariant poloidal component of magnetic field, second derivative wrt poloidal angle
B_theta_tz	\(\partial_{\theta\zeta} B_{\theta}\)	Tesla * meters	Covariant poloidal component of magnetic field, second derivative wrt poloidal and toroidal angles	B_theta_zt
B_theta_z	\(\partial_{\zeta} B_{\theta}\)	Tesla * meters	Covariant poloidal component of magnetic field, derivative wrt toroidal angle
B_theta_zz	\(\partial_{\zeta\zeta} B_{\theta}\)	Tesla * meters	Covariant poloidal component of magnetic field, second derivative wrt toroidal angle
B_tt	\(\partial_{\theta\theta} \mathbf{B}\)	Tesla	Magnetic field, second derivative wrt poloidal angle
B_tz	\(\partial_{\theta\zeta} \mathbf{B}\)	Tesla	Magnetic field, second derivative wrt poloidal and toroidal angles	B_zt
B_z	\(\partial_{\zeta} \mathbf{B}\)	Tesla	Magnetic field, derivative wrt toroidal angle
B_zeta	\(B_{\zeta}\)	Tesla * meters	Covariant toroidal component of magnetic field
B_zeta_mn	\(B_{\zeta, m, n}\)	Tesla * meters	Fourier coefficients for covariant toroidal component of magnetic field		M_booz, N_booz
B_zeta_r	\(\partial_{\rho} B_{\zeta}\)	Tesla * meters	Covariant toroidal component of magnetic field, derivative wrt radial coordinate
B_zeta_rr	\(\partial_{\rho\rho} B_{\zeta}\)	Tesla * meters	Covariant toroidal component of magnetic field, second derivative wrt radial coordinate
B_zeta_rt	\(\partial_{\rho\theta} B_{\zeta}\)	Tesla * meters	Covariant toroidal component of magnetic field, second derivative wrt radial coordinate and poloidal angle	B_zeta_tr
B_zeta_rz	\(\partial_{\rho\zeta} B_{\zeta}\)	Tesla * meters	Covariant toroidal component of magnetic field, second derivative wrt radial coordinate and toroidal angle	B_zeta_zr
B_zeta_t	\(\partial_{\theta} B_{\zeta}\)	Tesla * meters	Covariant toroidal component of magnetic field, derivative wrt poloidal angle
B_zeta_tt	\(\partial_{\theta\theta} B_{\zeta}\)	Tesla * meters	Covariant toroidal component of magnetic field, second derivative wrt poloidal angle
B_zeta_tz	\(\partial_{\theta\zeta} B_{\zeta}\)	Tesla * meters	Covariant toroidal component of magnetic field, second derivative wrt poloidal and toroidal angles	B_zeta_zt
B_zeta_z	\(\partial_{\zeta} B_{\zeta}\)	Tesla * meters	Covariant toroidal component of magnetic field, derivative wrt toroidal angle
B_zeta_zz	\(\partial_{\zeta\zeta} B_{\zeta}\)	Tesla * meters	Covariant toroidal component of magnetic field, second derivative wrt toroidal angle
B_zz	\(\partial_{\zeta\zeta} \mathbf{B}\)	Tesla	Magnetic field, second derivative wrt toroidal angle
D_Mercier	\(D_{\mathrm{Mercier}}\)	Inverse Webers squared	Mercier stability criterion (positive/negative value denotes stability/instability)
D_current	\(D_{\mathrm{current}}\)	Inverse Webers squared	Mercier stability criterion toroidal current term
D_geodesic	\(D_{\mathrm{geodesic}}\)	Inverse Webers squared	Mercier stability criterion geodesic curvature term
D_shear	\(D_{\mathrm{shear}}\)	Inverse Webers squared	Mercier stability criterion magnetic shear term
D_well	\(D_{\mathrm{well}}\)	Inverse Webers squared	Mercier stability criterion magnetic well term
F	\(\mathbf{J} \times \mathbf{B} - \nabla p\)	Newtons / cubic meter	Force balance error
F_anisotropic	\(F_{anisotropic}\)	Newtons / cubic meter	Anisotropic force balance error
F_helical	\(F_{\mathrm{helical}}\)	Amperes	Covariant helical component of force balance error
F_rho	\(F_{\rho}\)	Newtons / square meter	Covariant radial component of force balance error
F_theta	\(F_{\theta}\)	Newtons / square meter	Covariant poloidal component of force balance error
F_zeta	\(F_{\zeta}\)	Newtons / square meter	Covariant toroidal component of force balance error
G	\(G\)	Tesla * meters	Covariant toroidal component of magnetic field in Boozer coordinates (proportional to poloidal current)
G_r	\(\partial_{\rho} G\)	Tesla * meters	Covariant toroidal component of magnetic field in Boozer coordinates (proportional to poloidal current), derivative wrt radial coordinate
G_rr	\(\partial_{\rho\rho} G\)	Tesla * meters	Boozer poloidal current enclosed by flux surfaces, second derivative wrt radial coordinate
I	\(I\)	Tesla * meters	Covariant poloidal component of magnetic field in Boozer coordinates (proportional to toroidal current)
I_r	\(\partial_{\rho} I\)	Tesla * meters	Covariant poloidal component of magnetic field in Boozer coordinates (proportional to toroidal current), derivative wrt radial coordinate
I_rr	\(\partial_{\rho\rho} I\)	Tesla * meters	Boozer toroidal current enclosed by flux surfaces, second derivative wrt radial coordinate
J	\(\mathbf{J}\)	Amperes / square meter	Plasma current density
J*B	\(\mathbf{J} \cdot \mathbf{B}\)	Newtons / cubic meter	Current density parallel to magnetic field, times field strength (note units are not Amperes)
J*sqrt(g)	\(\mathbf{J} \sqrt{g}\)	Ampere meters	Plasma current density weighted by 3-D volume Jacobian
J^rho	\(J^{\rho}\)	Amperes / cubic meter	Contravariant radial component of plasma current density
J^theta	\(J^{\theta}\)	Amperes / cubic meter	Contravariant poloidal component of plasma current density
J^theta*sqrt(g)	\(J^{\theta} \sqrt{g}\)	Amperes	Contravariant poloidal component of plasma current density, weighted by 3-D volume Jacobian
J^zeta	\(J^{\zeta}\)	Amperes / cubic meter	Contravariant toroidal component of plasma current density
J_R	\(J_{R}\)	Amperes / square meter	Radial component of plasma current density in lab frame
J_Z	\(J_{Z}\)	Amperes / square meter	Vertical component of plasma current density in lab frame
J_parallel	\(\mathbf{J} \cdot \hat{\mathbf{b}}\)	Amperes / square meter	Plasma current density parallel to magnetic field
J_phi	\(J_{\phi}\)	Amperes / square meter	Toroidal component of plasma current density in lab frame
J_rho	\(J_{\rho}\)	Amperes / meter	Covariant radial component of plasma current density
J_theta	\(J_{\theta}\)	Amperes / meter	Covariant poloidal component of plasma current density
J_zeta	\(J_{\zeta}\)	Amperes / meter	Covariant toroidal component of plasma current density
K_vc	\(\mathbf{K}_{VC} = \frac{1}{\mu_0}\mathbf{n} \times \mathbf{B}\)	Amps / meter	Virtual casing sheet current
L_grad(B)	\(L_{\nabla \mathbf{B}} = \frac{\sqrt{2}|B|}{|\nabla \mathbf{B}|}\)	meters	Magnetic field length scale based on Frobenius norm of gradient of magnetic field vector
L_sff_rho	\(L_{\mathrm{SFF},\rho}\)	meters	L coefficient of second fundamental form of constant rho surface
L_sff_theta	\(L_{\mathrm{SFF},\theta}\)	meters	L coefficient of second fundamental form of constant theta surface
L_sff_zeta	\(L_{\mathrm{SFF},\zeta}\)	meters	L coefficient of second fundamental form of constant zeta surface
M_sff_rho	\(M_{\mathrm{SFF},\rho}\)	meters	M coefficient of second fundamental form of constant rho surface
M_sff_theta	\(M_{\mathrm{SFF},\theta}\)	meters	M coefficient of second fundamental form of constant theta surface
M_sff_zeta	\(M_{\mathrm{SFF},\zeta}\)	meters	M coefficient of second fundamental form of constant zeta surface
N_sff_rho	\(N_{\mathrm{SFF},\rho}\)	meters	N coefficient of second fundamental form of constant rho surface
N_sff_theta	\(N_{\mathrm{SFF},\theta}\)	meters	N coefficient of second fundamental form of constant theta surface
N_sff_zeta	\(N_{\mathrm{SFF},\zeta}\)	meters	N coefficient of second fundamental form of constant zeta surface
Psi	\(\Psi\)	Webers	Toroidal flux
R	\(R\)	meters	Major radius in lab frame
R0	\(R_{0}\)	meters	Average major radius
R0/a	\(R_{0} / a\)	None	Aspect ratio
R_r	\(\partial_{\rho} R\)	meters	Major radius in lab frame, first radial derivative
R_rr	\(\partial_{\rho \rho} R\)	meters	Major radius in lab frame, second radial derivative
R_rrr	\(\partial_{\rho \rho \rho} R\)	meters	Major radius in lab frame, third radial derivative
R_rrrr	\(\partial_{\rho \rho \rho \rho} R\)	meters	Major radius in lab frame, fourth radial derivative
R_rrrt	\(\partial_{\rho \rho \rho \theta} R\)	meters	Major radius in lab frame, fourth derivative wrt radial coordinate thrice and poloidal once	R_rrtr, R_rtrr, R_trrr
R_rrrz	\(\partial_{\rho \rho \rho \zeta} R\)	meters	Major radius in lab frame, fourth derivative wrt radial coordinate thrice and toroidal once	R_rrzr, R_rzrr, R_zrrr
R_rrt	\(\partial_{\rho \rho \theta} R\)	meters	Major radius in lab frame, third derivative, wrt radius twice and poloidal angle	R_rtr, R_trr
R_rrtt	\(\partial_{\rho \rho \theta \theta} R\)	meters	Major radius in lab frame, fourth derivative, wrt radius twice and poloidal angle twice	R_rttr, R_trrt, R_ttrr
R_rrtz	\(\partial_{\rho \rho \theta \zeta} R\)	meters	Major radius in lab frame, fourth derivative wrt radius twice, poloidal angle, and toroidal angle	R_rtzr, R_tzrr, R_zrrt
R_rrz	\(\partial_{\rho \rho \zeta} R\)	meters	Major radius in lab frame, third derivative, wrt radius twice and toroidal angle	R_rzr, R_zrr
R_rrzz	\(\partial_{\rho \rho \zeta \zeta} R\)	meters	Major radius in lab frame, fourth derivative, wrt radius twice and toroidal angle twice	R_rzzr, R_zrrz, R_zzrr
R_rt	\(\partial_{\rho \theta} R\)	meters	Major radius in lab frame, second derivative wrt radius and poloidal angle	R_tr
R_rtt	\(\partial_{\rho \theta \theta} R\)	meters	Major radius in lab frame, third derivative wrt radius and poloidal angle twice	R_trt, R_ttr
R_rttt	\(\partial_{\rho \theta \theta \theta} R\)	meters	Major radius in lab frame, fourth derivative wrt radius and poloidal angle thrice	R_trtt, R_ttrt, R_tttr
R_rttz	\(\partial_{\rho \theta \theta \zeta} R\)	meters	Major radius in lab frame, fourth derivative wrt radius once, poloidal angle twice, and toroidal angle once	R_ttzr, R_tzrt, R_zrtt
R_rtz	\(\partial_{\rho \theta \zeta} R\)	meters	Major radius in lab frame, third derivative wrt radius, poloidal angle, and toroidal angle	R_tzr, R_zrt
R_rtzz	\(\partial_{\rho \theta \zeta \zeta} R\)	meters	Major radius in lab frame, fourth derivative wrt radius, poloidal angle, and toroidal angle twice	R_tzzr, R_zrtz, R_zzrt
R_rz	\(\partial_{\rho \zeta} R\)	meters	Major radius in lab frame, second derivative wrt radius and toroidal angle	R_zr
R_rzz	\(\partial_{\rho \zeta \zeta} R\)	meters	Major radius in lab frame, third derivative wrt radius and toroidal angle twice	R_zrz, R_zzr
R_rzzz	\(\partial_{\rho \zeta \zeta \zeta} R\)	meters	Major radius in lab frame, fourth derivative wrt radius and toroidal angle thrice	R_zrzz, R_zzrz, R_zzzr
R_t	\(\partial_{\theta} R\)	meters	Major radius in lab frame, first poloidal derivative
R_tt	\(\partial_{\theta \theta} R\)	meters	Major radius in lab frame, second poloidal derivative
R_ttt	\(\partial_{\theta \theta \theta} R\)	meters	Major radius in lab frame, third poloidal derivative
R_ttz	\(\partial_{\theta \theta \zeta} R\)	meters	Major radius in lab frame, third derivative wrt poloidal angle twice and toroidal angle	R_tzt, R_ztt
R_tz	\(\partial_{\theta \zeta} R\)	meters	Major radius in lab frame, second derivative wrt poloidal and toroidal angles	R_zt
R_tzz	\(\partial_{\theta \zeta \zeta} R\)	meters	Major radius in lab frame, third derivative wrt poloidal angle and toroidal angle twice	R_ztz, R_zzt
R_z	\(\partial_{\zeta} R\)	meters	Major radius in lab frame, first toroidal derivative
R_zz	\(\partial_{\zeta \zeta} R\)	meters	Major radius in lab frame, second toroidal derivative
R_zzz	\(\partial_{\zeta \zeta \zeta} R\)	meters	Major radius in lab frame, third toroidal derivative
S	\(S\)	square meters	Surface area of outermost flux surface
S(r)	\(S(\rho)\)	square meters	Surface area of flux surfaces
S_r(r)	\(\partial_{\rho} S(\rho)\)	square meters	Surface area of flux surfaces, derivative wrt radial coordinate
S_rr(r)	\(\partial_{\rho\rho} S(\rho)\)	square meters	Surface area of flux surfaces, second derivative wrt radial coordinate
Te	\(T_e\)	electron-Volts	Electron temperature
Te_r	\(\partial_{\rho} T_e\)	electron-Volts	Electron temperature, first radial derivative
Te_rr	\(\partial_{\rho \rho} T_e\)	electron-Volts	Electron temperature, second radial derivative
Ti	\(T_i\)	electron-Volts	Ion temperature
Ti_r	\(\partial_{\rho} T_i\)	electron-Volts	Ion temperature, first radial derivative
Ti_rr	\(\partial_{\rho \rho} T_i\)	electron-Volts	Ion temperature, second radial derivative
V	\(V\)	cubic meters	Volume
V(r)	\(V(\rho)\)	cubic meters	Volume enclosed by flux surfaces
V_r(r)	\(\partial_{\rho} V(\rho)\)	cubic meters	Volume enclosed by flux surfaces, derivative wrt radial coordinate
V_rr(r)	\(\partial_{\rho\rho} V(\rho)\)	cubic meters	Volume enclosed by flux surfaces, second derivative wrt radial coordinate
V_rrr(r)	\(\partial_{\rho\rho\rho} V(\rho)\)	cubic meters	Volume enclosed by flux surfaces, third derivative wrt radial coordinate
W	\(W\)	Joules	Plasma total energy
W_B	\(W_B\)	Joules	Plasma magnetic energy
W_Bpol	\(W_{B,pol}\)	Joules	Plasma magnetic energy in poloidal field
W_Btor	\(W_{B,tor}\)	Joules	Plasma magnetic energy in toroidal field
W_p	\(W_p\)	Joules	Plasma thermodynamic energy		gamma
X	\(X = R \cos{\phi}\)	meters	Cartesian X coordinate
X_r	\(\partial_{\rho} X\)	meters	Cartesian X coordinate, derivative wrt radial coordinate
X_t	\(\partial_{\theta} X\)	meters	Cartesian X coordinate, derivative wrt poloidal coordinate
X_z	\(\partial_{\zeta} X\)	meters	Cartesian X coordinate, derivative wrt toroidal coordinate
Y	\(Y = R \sin{\phi}\)	meters	Cartesian Y coordinate
Y_r	\(\partial_{\rho} Y\)	meters	Cartesian Y coordinate, derivative wrt radial coordinate
Y_t	\(\partial_{\theta} Y\)	meters	Cartesian Y coordinate, derivative wrt poloidal coordinate
Y_z	\(\partial_{\zeta} Y\)	meters	Cartesian Y coordinate, derivative wrt toroidal coordinate
Z	\(Z\)	meters	Vertical coordinate in lab frame
Z_r	\(\partial_{\rho} Z\)	meters	Vertical coordinate in lab frame, first radial derivative
Z_rr	\(\partial_{\rho \rho} Z\)	meters	Vertical coordinate in lab frame, second radial derivative
Z_rrr	\(\partial_{\rho \rho \rho} Z\)	meters	Vertical coordinate in lab frame, third radial derivative
Z_rrrr	\(\partial_{\rho \rho \rho \rho} Z\)	meters	Vertical coordinate in lab frame, fourth radial derivative
Z_rrrt	\(\partial_{\rho \rho \rho \theta} Z\)	meters	Vertical coordinate in lab frame, fourth derivative wrt radial coordinate thrice and poloidal once	Z_rrtr, Z_rtrr, Z_trrr
Z_rrrz	\(\partial_{\rho \rho \rho \zeta} Z\)	meters	Vertical coordinate in lab frame, fourth derivative wrt radial coordinate thrice and toroidal once	Z_rrzr, Z_rzrr, Z_zrrr
Z_rrt	\(\partial_{\rho \rho \theta} Z\)	meters	Vertical coordinate in lab frame, third derivative, wrt radius twice and poloidal angle	Z_rtr, Z_trr
Z_rrtt	\(\partial_{\rho \rho \theta} Z\)	meters	Vertical coordinate in lab frame, fourth derivative, wrt radius twice and poloidal angle twice	Z_rttr, Z_trrt, Z_ttrr
Z_rrtz	\(\partial_{\rho \rho \theta \zeta} Z\)	meters	Vertical coordinate in lab frame, fourth derivative wrt radiustwice, poloidal angle, and toroidal angle	Z_rtzr, Z_tzrr, Z_zrrt
Z_rrz	\(\partial_{\rho \rho \zeta} Z\)	meters	Vertical coordinate in lab frame, third derivative, wrt radius twice and toroidal angle	Z_rzr, Z_zrr
Z_rrzz	\(\partial_{\rho \rho \zeta \zeta} Z\)	meters	Vertical coordinate in lab frame, fourth derivative, wrt radius twice and toroidal angle twice	Z_rzzr, Z_zrrz, Z_zzrr
Z_rt	\(\partial_{\rho \theta} Z\)	meters	Vertical coordinate in lab frame, second derivative wrt radius and poloidal angle	Z_tr
Z_rtt	\(\partial_{\rho \theta \theta} Z\)	meters	Vertical coordinate in lab frame, third derivative wrt radius and poloidal angle twice	Z_trt, Z_ttr
Z_rttt	\(\partial_{\rho \theta \theta \theta} Z\)	meters	Vertical coordinate in lab frame, third derivative wrt radius and poloidal angle thrice	Z_trtt, Z_ttrt, Z_tttr
Z_rttz	\(\partial_{\rho \theta \theta \zeta} Z\)	meters	Vertical coordinate in lab frame, fourth derivative wrt radius once, poloidal angle twice, and toroidal angle once	Z_ttzr, Z_tzrt, Z_zrtt
Z_rtz	\(\partial_{\rho \theta \zeta} Z\)	meters	Vertical coordinate in lab frame, third derivative wrt radius, poloidal angle, and toroidal angle	Z_tzr, Z_zrt
Z_rtzz	\(\partial_{\rho \theta \zeta \zeta} Z\)	meters	Vertical coordinate in lab frame, fourth derivative wrt radius, poloidal angle, and toroidal angle twice	Z_tzzr, Z_zrtz, Z_zzrt
Z_rz	\(\partial_{\rho \zeta} Z\)	meters	Vertical coordinate in lab frame, second derivative wrt radius and toroidal angle	Z_zr
Z_rzz	\(\partial_{\rho \zeta \zeta} Z\)	meters	Vertical coordinate in lab frame, third derivative wrt radius and toroidal angle twice	Z_zrz, Z_zzr
Z_rzzz	\(\partial_{\rho \zeta \zeta \zeta} Z\)	meters	Vertical coordinate in lab frame, third derivative wrt radius and toroidal angle thrice	Z_zrzz, Z_zzrz, Z_zzzr
Z_t	\(\partial_{\theta} Z\)	meters	Vertical coordinate in lab frame, first poloidal derivative
Z_tt	\(\partial_{\theta \theta} Z\)	meters	Vertical coordinate in lab frame, second poloidal derivative
Z_ttt	\(\partial_{\theta \theta \theta} Z\)	meters	Vertical coordinate in lab frame, third poloidal derivative
Z_ttz	\(\partial_{\theta \theta \zeta} Z\)	meters	Vertical coordinate in lab frame, third derivative wrt poloidal angle twice and toroidal angle	Z_tzt, Z_ztt
Z_tz	\(\partial_{\theta \zeta} Z\)	meters	Vertical coordinate in lab frame, second derivative wrt poloidal and toroidal angles	Z_zt
Z_tzz	\(\partial_{\theta \zeta \zeta} Z\)	meters	Vertical coordinate in lab frame, third derivative wrt poloidal angle and toroidal angle twice	Z_ztz, Z_zzt
Z_z	\(\partial_{\zeta} Z\)	meters	Vertical coordinate in lab frame, first toroidal derivative
Z_zz	\(\partial_{\zeta \zeta} Z\)	meters	Vertical coordinate in lab frame, second toroidal derivative
Z_zzz	\(\partial_{\zeta \zeta \zeta} Z\)	meters	Vertical coordinate in lab frame, third toroidal derivative
Zeff	\(Z_{eff}\)	None	Effective atomic number
Zeff_r	\(\partial_{\rho} Z_{eff}\)	None	Effective atomic number, first radial derivative
a	\(a\)	meters	Average minor radius
a_major/a_minor	\(a_{\mathrm{major}} / a_{\mathrm{minor}}\)	None	Elongation at a toroidal cross-section
alpha	\(\alpha\)	None	Field line label, defined on [0, 2pi)
alpha_r	\(\partial_\rho \alpha\)	None	Field line label, derivative wrt radial coordinate
alpha_t	\(\partial_\theta \alpha\)	None	Field line label, derivative wrt poloidal coordinate
alpha_z	\(\partial_\zeta \alpha\)	None	Field line label, derivative wrt toroidal coordinate
b	\(\hat{b}\)	None	Unit vector along magnetic field
beta_a	\(\beta_a = \mu_0 (p_{||} - p_{\perp})/B^2\)	None	Pressure anisotropy
beta_a_r	\(\partial_{\rho} \beta_a = \mu_0 (p_{||} - p_{\perp})/B^2\)	None	Pressure anisotropy, first radial derivative
beta_a_t	\(\partial_{\theta} \beta_a = \mu_0 (p_{||} - p_{\perp})/B^2\)	None	Pressure anisotropy, first poloidal derivative
beta_a_z	\(\partial_{\zeta} \beta_a = \mu_0 (p_{||} - p_{\perp})/B^2\)	None	Pressure anisotropy, first toroidal derivative
chi	\(\chi\)	Webers	Poloidal flux (normalized by 2pi)
chi_r	\(\partial_{\rho} \chi\)	Webers	Poloidal flux (normalized by 2pi), first radial derivative
curl(B)xB	\((\nabla \times \mathbf{B}) \times \mathbf{B}\)	Tesla squared / meters	Lorentz force
current	\(\frac{2\pi}{\mu_0} I\)	Amperes	Net toroidal current enclosed by flux surfaces
current Redl	\(\frac{2\pi}{\mu_0} I_{Redl}\)	Amperes	Net toroidal current enclosed by flux surfaces, consistent with bootstrap current from Redl formula		degree
current_r	\(\frac{2\pi}{\mu_0} \partial_{\rho} I\)	Amperes	Net toroidal current enclosed by flux surfaces, derivative wrt radial coordinate
current_rr	\(\frac{2\pi}{\mu_0} \partial_{\rho\rho} I\)	Amperes	Net toroidal current enclosed by flux surfaces, second derivative wrt radial coordinate
curvature_H_rho	\(H_{\rho}\)	meters	Mean curvature of constant rho surfaces
curvature_H_theta	\(H_{\theta}\)	meters	Mean curvature of constant theta surfaces
curvature_H_zeta	\(H_{\zeta}\)	meters	Mean curvature of constant zeta surfaces
curvature_K_rho	\(K_{\rho}\)	meters squared	Gaussian curvature of constant rho surfaces
curvature_K_theta	\(K_{\theta}\)	meters squared	Gaussian curvature of constant theta surfaces
curvature_K_zeta	\(K_{\zeta}\)	meters squared	Gaussian curvature of constant zeta surfaces
curvature_k1_rho	\(k_{1,\rho}\)	Inverse meters	First principle curvature of constant rho surfaces
curvature_k1_theta	\(k_{1,\theta}\)	Inverse meters	First principle curvature of constant theta surfaces
curvature_k1_zeta	\(k_{1,\zeta}\)	Inverse meters	First principle curvature of constant zeta surfaces
curvature_k2_rho	\(k_{2,\rho}\)	Inverse meters	Second principle curvature of constant rho surfaces
curvature_k2_theta	\(k_{2,\theta}\)	Inverse meters	Second principle curvature of constant theta surfaces
curvature_k2_zeta	\(k_{2,\zeta}\)	Inverse meters	Second principle curvature of constant zeta surfaces
cvdrift	\(\mathrm{cvdrift} = 1/B^{3} (\mathbf{b}\times\nabla(p + B^2/2))\cdot \nabla \alpha\)	inverse Tesla meters^2	Binormal component of the geometric part of the curvature drift used for local stability analyses, Gamma_c, epsilon_eff etc.
cvdrift0	\(\mathrm{cvdrift0} = 1/B^{2} (\mathbf{b}\times\nabla B)\cdot \nabla \rho\)	inverse Tesla meters^2	Radial component of the geometric part of the curvature drift used for local stability analyses, Gamma_c, epsilon_eff etc.
e^helical	\(B^{\theta} \nabla \zeta - B^{\zeta} \nabla \theta\)	Tesla / square meter	Helical basis vector
e^helical*sqrt(g)	\(\sqrt{g}(B^{\theta} \nabla \zeta - B^{\zeta} \nabla \theta)\)	Tesla * square meter	Helical basis vector weighted by 3-D volume Jacobian
e^rho	\(\mathbf{e}^{\rho}\)	inverse meters	Contravariant radial basis vector
e^rho_r	\(\partial_{\rho} \mathbf{e}^{\rho}\)	inverse meters	Contravariant radial basis vector, derivative wrt radial coordinate
e^rho_rr	\(\partial_{\rho\rho} \mathbf{e}^{\rho}\)	inverse square meters	Contravariant Radial basis vector, 2nd derivative wrt radial coordinate
e^rho_rt	\(\partial_{\rho\theta} \mathbf{e}^{\rho}\)	inverse square meters	Contravariant Radial basis vector, derivative wrt radial and poloidal coordinate	e^rho_tr
e^rho_rz	\(\partial_{\rho\zeta} \mathbf{e}^{\rho}\)	inverse square meters	Contravariant Radial basis vector, derivative wrt radial and toroidal coordinate	e^rho_zr
e^rho_t	\(\partial_{\theta} \mathbf{e}^{\rho}\)	inverse meters	Contravariant radial basis vector, derivative wrt poloidal coordinate
e^rho_tt	\(\partial_{\theta\theta} \mathbf{e}^{\rho}\)	inverse square meters	Contravariant Radial basis vector, 2nd derivative wrt poloidal coordinate
e^rho_tz	\(\partial_{\theta\zeta} \mathbf{e}^{\rho}\)	inverse square meters	Contravariant Radial basis vector, derivative wrt poloidal and toroidal coordinate	e^rho_zt
e^rho_z	\(\partial_{\zeta} \mathbf{e}^{\rho}\)	inverse meters	Contravariant radial basis vector, derivative wrt toroidal coordinate
e^rho_zz	\(\partial_{\zeta\zeta} \mathbf{e}^{\rho}\)	inverse square meters	Contravariant Radial basis vector, 2nd derivative wrt toroidal coordinate
e^theta	\(\mathbf{e}^{\theta}\)	inverse meters	Contravariant poloidal basis vector
e^theta*sqrt(g)	\(\mathbf{e}^{\theta} \sqrt{g}\)	square meters	Contravariant poloidal basis vector weighted by 3-D volume Jacobian
e^theta_r	\(\partial_{\rho} \mathbf{e}^{\theta}\)	inverse meters	Contravariant poloidal basis vector, derivative wrt radial coordinate
e^theta_rr	\(\partial_{\rho\rho} \mathbf{e}^{\theta}\)	inverse square meters	Contravariant Poloidal basis vector, 2nd derivative wrt radial coordinate
e^theta_rt	\(\partial_{\rho\theta} \mathbf{e}^{\theta}\)	inverse square meters	Contravariant Poloidal basis vector, derivative wrt radial and poloidal coordinate	e^theta_tr
e^theta_rz	\(\partial_{\rho\zeta} \mathbf{e}^{\theta}\)	inverse square meters	Contravariant Poloidal basis vector, derivative wrt radial and toroidal coordinate	e^theta_zr
e^theta_t	\(\partial_{\theta} \mathbf{e}^{\theta}\)	inverse meters	Contravariant poloidal basis vector, derivative wrt poloidal coordinate
e^theta_tt	\(\partial_{\theta\theta} \mathbf{e}^{\theta}\)	inverse square meters	Contravariant Poloidal basis vector, 2nd derivative wrt poloidal coordinate
e^theta_tz	\(\partial_{\theta\zeta} \mathbf{e}^{\theta}\)	inverse square meters	Contravariant Poloidal basis vector, derivative wrt poloidal and toroidal coordinate	e^theta_zt
e^theta_z	\(\partial_{\zeta} \mathbf{e}^{\theta}\)	inverse meters	Contravariant poloidal basis vector, derivative wrt toroidal coordinate
e^theta_zz	\(\partial_{\zeta\zeta} \mathbf{e}^{\theta}\)	inverse square meters	Contravariant Poloidal basis vector, 2nd derivative wrt toroidal coordinate
e^zeta	\(\mathbf{e}^{\zeta}\)	inverse meters	Contravariant toroidal basis vector
e^zeta_r	\(\partial_{\rho} \mathbf{e}^{\zeta}\)	inverse meters	Contravariant toroidal basis vector, derivative wrt radial coordinate
e^zeta_rr	\(\partial_{\rho\rho} \mathbf{e}^{\zeta}\)	inverse square meters	Contravariant Toroidal basis vector, 2nd derivative wrt radial coordinate
e^zeta_rt	\(\partial_{\rho\theta} \mathbf{e}^{\zeta}\)	inverse square meters	Contravariant Toroidal basis vector, derivative wrt radial and poloidal coordinate	e^zeta_tr
e^zeta_rz	\(\partial_{\rho\zeta} \mathbf{e}^{\zeta}\)	inverse square meters	Contravariant Toroidal basis vector, derivative wrt radial and toroidal coordinate	e^zeta_zr
e^zeta_t	\(\partial_{\theta} \mathbf{e}^{\zeta}\)	inverse meters	Contravariant toroidal basis vector, derivative wrt poloidal coordinate
e^zeta_tt	\(\partial_{\theta\theta} \mathbf{e}^{\zeta}\)	inverse square meters	Contravariant Toroidal basis vector, 2nd derivative wrt poloidal coordinate
e^zeta_tz	\(\partial_{\theta\zeta} \mathbf{e}^{\zeta}\)	inverse square meters	Contravariant Toroidal basis vector, derivative wrt poloidal and toroidal coordinate	e^zeta_zt
e^zeta_z	\(\partial_{\zeta} \mathbf{e}^{\zeta}\)	inverse meters	Contravariant toroidal basis vector, derivative wrt toroidal coordinate
e^zeta_zz	\(\partial_{\zeta\zeta} \mathbf{e}^{\zeta}\)	inverse square meters	Contravariant Toroidal basis vector, 2nd derivative wrt toroidal coordinate
e_phi	\(\mathbf{e}_{\phi}\)	meters	Covariant cylindrical toroidal basis vector
e_rho	\(\mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector
e_rho_r	\(\partial_{\rho} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, derivative wrt radial coordinate
e_rho_rr	\(\partial_{\rho \rho} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, second derivative wrt radial and radial coordinates
e_rho_rrr	\(\partial_{\rho \rho \rho} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, third derivative wrt radial coordinate
e_rho_rrt	\(\partial_{\rho \rho \theta} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, third derivative wrt radial coordinate twice and poloidal once	e_rho_rtr, e_rho_trr, e_theta_rrr
e_rho_rrz	\(\partial_{\rho \rho \zeta} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, third derivative wrt radial coordinate twice and toroidal once	e_rho_rzr, e_rho_zrr, e_zeta_rrr
e_rho_rt	\(\partial_{\rho \theta} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, second derivative wrt radial and poloidal coordinates	e_rho_tr, e_theta_rr, x_rrt, x_rtr, x_trr
e_rho_rtt	\(\partial_{\rho \theta \theta} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, third derivative wrt radial coordinateonce and poloidal twice	e_rho_trt, e_rho_ttr, e_theta_rrt, e_theta_rtr, e_theta_trr
e_rho_rtz	\(\partial_{\rho \theta \zeta} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, third derivative wrt radial, poloidal, and toroidal coordinates	e_rho_tzr, e_rho_zrt, e_theta_rrz, e_theta_rzr, e_theta_zrr, e_zeta_rrt, e_zeta_rtr, e_zeta_trr
e_rho_rz	\(\partial_{\rho \zeta} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, second derivative wrt radial and toroidal coordinates	e_rho_zr, e_zeta_rr
e_rho_rzz	\(\partial_{\rho \zeta \zeta} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, third derivative wrt radial coordinate once and toroidal twice	e_rho_zrz, e_rho_zzr, e_zeta_rrz, e_zeta_rzr, e_zeta_zrr
e_rho_t	\(\partial_{\theta} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, derivative wrt poloidal coordinate	e_theta_r
e_rho_tt	\(\partial_{\theta \theta} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, second derivative wrt poloidal and poloidal coordinates	e_theta_rt, e_theta_tr
e_rho_tz	\(\partial_{\theta \zeta} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, second derivative wrt poloidal and toroidal coordinates	e_rho_zt, e_theta_rz, e_theta_zr, e_zeta_rt, e_zeta_tr
e_rho_z	\(\partial_{\zeta} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, derivative wrt toroidal coordinate	e_zeta_r
e_rho_zz	\(\partial_{\zeta \zeta} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, second derivative wrt toroidal and toroidal coordinates	e_zeta_rz, e_zeta_zr
e_theta	\(\mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector
e_theta/sqrt(g)	\(\mathbf{e}_{\theta} / \sqrt{g}\)	meters	Covariant Poloidal basis vector divided by 3-D volume Jacobian
e_theta_PEST	\(\mathbf{e}_{\theta_{PEST}}\)	meters	Covariant straight field line (PEST) poloidal basis vector
e_theta_rtt	\(\partial_{\rho \theta \theta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, third derivative wrt radial coordinate once and poloidal twice	e_rho_ttt, e_theta_trt, e_theta_ttr
e_theta_rtz	\(\partial_{\rho \theta \zeta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, third derivative wrt radial, poloidal, and toroidal coordinates	e_rho_ttz, e_rho_tzt, e_rho_ztt, e_theta_tzr, e_theta_zrt, e_zeta_rtt, e_zeta_trt, e_zeta_ttr
e_theta_rzz	\(\partial_{\rho \zeta \zeta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, third derivative wrt radial coordinate once and toroidal twice	e_rho_tzz, e_rho_ztz, e_rho_zzt, e_theta_zrz, e_theta_zzr, e_zeta_rtz, e_zeta_tzr, e_zeta_zrt
e_theta_t	\(\partial_{\theta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, derivative wrt poloidal coordinate
e_theta_tt	\(\partial_{\theta \theta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, second derivative wrt poloidal and poloidal coordinates
e_theta_tz	\(\partial_{\theta \zeta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, second derivative wrt poloidal and toroidal coordinates	e_theta_zt, e_zeta_tt
e_theta_z	\(\partial_{\zeta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, derivative wrt toroidal coordinate	e_zeta_t
e_theta_zz	\(\partial_{\zeta \zeta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, second derivative wrt toroidal and toroidal coordinates	e_zeta_tz, e_zeta_zt
e_theta|r,p	\(\mathbf{e}_{\theta} |_{\rho, \phi}\)	meters	Covariant poloidal basis vector in (ρ,θ,ϕ) coordinates. ϕ increases counterclockwise when viewed from above (cylindrical R,ϕ plane with Z out of page).
e_zeta	\(\mathbf{e}_{\zeta}\)	meters	Covariant Toroidal basis vector
e_zeta_rzz	\(\partial_{\rho \zeta \zeta} \mathbf{e}_{\zeta}\)	meters	Covariant Toroidal basis vector, third derivative wrt radial coordinate once and toroidal twice	e_zeta_zrz, e_zeta_zzr
e_zeta_z	\(\partial_{\zeta} \mathbf{e}_{\zeta}\)	meters	Covariant Toroidal basis vector, derivative wrt toroidal coordinate
e_zeta_zz	\(\partial_{\zeta \zeta} \mathbf{e}_{\zeta}\)	meters	Covariant Toroidal basis vector, second derivative wrt toroidal and toroidal coordinates
effective r/R0	\((r / R_0)_{\mathrm{effective}}\)	None	Effective local inverse aspect ratio, based on max and min |B|
f_C	\([(M \iota - N) (\mathbf{B} \times \nabla \psi) - (M G + N I) \mathbf{B}] \cdot \nabla B\)	Tesla cubed	Two-term quasisymmetry metric		helicity
f_T	\(\nabla \psi \times \nabla B \cdot \nabla (\mathbf{B} \cdot \nabla B)\)	Tesla quarted / square meters	Triple product quasisymmetry metric
g^rr	\(g^{\rho\rho}\)	inverse square meters	Radial/Radial element of contravariant metric tensor
g^rr_r	\(\partial_{\rho} g^{\rho \rho}\)	inverse square meters	Radial/Radial element of contravariant metric tensor, first radial derivative
g^rr_t	\(\partial_{\theta} g^{\rho \rho}\)	inverse square meters	Radial/Radial element of contravariant metric tensor, first poloidal derivative
g^rr_z	\(\partial_{\zeta} g^{\rho \rho}\)	inverse square meters	Radial/Radial element of contravariant metric tensor, first toroidal derivative
g^rt	\(g^{\rho\theta}\)	inverse square meters	Radial/Poloidal element of contravariant metric tensor
g^rt_r	\(\partial_{\rho} g^{\rho \theta}\)	inverse square meters	Radial/Poloidal element of contravariant metric tensor, first radial derivative
g^rt_t	\(\partial_{\theta} g^{\rho \theta}\)	inverse square meters	Radial/Poloidal element of contravariant metric tensor, first poloidal derivative
g^rt_z	\(\partial_{\zeta} g^{\rho \theta}\)	inverse square meters	Radial/Poloidal element of contravariant metric tensor, first toroidal derivative
g^rz	\(g^{\rho\zeta}\)	inverse square meters	Radial/Toroidal element of contravariant metric tensor
g^rz_r	\(\partial_{\rho} g^{\rho \zeta}\)	inverse square meters	Radial/Toroidal element of contravariant metric tensor, first radial derivative
g^rz_t	\(\partial_{\theta} g^{\rho \zeta}\)	inverse square meters	Radial/Toroidal element of contravariant metric tensor, first poloidal derivative
g^rz_z	\(\partial_{\zeta} g^{\rho \zeta}\)	inverse square meters	Radial/Toroidal element of contravariant metric tensor, first toroidal derivative
g^tt	\(g^{\theta\theta}\)	inverse square meters	Poloidal/Poloidal element of contravariant metric tensor
g^tt_r	\(\partial_{\rho} g^{\theta \theta}\)	inverse square meters	Poloidal/Poloidal element of contravariant metric tensor, first radial derivative
g^tt_t	\(\partial_{\theta} g^{\theta \theta}\)	inverse square meters	Poloidal/Poloidal element of contravariant metric tensor, first poloidal derivative
g^tt_z	\(\partial_{\zeta} g^{\theta \theta}\)	inverse square meters	Poloidal/Poloidal element of contravariant metric tensor, first toroidal derivative
g^tz	\(g^{\theta\zeta}\)	inverse square meters	Poloidal/Toroidal element of contravariant metric tensor	g^zt
g^tz_r	\(\partial_{\rho} g^{\theta \zeta}\)	inverse square meters	Poloidal/Toroidal element of contravariant metric tensor, first radial derivative
g^tz_t	\(\partial_{\theta} g^{\theta \zeta}\)	inverse square meters	Poloidal/Toroidal element of contravariant metric tensor, first poloidal derivative
g^tz_z	\(\partial_{\zeta} g^{\theta \zeta}\)	inverse square meters	Poloidal/Toroidal element of contravariant metric tensor, first toroidal derivative
g^zz	\(g^{\zeta\zeta}\)	inverse square meters	Toroidal/Toroidal element of contravariant metric tensor
g^zz_r	\(\partial_{\rho} g^{\zeta \zeta}\)	inverse square meters	Toroidal/Toroidal element of contravariant metric tensor, first radial derivative
g^zz_t	\(\partial_{\theta} g^{\zeta \zeta}\)	inverse square meters	Toroidal/Toroidal element of contravariant metric tensor, first poloidal derivative
g^zz_z	\(\partial_{\zeta} g^{\zeta \zeta}\)	inverse square meters	Toroidal/Toroidal element of contravariant metric tensor, first toroidal derivative
g_rr	\(g_{\rho\rho}\)	square meters	Radial/Radial element of covariant metric tensor
g_rt	\(g_{\rho\theta}\)	square meters	Radial/Poloidal element of covariant metric tensor	g_tr
g_rz	\(g_{\rho\zeta}\)	square meters	Radial/Toroidal element of covariant metric tensor	g_zr
g_tt	\(g_{\theta\theta}\)	square meters	Poloidal/Poloidal element of covariant metric tensor
g_tt_r	\(\partial_{\rho} g_{\theta\theta}\)	square meters	Poloidal/Poloidal element of covariant metric tensor, derivative wrt rho
g_tt_rr	\(\partial_{\rho\rho} g_{\theta\theta}\)	square meters	Poloidal/Poloidal element of covariant metric tensor, second derivative wrt rho
g_tt_rrr	\(\partial_{\rho\rho\rho} g_{\theta\theta}\)	square meters	Poloidal/Poloidal element of covariant metric tensor, third derivative wrt rho
g_tz	\(g_{\theta\zeta}\)	square meters	Poloidal/Toroidal element of covariant metric tensor	g_zt
g_tz_r	\(\partial_{\rho} g_{\theta\zeta}\)	square meters	Poloidal/Toroidal element of covariant metric tensor, derivative wrt rho
g_tz_rr	\(\partial_{\rho\rho} g_{\theta\zeta}\)	square meters	Poloidal/Toroidal element of covariant metric tensor, second derivative wrt rho
g_tz_rrr	\(\partial_{\rho\rho\rho} g_{\theta\zeta}\)	square meters	Poloidal/Toroidal element of covariant metric tensor, third derivative wrt rho
g_zz	\(g_{\zeta\zeta}\)	square meters	Toroidal/Toroidal element of covariant metric tensor
gbdrift	\(\mathrm{gbdrift} = 1/B^{2} (\mathbf{b}\times\nabla B) \cdot\nabla \alpha\)	inverse Tesla meters^2	Binormal component of the geometric part of the gradB drift used for local stability analyses, Gamma_c, epsilon_eff etc.
grad(B)	\(\nabla \mathbf{B}\)	Tesla / meter	Gradient of magnetic field vector
grad(alpha)	\(\nabla \alpha\)	Inverse meters	Gradient of field line label, which is perpendicular to the field line
grad(beta_a)	\(\nabla \beta_a = \nabla \mu_0 (p_{||} - p_{\perp})/B^2\)	Inverse meters	Pressure anisotropy gradient
grad(p)	\(\nabla p\)	Newtons / cubic meter	Pressure gradient
grad(psi)	\(\nabla\psi\)	Webers per meter	Toroidal flux gradient (normalized by 2pi)
grad(|B|)	\(\nabla |\mathbf{B}|\)	Tesla / meters	Gradient of magnetic field magnitude
grad(|B|^2)	\(\nabla |B|^{2}\)	Tesla squared / meters	Magnetic pressure gradient
grad(|B|^2)_rho	\((\nabla |B|^{2})_{\rho}\)	Tesla squared	Covariant radial component of magnetic pressure gradient
grad(|B|^2)_theta	\((\nabla |B|^{2})_{\theta}\)	Tesla squared	Covariant poloidal component of magnetic pressure gradient
grad(|B|^2)_zeta	\((\nabla |B|^{2})_{\zeta}\)	Tesla squared	Covariant toroidal component of magnetic pressure gradient
iota	\(\iota\)	None	Rotational transform (normalized by 2pi)
iota current	\(\iota~\mathrm{from~current}\)	None	Rotational transform (normalized by 2pi), current contribution
iota vacuum	\(\iota~\mathrm{in~vacuum}\)	None	Rotational transform (normalized by 2pi), vacuum contribution
iota_den	\(\iota_{\mathrm{denominator}}\)	inverse meters	Denominator of rotational transform formula
iota_den_r	\(\partial_{\rho} \iota_{\mathrm{denominator}}\)	inverse meters	Denominator of rotational transform formula, first radial derivative
iota_den_rr	\(\partial_{\rho\rho} \iota_{\mathrm{denominator}}\)	inverse meters	Denominator of rotational transform formula, second radial derivative
iota_den_rrr	\(\partial_{\rho\rho\rho} \iota_{\mathrm{denominator}}\)	inverse meters	Denominator of rotational transform formula, third radial derivative
iota_num	\(\iota_{\mathrm{numerator}}\)	inverse meters	Numerator of rotational transform formula
iota_num current	\(\iota_{\mathrm{numerator}}~\mathrm{from~current}\)	inverse meters	Numerator of rotational transform formula, current contribution
iota_num vacuum	\(\iota_{\mathrm{numerator}}~\mathrm{in~vacuum}\)	inverse meters	Numerator of rotational transform formula, vacuum contribution
iota_num_r	\(\partial_{\rho} \iota_{\mathrm{numerator}}\)	inverse meters	Numerator of rotational transform formula, first radial derivative
iota_num_r current	\(\partial_{\rho} \iota_{\mathrm{numerator}}~\mathrm{from~current}\)	inverse meters	Numerator of rotational transform formula, current contribution, first radial derivative
iota_num_r vacuum	\(\partial_{\rho} \iota_{\mathrm{numerator}}~\mathrm{in~vacuum}\)	inverse meters	Numerator of rotational transform formula, vacuum contribution, first radial derivative
iota_num_rr	\(\partial_{\rho\rho} \iota_{\mathrm{numerator}}\)	inverse meters	Numerator of rotational transform formula, second radial derivative
iota_num_rrr	\(\partial_{\rho\rho\rho} \iota_{\mathrm{numerator}}\)	inverse meters	Numerator of rotational transform formula, third radial derivative
iota_psi	\(\partial_{\psi} \iota\)	Inverse Webers	Rotational transform, radial derivative wrt toroidal flux
iota_r	\(\partial_{\rho} \iota\)	None	Rotational transform (normalized by 2pi), first radial derivative
iota_rr	\(\partial_{\rho\rho} \iota\)	None	Rotational transform (normalized by 2pi), second radial derivative
isodynamicity	\(1/|B|^2 (\mathbf{b} \times \nabla B) \cdot \nabla \psi\)	None	Measure of cross field drift at each point, unweighted by particle energy
kappa	\(\kappa\)	Inverse meters	Curvature vector of magnetic field lines
kappa_g	\(\kappa_g\)	Inverse meters	Geodesic curvature vector of magnetic field lines
kappa_n	\(\kappa_n\)	Inverse meters	Normal curvature vector of magnetic field lines
lambda	\(\lambda\)	radians	Poloidal stream function
lambda_r	\(\partial_{\rho} \lambda\)	radians	Poloidal stream function, first radial derivative
lambda_rr	\(\partial_{\rho \rho} \lambda\)	radians	Poloidal stream function, second radial derivative
lambda_rrr	\(\partial_{\rho \rho \rho} \lambda\)	radians	Poloidal stream function, third radial derivative
lambda_rrrt	\(\partial_{\rho \rho \rho \theta} \lambda\)	radians	Poloidal stream function, third radial derivative and first poloidal derivative	lambda_rrtr, lambda_rtrr, lambda_trrr
lambda_rrrz	\(\partial_{\rho \rho \rho \zeta} \lambda\)	radians	Poloidal stream function, third radial derivative and first toroidal derivative	lambda_rrzr, lambda_rzrr, lambda_zrrr
lambda_rrt	\(\partial_{\rho \rho \theta} \lambda\)	radians	Poloidal stream function, third derivative, wrt radius twice and poloidal angle	lambda_rtr, lambda_trr
lambda_rrz	\(\partial_{\rho \rho \zeta} \lambda\)	radians	Poloidal stream function, third derivative, wrt radius twice and toroidal angle	lambda_rzr, lambda_zrr
lambda_rt	\(\partial_{\rho \theta} \lambda\)	radians	Poloidal stream function, second derivative wrt radius and poloidal angle	lambda_tr
lambda_rtt	\(\partial_{\rho \theta \theta} \lambda\)	radians	Poloidal stream function, third derivative wrt radius and poloidal angle twice	lambda_trt, lambda_ttr
lambda_rtz	\(\partial_{\rho \theta \zeta} \lambda\)	radians	Poloidal stream function, third derivative wrt radius, poloidal angle, and toroidal angle	lambda_tzr, lambda_zrt
lambda_rz	\(\partial_{\rho \zeta} \lambda\)	radians	Poloidal stream function, second derivative wrt radius and toroidal angle	lambda_zr
lambda_rzz	\(\partial_{\rho \zeta \zeta} \lambda\)	radians	Poloidal stream function, third derivative wrt radius and toroidal angle twice	lambda_zrz, lambda_zzr
lambda_t	\(\partial_{\theta} \lambda\)	radians	Poloidal stream function, first poloidal derivative
lambda_tt	\(\partial_{\theta \theta} \lambda\)	radians	Poloidal stream function, second poloidal derivative
lambda_ttt	\(\partial_{\theta \theta \theta} \lambda\)	radians	Poloidal stream function, third poloidal derivative
lambda_ttz	\(\partial_{\theta \theta \zeta} \lambda\)	radians	Poloidal stream function, third derivative wrt poloidal angle twice and toroidal angle	lambda_tzt, lambda_ztt
lambda_tz	\(\partial_{\theta \zeta} \lambda\)	radians	Poloidal stream function, second derivative wrt poloidal and toroidal angles	lambda_zt
lambda_tzz	\(\partial_{\theta \zeta \zeta} \lambda\)	radians	Poloidal stream function, third derivative wrt poloidal angle and toroidal angle twice	lambda_ztz, lambda_zzt
lambda_z	\(\partial_{\zeta} \lambda\)	radians	Poloidal stream function, first toroidal derivative
lambda_zz	\(\partial_{\zeta \zeta} \lambda\)	radians	Poloidal stream function, second toroidal derivative
lambda_zzz	\(\partial_{\zeta \zeta \zeta} \lambda\)	radians	Poloidal stream function, third toroidal derivative
magnetic well	\(\mathrm{Magnetic~Well}\)	None	Magnetic well proxy for MHD stability (positive/negative value denotes stability/instability)
max_tz |B|	\(\max_{\theta \zeta} |\mathbf{B}|\)	Tesla	Maximum field strength on each flux surface
min_tz |B|	\(\min_{\theta \zeta} |\mathbf{B}|\)	Tesla	Minimum field strength on each flux surface
mirror ratio	\((B_{max} - B_{min}) / (B_{min} + B_{max})\)	None	Mirror ratio on each flux surface
n_rho	\(\hat{\mathbf{n}}_{\rho}\)	None	Unit vector normal to constant rho surface (direction of e^rho)
n_rho_z	\(\partial_{\zeta}\hat{\mathbf{n}}_{\rho}\)	None	Unit vector normal to constant rho surface (direction of e^rho), derivative wrt toroidal angle
n_theta	\(\hat{\mathbf{n}}_{\theta}\)	None	Unit vector normal to constant theta surface (direction of e^theta)
n_zeta	\(\hat{\mathbf{n}}_{\zeta}\)	None	Unit vector normal to constant zeta surface (direction of e^zeta)
ne	\(n_e\)	1 / cubic meters	Electron density
ne_r	\(\partial_{\rho} n_e\)	1 / cubic meters	Electron density, first radial derivative
ne_rr	\(\partial_{\rho \rho} n_e\)	1 / cubic meters	Electron density, second radial derivative
nu	\(\nu = \zeta_{B} - \zeta\)	radians	Boozer toroidal stream function
nu_t	\(\partial_{\theta} \nu\)	radians	Boozer toroidal stream function, derivative wrt poloidal angle
nu_z	\(\partial_{\zeta} \nu\)	radians	Boozer toroidal stream function, derivative wrt toroidal angle
omega	\(\omega\)	radians	Toroidal stream function
omega_r	\(\partial_{\rho} \omega\)	radians	Toroidal stream function, first radial derivative
omega_rr	\(\partial_{\rho \rho} \omega\)	radians	Toroidal stream function, second radial derivative
omega_rrr	\(\partial_{\rho \rho \rho} \omega\)	radians	Toroidal stream function, third radial derivative
omega_rrrr	\(\partial_{\rho \rho \rho \rho} \omega\)	radians	Toroidal stream function, fourth radial derivative
omega_rrrt	\(\partial_{\rho \rho \rho \theta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radial coordinate thrice and poloidal once	omega_rrtr, omega_rtrr, omega_trrr
omega_rrrz	\(\partial_{\rho \rho \rho \zeta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radial coordinate thrice and toroidal once	omega_rrzr, omega_rzrr, omega_zrrr
omega_rrt	\(\partial_{\rho \rho \theta} \omega\)	radians	Toroidal stream function, third derivative, wrt radius twice and poloidal angle	omega_rtr, omega_trr
omega_rrtt	\(\partial_{\rho \rho \theta \theta} \omega\)	radians	Toroidal stream function, fourth derivative, wrt radius twice and poloidal angle twice	omega_rttr, omega_trrt, omega_ttrr
omega_rrtz	\(\partial_{\rho \theta \zeta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radius twice, poloidal angle, and toroidal angle	omega_rtzr, omega_tzrr, omega_zrrt
omega_rrz	\(\partial_{\rho \rho \zeta} \omega\)	radians	Toroidal stream function, third derivative, wrt radius twice and toroidal angle	omega_rzr, omega_zrr
omega_rrzz	\(\partial_{\rho \rho \zeta \zeta} \omega\)	radians	Toroidal stream function, fourth derivative, wrt radius twice and toroidal angle twice	omega_rzzr, omega_zrrz, omega_zzrr
omega_rt	\(\partial_{\rho \theta} \omega\)	radians	Toroidal stream function, second derivative wrt radius and poloidal angle	omega_tr
omega_rtt	\(\partial_{\rho \theta \theta} \omega\)	radians	Toroidal stream function, third derivative wrt radius and poloidal angle twice	omega_trt, omega_ttr
omega_rttt	\(\partial_{\rho \theta \theta \theta} \omega\)	radians	Toroidal stream function, third derivative wrt radius and poloidal angle thrice	omega_trtt, omega_ttrt, omega_tttr
omega_rttz	\(\partial_{\rho \theta \theta \zeta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radius once, poloidal angle twice, and toroidal angle once	omega_ttzr, omega_tzrt, omega_zrtt
omega_rtz	\(\partial_{\rho \theta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt radius, poloidal angle, and toroidal angle	omega_tzr, omega_zrt
omega_rtzz	\(\partial_{\rho \theta \zeta \zeta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radius, poloidal angle, and toroidal angle twice	omega_tzzr, omega_zrtz, omega_zzrt
omega_rz	\(\partial_{\rho \zeta} \omega\)	radians	Toroidal stream function, second derivative wrt radius and toroidal angle	omega_zr
omega_rzz	\(\partial_{\rho \zeta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt radius and toroidal angle twice	omega_zrz, omega_zzr
omega_rzzz	\(\partial_{\rho \zeta \zeta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt radius and toroidal angle thrice	omega_zrzz, omega_zzrz, omega_zzzr
omega_t	\(\partial_{\theta} \omega\)	radians	Toroidal stream function, first poloidal derivative
omega_tt	\(\partial_{\theta \theta} \omega\)	radians	Toroidal stream function, second poloidal derivative
omega_ttt	\(\partial_{\theta \theta \theta} \omega\)	radians	Toroidal stream function, third poloidal derivative
omega_ttz	\(\partial_{\theta \theta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt poloidal angle twice and toroidal angle	omega_tzt, omega_ztt
omega_tz	\(\partial_{\theta \zeta} \omega\)	radians	Toroidal stream function, second derivative wrt poloidal and toroidal angles	omega_zt
omega_tzz	\(\partial_{\theta \zeta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt poloidal angle and toroidal angle twice	omega_ztz, omega_zzt
omega_z	\(\partial_{\zeta} \omega\)	radians	Toroidal stream function, first toroidal derivative
omega_zz	\(\partial_{\zeta \zeta} \omega\)	radians	Toroidal stream function, second toroidal derivative
omega_zzz	\(\partial_{\zeta \zeta \zeta} \omega\)	radians	Toroidal stream function, third toroidal derivative
p	\(p\)	Pascals	Pressure
p_r	\(\partial_{\rho} p\)	Pascals	Pressure, first radial derivative
p_t	\(\partial_{\theta} p\)	Pascals	Pressure, first poloidal derivative
p_z	\(\partial_{\zeta} p\)	Pascals	Pressure, first toroidal derivative
perimeter(z)	\(P(\zeta)\)	meters	Perimeter of enclosed cross-section (enclosed constant phi surface), scaled by max(ρ)⁻¹, as function of zeta
phi	\(\phi\)	radians	Toroidal angle in lab frame
phi_r	\(\partial_{\rho} \phi\)	radians	Toroidal angle in lab frame, derivative wrt radial coordinate
phi_rr	\(\partial_{\rho \rho} \phi\)	radians	Toroidal angle in lab frame, second derivative wrt radial coordinate
phi_rt	\(\partial_{\rho \theta} \phi\)	radians	Toroidal angle in lab frame, second derivative wrt radial and poloidal coordinate	phi_tr
phi_rz	\(\partial_{\rho \zeta} \phi\)	radians	Toroidal angle in lab frame, second derivative wrt radial and toroidal coordinate	phi_zr
phi_t	\(\partial_{\theta} \phi\)	radians	Toroidal angle in lab frame, derivative wrt poloidal coordinate
phi_tt	\(\partial_{\theta \theta} \phi\)	radians	Toroidal angle in lab frame, second derivative wrt poloidal coordinate
phi_tz	\(\partial_{\theta \zeta} \phi\)	radians	Toroidal angle in lab frame, second derivative wrt poloidal and toroidal coordinate	phi_zt
phi_z	\(\partial_{\zeta} \phi\)	radians	Toroidal angle in lab frame, derivative wrt toroidal coordinate
phi_zz	\(\partial_{\zeta \zeta} \phi\)	radians	Toroidal angle in lab frame, second derivative wrt toroidal coordinate
psi	\(\psi = \Psi / (2 \pi)\)	Webers	Toroidal flux (normalized by 2pi)
psi_r	\(\partial_{\rho} \psi = \partial_{\rho} \Psi / (2 \pi)\)	Webers	Toroidal flux (normalized by 2pi), first radial derivative
psi_rr	\(\partial_{\rho\rho} \psi = \partial_{\rho\rho} \Psi / (2 \pi)\)	Webers	Toroidal flux (normalized by 2pi), second radial derivative
psi_rrr	\(\partial_{\rho\rho\rho} \psi = \partial_{\rho\rho\rho} \Psi / (2 \pi)\)	Webers	Toroidal flux (normalized by 2pi), third radial derivative
q	\(q = 1/\iota\)	None	Safety factor ‘q’, inverse of rotational transform.
rho	\(\rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux
rho_r	\(\partial_{\rho} \rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux, derivative wrt radial coordinate
rho_t	\(\partial_{\theta} \rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux, derivative wrt poloidal coordinate
rho_z	\(\partial_{\zeta} \rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux, derivative wrt toroidal coordinate
shear	\(-\rho \frac{\partial_{\rho}\iota}{\iota}\)	None	Global magnetic shear
sqrt(g)	\(\sqrt{g}\)	cubic meters	Jacobian determinant of flux coordinate system
sqrt(g)_B	\(\sqrt{g}_{B}\)	None	Jacobian determinant of Boozer coordinates
sqrt(g)_PEST	\(\sqrt{g}_{PEST}\)	cubic meters	Jacobian determinant of PEST flux coordinate system
sqrt(g)_r	\(\partial_{\rho} \sqrt{g}\)	cubic meters	Jacobian determinant of flux coordinate system, derivative wrt radial coordinate
sqrt(g)_rr	\(\partial_{\rho\rho} \sqrt{g}\)	cubic meters	Jacobian determinant of flux coordinate system, second derivative wrt radial coordinate
sqrt(g)_rrr	\(\partial_{\rho\rho\rho} \sqrt{g}\)	cubic meters	Jacobian determinant of flux coordinate system, third derivative wrt radial coordinate
sqrt(g)_rrt	\(\partial_{\rho\rho\theta} \sqrt{g}\)	cubic meters	Jacobian determinant of flux coordinate system, third derivative wrt radial coordinate twice and poloidal angle once	sqrt(g)_rtr, sqrt(g)_trr
sqrt(g)_rrz	\(\partial_{\rho\rho\zeta} \sqrt{g}\)	cubic meters	Jacobian determinant of flux coordinate system, third derivative wrt radial coordinate twice and toroidal angle once	sqrt(g)_rzr, sqrt(g)_zrr
sqrt(g)_rt	\(\partial_{\rho\theta} \sqrt{g}\)	cubic meters	Jacobian determinant of flux coordinate system, second derivative wrt radial coordinate and poloidal angle	sqrt(g)_tr
sqrt(g)_rtt	\(\partial_{\rho\theta\theta} \sqrt{g}\)	cubic meters	Jacobian determinant of flux coordinate system, third derivative wrt radial coordinate once and poloidal angle twice.	sqrt(g)_trt, sqrt(g)_ttr
sqrt(g)_rtz	\(\partial_{\rho\theta\zeta} \sqrt{g}\)	cubic meters	Jacobian determinant of flux coordinate system, third derivative wrt radial, poloidal, and toroidal coordinate	sqrt(g)_tzr, sqrt(g)_zrt
sqrt(g)_rz	\(\partial_{\rho\zeta} \sqrt{g}\)	cubic meters	Jacobian determinant of flux coordinate system, second derivative wrt radial coordinate and toroidal angle	sqrt(g)_zr
sqrt(g)_rzz	\(\partial_{\rho\zeta\zeta} \sqrt{g}\)	cubic meters	Jacobian determinant of flux coordinate system, third derivative wrt radial coordinate once and toroidal angle twice	sqrt(g)_zrz, sqrt(g)_zzr
sqrt(g)_t	\(\partial_{\theta} \sqrt{g}\)	cubic meters	Jacobian determinant of flux coordinate system, derivative wrt poloidal angle
sqrt(g)_tt	\(\partial_{\theta\theta} \sqrt{g}\)	cubic meters	Jacobian determinant of flux coordinate system, second derivative wrt poloidal angle
sqrt(g)_tz	\(\partial_{\theta\zeta} \sqrt{g}\)	cubic meters	Jacobian determinant of flux coordinate system, second derivative wrt poloidal and toroidal angles	sqrt(g)_zt
sqrt(g)_z	\(\partial_{\zeta} \sqrt{g}\)	cubic meters	Jacobian determinant of flux coordinate system, derivative wrt toroidal angle
sqrt(g)_zz	\(\partial_{\zeta\zeta} \sqrt{g}\)	cubic meters	Jacobian determinant of flux coordinate system, second derivative wrt toroidal angle
theta	\(\theta\)	radians	Poloidal angular coordinate (geometric, not magnetic)
theta_B	\(\theta_{B}\)	radians	Boozer poloidal angular coordinate
theta_PEST	\(\vartheta\)	radians	PEST straight field line poloidal angular coordinate
theta_PEST_r	\(\partial_{\rho} \vartheta\)	radians	PEST straight field line poloidal angular coordinate, derivative wrt radial coordinate
theta_PEST_t	\(\partial_{\theta} \vartheta\)	radians	PEST straight field line poloidal angular coordinate, derivative wrt poloidal coordinate
theta_PEST_z	\(\partial_{\zeta} \vartheta\)	radians	PEST straight field line poloidal angular coordinate, derivative wrt toroidal coordinate
theta_r	\(\partial_{\rho} \theta\)	radians	Poloidal angular coordinate (geometric, not magnetic), derivative wrt radial coordinate
theta_t	\(\partial_{\theta} \theta\)	radians	Poloidal angular coordinate (geometric, not magnetic), derivative wrt poloidal coordinate
theta_z	\(\partial_{\zeta} \theta\)	radians	Poloidal angular coordinate (geometric, not magnetic), derivative wrt toroidal coordinate
trapped fraction	\(1 - \frac{3}{4} \langle |B|^2 \rangle \int_0^{1/Bmax} \frac{\lambda\; d\lambda}{\langle \sqrt{1 - \lambda B} \rangle}\)	None	Neoclassical effective trapped particle fraction		n_gauss
w_Boozer	\(w_{\mathrm{Boozer}}\)	Tesla * meters	Inverse Fourier transform of RHS of eq 10 in Hirshman 1995 ‘Transformation from VMEC to Boozer Coordinates’		M_booz, N_booz
w_Boozer_mn	\(w_{\mathrm{Boozer},m,n}\)	Tesla * meters	RHS of eq 10 in Hirshman 1995 ‘Transformation from VMEC to Boozer Coordinates’		M_booz, N_booz
w_Boozer_t	\(\partial_{\theta} w_{\mathrm{Boozer}}\)	Tesla * meters	Inverse Fourier transform of RHS of eq 10 in Hirshman 1995 ‘Transformation from VMEC to Boozer Coordinates’, poloidal derivative		M_booz, N_booz
w_Boozer_z	\(\partial_{\zeta} w_{\mathrm{Boozer}}\)	Tesla * meters	Inverse Fourier transform of RHS of eq 10 in Hirshman 1995 ‘Transformation from VMEC to Boozer Coordinates’, toroidal derivative		M_booz, N_booz
zeta	\(\zeta\)	radians	Toroidal angular coordinate
zeta_B	\(\zeta_{B}\)	radians	Boozer toroidal angular coordinate
zeta_r	\(\partial_{\rho} \zeta\)	radians	Toroidal angular coordinate derivative, wrt radial coordinate
zeta_t	\(\partial_{\theta} \zeta\)	radians	Toroidal angular coordinate, derivative wrt poloidal coordinate
zeta_z	\(\partial_{\zeta} \zeta\)	radians	Toroidal angular coordinate, derivative wrt toroidal coordinate
|(B*grad)B|	\(|(\mathbf{B} \cdot \nabla) \mathbf{B}|\)	Tesla squared / meters	Magnitude of magnetic tension
|B|	\(|\mathbf{B}|\)	Tesla	Magnitude of magnetic field
|B|^2	\(|\mathbf{B}|^{2}\)	Tesla squared	Magnitude of magnetic field, squared
|B|_mn	\(B_{mn}^{\mathrm{Boozer}}\)	Tesla	Boozer harmonics of magnetic field		M_booz, N_booz
|B|_r	\(\partial_{\rho} |\mathbf{B}|\)	Tesla	Magnitude of magnetic field, derivative wrt radial coordinate
|B|_rr	\(\partial_{\rho\rho} |\mathbf{B}|\)	Tesla	Magnitude of magnetic field, second derivative wrt radial coordinate
|B|_rt	\(\partial_{\rho\theta} |\mathbf{B}|\)	Tesla	Magnitude of magnetic field, derivative wrt radial coordinate and poloidal angle	|B|_tr
|B|_rz	\(\partial_{\rho\zeta} |\mathbf{B}|\)	Tesla	Magnitude of magnetic field, derivative wrt radial coordinate and toroidal angle	|B|_zr
|B|_t	\(\partial_{\theta} |\mathbf{B}|\)	Tesla	Magnitude of magnetic field, derivative wrt poloidal angle
|B|_tt	\(\partial_{\theta\theta} |\mathbf{B}|\)	Tesla	Magnitude of magnetic field, second derivative wrt poloidal angle
|B|_tz	\(\partial_{\theta\zeta} |\mathbf{B}|\)	Tesla	Magnitude of magnetic field, derivative wrt poloidal and toroidal angles	|B|_zt
|B|_z	\(\partial_{\zeta} |\mathbf{B}|\)	Tesla	Magnitude of magnetic field, derivative wrt toroidal angle
|B|_zz	\(\partial_{\zeta\zeta} |\mathbf{B}|\)	Tesla	Magnitude of magnetic field, second derivative wrt toroidal angle
|F|	\(|\mathbf{J} \times \mathbf{B} - \nabla p|\)	Newtons / cubic meter	Magnitude of force balance error
|J|	\(|\mathbf{J}|\)	Amperes / square meter	Magnitude of plasma current density
|e^helical*sqrt(g)|	\(|\sqrt{g}(B^{\theta} \nabla \zeta - B^{\zeta} \nabla \theta)|\)	Tesla * square meter	Magnitude of helical basis vector weighted by 3-D volume Jacobian
|e^helical|	\(|B^{\theta} \nabla \zeta - B^{\zeta} \nabla \theta|\)	Tesla / square meter	Magnitude of helical basis vector
|e_rho x e_theta|	\(|\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\)	square meters	2D Jacobian determinant for constant zeta surface
|e_rho x e_theta|_r	\(\partial_{\rho} |\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\)	square meters	2D Jacobian determinant for constant zeta surface derivative wrt radial coordinate
|e_rho x e_theta|_rr	\(\partial_{\rho \rho} |\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\)	square meters	2D Jacobian determinant for constant zeta surface second derivative wrt radial coordinate
|e_theta x e_zeta|	\(|\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\)	square meters	2D Jacobian determinant for constant rho surface
|e_theta x e_zeta|_r	\(\partial_{\rho} |\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\)	square meters	2D Jacobian determinant for constant rho surface derivative wrt radial coordinate
|e_theta x e_zeta|_rr	\(\partial_{\rho\rho} |\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\)	square meters	2D Jacobian determinant for constant rho surface second derivative wrt radial coordinate
|e_theta x e_zeta|_z	\(\partial_{\zeta}|e_{\theta} \times e_{\zeta}|\)	square meters	2D Jacobian determinant for constant rho surface,derivative wrt toroidal angle
|e_zeta x e_rho|	\(|\mathbf{e}_{\zeta} \times \mathbf{e}_{\rho}|\)	square meters	2D Jacobian determinant for constant theta surface
|grad(B)|	\(|\nabla \mathbf{B}|\)	Tesla / meter	Frobenius norm of gradient of magnetic field vector
|grad(p)|	\(|\nabla p|\)	Newtons per cubic meter	Magnitude of pressure gradient
|grad(p)|^2	\(|\nabla p|^{2}\)	Newtons per cubic meter squared	Magnitude of pressure gradient squared
|grad(psi)|	\(|\nabla\psi|\)	Webers per meter	Toroidal flux gradient (normalized by 2pi) magnitude
|grad(psi)|^2	\(|\nabla\psi|^{2}\)	Webers squared per square meter	Toroidal flux gradient (normalized by 2pi) magnitude squared
|grad(rho)|	\(|\nabla \rho|\)	inverse meters	Magnitude of contravariant radial basis vector
|grad(theta)|	\(|\nabla \theta|\)	inverse meters	Magnitude of contravariant poloidal basis vector
|grad(zeta)|	\(|\nabla \zeta|\)	inverse meters	Magnitude of contravariant toroidal basis vector
|grad(|B|^2)|/2mu0	\(|\nabla |B|^{2}/(2\mu_0)|\)	Newton / cubic meter	Magnitude of magnetic pressure gradient

desc.geometry.curve.FourierRZCurve

List of Variables: desc.geometry.curve.FourierRZCurve

Name	Label	Units	Description	Aliases	kwargs
0	\(0\)	None	Zeros
R	\(R\)	meters	Cylindrical radial position along curve
X	\(X\)	meters	Cartesian X coordinate.
Y	\(Y\)	meters	Cartesian Y coordinate.
Z	\(Z\)	meters	Cylindrical vertical position along curve
center	\(\langle\mathbf{x}\rangle\)	meters	Centroid of the curve
curvature	\(\kappa\)	Inverse meters	Scalar curvature of the curve, with the sign denoting the convexity/concavity relative to the center of the curve (a circle has positive curvature)
ds	\(ds\)	None	Spacing of curve parameter
frenet_binormal	\(\mathbf{B}_{\mathrm{Frenet-Serret}}\)	None	Binormal unit vector to curve in Frenet-Serret frame
frenet_normal	\(\mathbf{N}_{\mathrm{Frenet-Serret}}\)	None	Normal unit vector to curve in Frenet-Serret frame
frenet_tangent	\(\mathbf{T}_{\mathrm{Frenet-Serret}}\)	None	Tangent unit vector to curve in Frenet-Serret frame
length	\(L\)	meters	Length of the curve
phi	\(\phi\)	radians	Toroidal phi position along curve
s	\(s\)	None	Curve parameter, on [0, 2pi)
torsion	\(\tau\)	Inverse meters	Scalar torsion of the curve
x	\(\mathbf{x}\)	meters	Position vector along curve
x_s	\(\partial_{s} \mathbf{x}\)	meters	Position vector along curve, first derivative
x_ss	\(\partial_{ss} \mathbf{x}\)	meters	Position vector along curve, second derivative
x_sss	\(\partial_{sss} \mathbf{x}\)	meters	Position vector along curve, third derivative

desc.geometry.curve.FourierXYZCurve

List of Variables: desc.geometry.curve.FourierXYZCurve

Name	Label	Units	Description	Aliases	kwargs
0	\(0\)	None	Zeros
R	\(R\)	meters	Cylindrical radial position along curve
X	\(X\)	meters	Cartesian X coordinate.
Y	\(Y\)	meters	Cartesian Y coordinate.
Z	\(Z\)	meters	Cylindrical vertical position along curve
center	\(\langle\mathbf{x}\rangle\)	meters	Centroid of the curve
curvature	\(\kappa\)	Inverse meters	Scalar curvature of the curve, with the sign denoting the convexity/concavity relative to the center of the curve (a circle has positive curvature)
ds	\(ds\)	None	Spacing of curve parameter
frenet_binormal	\(\mathbf{B}_{\mathrm{Frenet-Serret}}\)	None	Binormal unit vector to curve in Frenet-Serret frame
frenet_normal	\(\mathbf{N}_{\mathrm{Frenet-Serret}}\)	None	Normal unit vector to curve in Frenet-Serret frame
frenet_tangent	\(\mathbf{T}_{\mathrm{Frenet-Serret}}\)	None	Tangent unit vector to curve in Frenet-Serret frame
length	\(L\)	meters	Length of the curve
phi	\(\phi\)	radians	Toroidal phi position along curve
s	\(s\)	None	Curve parameter, on [0, 2pi)
torsion	\(\tau\)	Inverse meters	Scalar torsion of the curve
x	\(\mathbf{x}\)	meters	Position vector along curve
x_s	\(\partial_{s} \mathbf{x}\)	meters	Position vector along curve, first derivative
x_ss	\(\partial_{ss} \mathbf{x}\)	meters	Position vector along curve, second derivative
x_sss	\(\partial_{sss} \mathbf{x}\)	meters	Position vector along curve, third derivative

desc.geometry.curve.FourierPlanarCurve

List of Variables: desc.geometry.curve.FourierPlanarCurve

Name	Label	Units	Description	Aliases	kwargs
0	\(0\)	None	Zeros
R	\(R\)	meters	Cylindrical radial position along curve
X	\(X\)	meters	Cartesian X coordinate.
Y	\(Y\)	meters	Cartesian Y coordinate.
Z	\(Z\)	meters	Cylindrical vertical position along curve
center	\(\langle\mathbf{x}\rangle\)	meters	Centroid of the curve		basis_in
curvature	\(\kappa\)	Inverse meters	Scalar curvature of the curve, with the sign denoting the convexity/concavity relative to the center of the curve (a circle has positive curvature)
ds	\(ds\)	None	Spacing of curve parameter
frenet_binormal	\(\mathbf{B}_{\mathrm{Frenet-Serret}}\)	None	Binormal unit vector to curve in Frenet-Serret frame
frenet_normal	\(\mathbf{N}_{\mathrm{Frenet-Serret}}\)	None	Normal unit vector to curve in Frenet-Serret frame
frenet_tangent	\(\mathbf{T}_{\mathrm{Frenet-Serret}}\)	None	Tangent unit vector to curve in Frenet-Serret frame
length	\(L\)	meters	Length of the curve
phi	\(\phi\)	radians	Toroidal phi position along curve
s	\(s\)	None	Curve parameter, on [0, 2pi)
torsion	\(\tau\)	Inverse meters	Scalar torsion of the curve
x	\(\mathbf{x}\)	meters	Position vector along curve		basis_in
x_s	\(\partial_{s} \mathbf{x}\)	meters	Position vector along curve, first derivative		basis_in
x_ss	\(\partial_{ss} \mathbf{x}\)	meters	Position vector along curve, second derivative		basis_in
x_sss	\(\partial_{sss} \mathbf{x}\)	meters	Position vector along curve, third derivative		basis_in

desc.geometry.curve.SplineXYZCurve

List of Variables: desc.geometry.curve.SplineXYZCurve

Name	Label	Units	Description	Aliases	kwargs
0	\(0\)	None	Zeros
R	\(R\)	meters	Cylindrical radial position along curve
X	\(X\)	meters	Cartesian X coordinate.
Y	\(Y\)	meters	Cartesian Y coordinate.
Z	\(Z\)	meters	Cylindrical vertical position along curve
center	\(\langle\mathbf{x}\rangle\)	meters	Centroid of the curve
curvature	\(\kappa\)	Inverse meters	Scalar curvature of the curve, with the sign denoting the convexity/concavity relative to the center of the curve (a circle has positive curvature)
ds	\(ds\)	None	Spacing of curve parameter
frenet_binormal	\(\mathbf{B}_{\mathrm{Frenet-Serret}}\)	None	Binormal unit vector to curve in Frenet-Serret frame
frenet_normal	\(\mathbf{N}_{\mathrm{Frenet-Serret}}\)	None	Normal unit vector to curve in Frenet-Serret frame
frenet_tangent	\(\mathbf{T}_{\mathrm{Frenet-Serret}}\)	None	Tangent unit vector to curve in Frenet-Serret frame
length	\(L\)	meters	Length of the curve		method
phi	\(\phi\)	radians	Toroidal phi position along curve
s	\(s\)	None	Curve parameter, on [0, 2pi)
torsion	\(\tau\)	Inverse meters	Scalar torsion of the curve
x	\(\mathbf{x}\)	meters	Position vector along curve		method
x_s	\(\partial_{s} \mathbf{x}\)	meters	Position vector along curve, first derivative		method
x_ss	\(\partial_{ss} \mathbf{x}\)	meters	Position vector along curve, second derivative		method
x_sss	\(\partial_{sss} \mathbf{x}\)	meters	Position vector along curve, third derivative		method

desc.geometry.surface.FourierRZToroidalSurface

List of Variables: desc.geometry.surface.FourierRZToroidalSurface

Name	Label	Units	Description	Aliases	kwargs
0	\(0\)	None	Zeros
A	\(A\)	square meters	Average cross-sectional area
A(z)	\(A(\zeta)\)	square meters	Area of enclosed cross-section (enclosed constant phi surface), scaled by max(ρ)⁻², as function of zeta
L_sff_rho	\(L_{\mathrm{SFF},\rho}\)	meters	L coefficient of second fundamental form of constant rho surface
M_sff_rho	\(M_{\mathrm{SFF},\rho}\)	meters	M coefficient of second fundamental form of constant rho surface
N_sff_rho	\(N_{\mathrm{SFF},\rho}\)	meters	N coefficient of second fundamental form of constant rho surface
R	\(R\)	meters	Cylindrical radial position along surface
R0	\(R_{0}\)	meters	Average major radius
R0/a	\(R_{0} / a\)	None	Aspect ratio
R_t	\(\partial_{\theta} R\)	meters	Major radius in lab frame, first poloidal derivative
R_tt	\(\partial_{\theta \theta} R\)	meters	Major radius in lab frame, second poloidal derivative
R_ttt	\(\partial_{\theta \theta \theta} R\)	meters	Major radius in lab frame, third poloidal derivative
R_ttz	\(\partial_{\theta \theta \zeta} R\)	meters	Major radius in lab frame, third derivative wrt poloidal angle twice and toroidal angle	R_tzt, R_ztt
R_tz	\(\partial_{\theta \zeta} R\)	meters	Major radius in lab frame, second derivative wrt poloidal and toroidal angles	R_zt
R_tzz	\(\partial_{\theta \zeta \zeta} R\)	meters	Major radius in lab frame, third derivative wrt poloidal angle and toroidal angle twice	R_ztz, R_zzt
R_z	\(\partial_{\zeta} R\)	meters	Major radius in lab frame, first toroidal derivative
R_zz	\(\partial_{\zeta \zeta} R\)	meters	Major radius in lab frame, second toroidal derivative
R_zzz	\(\partial_{\zeta \zeta \zeta} R\)	meters	Major radius in lab frame, third toroidal derivative
S	\(S\)	square meters	Surface area of outermost flux surface
V	\(V\)	cubic meters	Volume
X	\(X\)	meters	Cartesian X coordinate.
Y	\(Y\)	meters	Cartesian Y coordinate.
Z	\(Z\)	meters	Cylindrical vertical position along surface
Z_t	\(\partial_{\theta} Z\)	meters	Vertical coordinate in lab frame, first poloidal derivative
Z_tt	\(\partial_{\theta \theta} Z\)	meters	Vertical coordinate in lab frame, second poloidal derivative
Z_ttt	\(\partial_{\theta \theta \theta} Z\)	meters	Vertical coordinate in lab frame, third poloidal derivative
Z_ttz	\(\partial_{\theta \theta \zeta} Z\)	meters	Vertical coordinate in lab frame, third derivative wrt poloidal angle twice and toroidal angle	Z_tzt, Z_ztt
Z_tz	\(\partial_{\theta \zeta} Z\)	meters	Vertical coordinate in lab frame, second derivative wrt poloidal and toroidal angles	Z_zt
Z_tzz	\(\partial_{\theta \zeta \zeta} Z\)	meters	Vertical coordinate in lab frame, third derivative wrt poloidal angle and toroidal angle twice	Z_ztz, Z_zzt
Z_z	\(\partial_{\zeta} Z\)	meters	Vertical coordinate in lab frame, first toroidal derivative
Z_zz	\(\partial_{\zeta \zeta} Z\)	meters	Vertical coordinate in lab frame, second toroidal derivative
Z_zzz	\(\partial_{\zeta \zeta \zeta} Z\)	meters	Vertical coordinate in lab frame, third toroidal derivative
a	\(a\)	meters	Average minor radius
a_major/a_minor	\(a_{\mathrm{major}} / a_{\mathrm{minor}}\)	None	Elongation at a toroidal cross-section
curvature_H_rho	\(H_{\rho}\)	meters	Mean curvature of constant rho surfaces
curvature_K_rho	\(K_{\rho}\)	meters squared	Gaussian curvature of constant rho surfaces
curvature_k1_rho	\(k_{1,\rho}\)	Inverse meters	First principle curvature of constant rho surfaces
curvature_k2_rho	\(k_{2,\rho}\)	Inverse meters	Second principle curvature of constant rho surfaces
e^theta*sqrt(g)	\(\mathbf{e}^{\theta} \sqrt{g}\)	square meters	Contravariant poloidal basis vector weighted by 3-D volume Jacobian
e_phi	\(\mathbf{e}_{\phi}\)	meters	Covariant cylindrical toroidal basis vector
e_rho	\(\mathbf{e}_{\rho}\)	meters	Covariant radial basis vector
e_rho_r	\(\partial_{\rho} \mathbf{e}_{\rho}\)	meters	Covariant radial basis vector, derivative wrt radial coordinate
e_rho_rr	\(\partial_{\rho \rho} \mathbf{e}_{\rho}\)	meters	Covariant radial basis vector, second derivative wrt radial coordinate
e_rho_t	\(\partial_{\theta} \mathbf{e}_{\rho}\)	meters	Covariant radial basis vector, derivative wrt poloidal angle	e_theta_r
e_rho_z	\(\partial_{\zeta} \mathbf{e}_{\rho}\)	meters	Covariant radial basis vector, derivative wrt toroidal angle	e_zeta_r
e_theta	\(\mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector
e_theta_rr	\(\partial_{\rho \rho} \mathbf{e}_{\theta}\)	meters	Covariant poloidal basis vector, second derivative wrt radial coordinate	e_rho_rt, e_rho_tr
e_theta_t	\(\partial_{\theta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, derivative wrt poloidal coordinate
e_theta_tt	\(\partial_{\theta \theta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, second derivative wrt poloidal and poloidal coordinates
e_theta_tz	\(\partial_{\theta \zeta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, second derivative wrt poloidal and toroidal coordinates	e_theta_zt, e_zeta_tt
e_theta_z	\(\partial_{\zeta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, derivative wrt toroidal coordinate	e_zeta_t
e_theta_zz	\(\partial_{\zeta \zeta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, second derivative wrt toroidal and toroidal coordinates	e_zeta_tz, e_zeta_zt
e_theta|r,p	\(\mathbf{e}_{\theta} |_{\rho, \phi}\)	meters	Covariant poloidal basis vector in (ρ,θ,ϕ) coordinates. ϕ increases counterclockwise when viewed from above (cylindrical R,ϕ plane with Z out of page).
e_zeta	\(\mathbf{e}_{\zeta}\)	meters	Covariant Toroidal basis vector
e_zeta_rr	\(\partial_{\rho \rho} \mathbf{e}_{\zeta}\)	meters	Covariant toroidal basis vector, second derivative wrt radial coordinate	e_rho_rz, e_rho_zr
e_zeta_z	\(\partial_{\zeta} \mathbf{e}_{\zeta}\)	meters	Covariant Toroidal basis vector, derivative wrt toroidal coordinate
e_zeta_zz	\(\partial_{\zeta \zeta} \mathbf{e}_{\zeta}\)	meters	Covariant Toroidal basis vector, second derivative wrt toroidal and toroidal coordinates
g_rr	\(g_{\rho\rho}\)	square meters	Radial/Radial element of covariant metric tensor
g_rt	\(g_{\rho\theta}\)	square meters	Radial/Poloidal element of covariant metric tensor	g_tr
g_rz	\(g_{\rho\zeta}\)	square meters	Radial/Toroidal element of covariant metric tensor	g_zr
g_tt	\(g_{\theta\theta}\)	square meters	Poloidal/Poloidal element of covariant metric tensor
g_tt_r	\(\partial_{\rho} g_{\theta\theta}\)	square meters	Poloidal/Poloidal element of covariant metric tensor, derivative wrt rho
g_tz	\(g_{\theta\zeta}\)	square meters	Poloidal/Toroidal element of covariant metric tensor	g_zt
g_tz_r	\(\partial_{\rho} g_{\theta\zeta}\)	square meters	Poloidal/Toroidal element of covariant metric tensor, derivative wrt rho
g_zz	\(g_{\zeta\zeta}\)	square meters	Toroidal/Toroidal element of covariant metric tensor
n_rho	\(\hat{\mathbf{n}}_{\rho}\)	None	Unit vector normal to constant rho surface (direction of e^rho)
n_rho_z	\(\partial_{\zeta}\hat{\mathbf{n}}_{\rho}\)	None	Unit vector normal to constant rho surface (direction of e^rho), derivative wrt toroidal angle
n_theta	\(\hat{\mathbf{n}}_{\theta}\)	None	Unit vector normal to constant theta surface (direction of e^theta)
n_zeta	\(\hat{\mathbf{n}}_{\zeta}\)	None	Unit vector normal to constant zeta surface (direction of e^zeta)
omega	\(\omega\)	radians	Toroidal stream function
omega_r	\(\partial_{\rho} \omega\)	radians	Toroidal stream function, first radial derivative
omega_rr	\(\partial_{\rho \rho} \omega\)	radians	Toroidal stream function, second radial derivative
omega_rrr	\(\partial_{\rho \rho \rho} \omega\)	radians	Toroidal stream function, third radial derivative
omega_rrrr	\(\partial_{\rho \rho \rho \rho} \omega\)	radians	Toroidal stream function, fourth radial derivative
omega_rrrt	\(\partial_{\rho \rho \rho \theta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radial coordinate thrice and poloidal once	omega_rrtr, omega_rtrr, omega_trrr
omega_rrrz	\(\partial_{\rho \rho \rho \zeta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radial coordinate thrice and toroidal once	omega_rrzr, omega_rzrr, omega_zrrr
omega_rrt	\(\partial_{\rho \rho \theta} \omega\)	radians	Toroidal stream function, third derivative, wrt radius twice and poloidal angle	omega_rtr, omega_trr
omega_rrtt	\(\partial_{\rho \rho \theta \theta} \omega\)	radians	Toroidal stream function, fourth derivative, wrt radius twice and poloidal angle twice	omega_rttr, omega_trrt, omega_ttrr
omega_rrtz	\(\partial_{\rho \theta \zeta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radius twice, poloidal angle, and toroidal angle	omega_rtzr, omega_tzrr, omega_zrrt
omega_rrz	\(\partial_{\rho \rho \zeta} \omega\)	radians	Toroidal stream function, third derivative, wrt radius twice and toroidal angle	omega_rzr, omega_zrr
omega_rrzz	\(\partial_{\rho \rho \zeta \zeta} \omega\)	radians	Toroidal stream function, fourth derivative, wrt radius twice and toroidal angle twice	omega_rzzr, omega_zrrz, omega_zzrr
omega_rt	\(\partial_{\rho \theta} \omega\)	radians	Toroidal stream function, second derivative wrt radius and poloidal angle	omega_tr
omega_rtt	\(\partial_{\rho \theta \theta} \omega\)	radians	Toroidal stream function, third derivative wrt radius and poloidal angle twice	omega_trt, omega_ttr
omega_rttt	\(\partial_{\rho \theta \theta \theta} \omega\)	radians	Toroidal stream function, third derivative wrt radius and poloidal angle thrice	omega_trtt, omega_ttrt, omega_tttr
omega_rttz	\(\partial_{\rho \theta \theta \zeta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radius once, poloidal angle twice, and toroidal angle once	omega_ttzr, omega_tzrt, omega_zrtt
omega_rtz	\(\partial_{\rho \theta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt radius, poloidal angle, and toroidal angle	omega_tzr, omega_zrt
omega_rtzz	\(\partial_{\rho \theta \zeta \zeta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radius, poloidal angle, and toroidal angle twice	omega_tzzr, omega_zrtz, omega_zzrt
omega_rz	\(\partial_{\rho \zeta} \omega\)	radians	Toroidal stream function, second derivative wrt radius and toroidal angle	omega_zr
omega_rzz	\(\partial_{\rho \zeta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt radius and toroidal angle twice	omega_zrz, omega_zzr
omega_rzzz	\(\partial_{\rho \zeta \zeta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt radius and toroidal angle thrice	omega_zrzz, omega_zzrz, omega_zzzr
omega_t	\(\partial_{\theta} \omega\)	radians	Toroidal stream function, first poloidal derivative
omega_tt	\(\partial_{\theta \theta} \omega\)	radians	Toroidal stream function, second poloidal derivative
omega_ttt	\(\partial_{\theta \theta \theta} \omega\)	radians	Toroidal stream function, third poloidal derivative
omega_ttz	\(\partial_{\theta \theta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt poloidal angle twice and toroidal angle	omega_tzt, omega_ztt
omega_tz	\(\partial_{\theta \zeta} \omega\)	radians	Toroidal stream function, second derivative wrt poloidal and toroidal angles	omega_zt
omega_tzz	\(\partial_{\theta \zeta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt poloidal angle and toroidal angle twice	omega_ztz, omega_zzt
omega_z	\(\partial_{\zeta} \omega\)	radians	Toroidal stream function, first toroidal derivative
omega_zz	\(\partial_{\zeta \zeta} \omega\)	radians	Toroidal stream function, second toroidal derivative
omega_zzz	\(\partial_{\zeta \zeta \zeta} \omega\)	radians	Toroidal stream function, third toroidal derivative
perimeter(z)	\(P(\zeta)\)	meters	Perimeter of enclosed cross-section (enclosed constant phi surface), scaled by max(ρ)⁻¹, as function of zeta
phi	\(\phi\)	radians	Toroidal phi position along surface
phi_r	\(\partial_{\rho} \phi\)	radians	Toroidal angle in lab frame, derivative wrt radial coordinate
phi_t	\(\partial_{\theta} \phi\)	radians	Toroidal angle in lab frame, derivative wrt poloidal coordinate
phi_z	\(\partial_{\zeta} \phi\)	radians	Toroidal angle in lab frame, derivative wrt toroidal coordinate
rho	\(\rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux
rho_r	\(\partial_{\rho} \rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux, derivative wrt radial coordinate
rho_t	\(\partial_{\theta} \rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux, derivative wrt poloidal coordinate
rho_z	\(\partial_{\zeta} \rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux, derivative wrt toroidal coordinate
theta	\(\theta\)	radians	Poloidal angular coordinate (geometric, not magnetic)
theta_r	\(\partial_{\rho} \theta\)	radians	Poloidal angular coordinate (geometric, not magnetic), derivative wrt radial coordinate
theta_t	\(\partial_{\theta} \theta\)	radians	Poloidal angular coordinate (geometric, not magnetic), derivative wrt poloidal coordinate
theta_z	\(\partial_{\zeta} \theta\)	radians	Poloidal angular coordinate (geometric, not magnetic), derivative wrt toroidal coordinate
x	\(\mathbf{r}\)	meters	Position vector along surface
zeta	\(\zeta\)	radians	Toroidal angular coordinate
zeta_r	\(\partial_{\rho} \zeta\)	radians	Toroidal angular coordinate derivative, wrt radial coordinate
zeta_t	\(\partial_{\theta} \zeta\)	radians	Toroidal angular coordinate, derivative wrt poloidal coordinate
zeta_z	\(\partial_{\zeta} \zeta\)	radians	Toroidal angular coordinate, derivative wrt toroidal coordinate
|e_rho x e_theta|	\(|\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\)	square meters	2D Jacobian determinant for constant zeta surface
|e_rho x e_theta|_r	\(\partial_{\rho} |\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\)	square meters	2D Jacobian determinant for constant zeta surface derivative wrt radial coordinate
|e_rho x e_theta|_rr	\(\partial_{\rho \rho} |\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\)	square meters	2D Jacobian determinant for constant zeta surface second derivative wrt radial coordinate
|e_theta x e_zeta|	\(|\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\)	square meters	2D Jacobian determinant for constant rho surface
|e_theta x e_zeta|_r	\(\partial_{\rho} |\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\)	square meters	2D Jacobian determinant for constant rho surface derivative wrt radial coordinate
|e_theta x e_zeta|_rr	\(\partial_{\rho\rho} |\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\)	square meters	2D Jacobian determinant for constant rho surface second derivative wrt radial coordinate
|e_theta x e_zeta|_z	\(\partial_{\zeta}|e_{\theta} \times e_{\zeta}|\)	square meters	2D Jacobian determinant for constant rho surface,derivative wrt toroidal angle
|e_zeta x e_rho|	\(|\mathbf{e}_{\zeta} \times \mathbf{e}_{\rho}|\)	square meters	2D Jacobian determinant for constant theta surface

desc.geometry.surface.ZernikeRZToroidalSection

List of Variables: desc.geometry.surface.ZernikeRZToroidalSection

Name	Label	Units	Description	Aliases	kwargs
0	\(0\)	None	Zeros
A	\(A\)	square meters	Average cross-sectional area
A(z)	\(A(\zeta)\)	square meters	Cross-sectional area as function of zeta
L_sff_zeta	\(L_{\mathrm{SFF},\zeta}\)	meters	L coefficient of second fundamental form of constant zeta surface
M_sff_zeta	\(M_{\mathrm{SFF},\zeta}\)	meters	M coefficient of second fundamental form of constant zeta surface
N_sff_zeta	\(N_{\mathrm{SFF},\zeta}\)	meters	N coefficient of second fundamental form of constant zeta surface
R	\(R\)	meters	Cylindrical radial position along surface
R_r	\(\partial_{\rho} R\)	meters	Major radius in lab frame, first radial derivative
R_rr	\(\partial_{\rho \rho} R\)	meters	Major radius in lab frame, second radial derivative
R_rrr	\(\partial_{\rho \rho \rho} R\)	meters	Major radius in lab frame, third radial derivative
R_rrrr	\(\partial_{\rho \rho \rho \rho} R\)	meters	Major radius in lab frame, fourth radial derivative
R_rrrt	\(\partial_{\rho \rho \rho \theta} R\)	meters	Major radius in lab frame, fourth derivative wrt radial coordinate thrice and poloidal once	R_rrtr, R_rtrr, R_trrr
R_rrt	\(\partial_{\rho \rho \theta} R\)	meters	Major radius in lab frame, third derivative, wrt radius twice and poloidal angle	R_rtr, R_trr
R_rrtt	\(\partial_{\rho \rho \theta \theta} R\)	meters	Major radius in lab frame, fourth derivative, wrt radius twice and poloidal angle twice	R_rttr, R_trrt, R_ttrr
R_rrtz	\(\partial_{\rho \rho \theta \zeta} R\)	meters	Major radius in lab frame, fourth derivative wrt radius twice, poloidal angle, and toroidal angle	R_rtzr, R_tzrr, R_zrrt
R_rt	\(\partial_{\rho \theta} R\)	meters	Major radius in lab frame, second derivative wrt radius and poloidal angle	R_tr
R_rtt	\(\partial_{\rho \theta \theta} R\)	meters	Major radius in lab frame, third derivative wrt radius and poloidal angle twice	R_trt, R_ttr
R_rttt	\(\partial_{\rho \theta \theta \theta} R\)	meters	Major radius in lab frame, fourth derivative wrt radius and poloidal angle thrice	R_trtt, R_ttrt, R_tttr
R_t	\(\partial_{\theta} R\)	meters	Major radius in lab frame, first poloidal derivative
R_tt	\(\partial_{\theta \theta} R\)	meters	Major radius in lab frame, second poloidal derivative
R_ttt	\(\partial_{\theta \theta \theta} R\)	meters	Major radius in lab frame, third poloidal derivative
X	\(X\)	meters	Cartesian X coordinate.
Y	\(Y\)	meters	Cartesian Y coordinate.
Z	\(Z\)	meters	Cylindrical vertical position along surface
Z_r	\(\partial_{\rho} Z\)	meters	Vertical coordinate in lab frame, first radial derivative
Z_rr	\(\partial_{\rho \rho} Z\)	meters	Vertical coordinate in lab frame, second radial derivative
Z_rrr	\(\partial_{\rho \rho \rho} Z\)	meters	Vertical coordinate in lab frame, third radial derivative
Z_rrrr	\(\partial_{\rho \rho \rho \rho} Z\)	meters	Vertical coordinate in lab frame, fourth radial derivative
Z_rrrt	\(\partial_{\rho \rho \rho \theta} Z\)	meters	Vertical coordinate in lab frame, fourth derivative wrt radial coordinate thrice and poloidal once	Z_rrtr, Z_rtrr, Z_trrr
Z_rrt	\(\partial_{\rho \rho \theta} Z\)	meters	Vertical coordinate in lab frame, third derivative, wrt radius twice and poloidal angle	Z_rtr, Z_trr
Z_rrtt	\(\partial_{\rho \rho \theta} Z\)	meters	Vertical coordinate in lab frame, fourth derivative, wrt radius twice and poloidal angle twice	Z_rttr, Z_trrt, Z_ttrr
Z_rt	\(\partial_{\rho \theta} Z\)	meters	Vertical coordinate in lab frame, second derivative wrt radius and poloidal angle	Z_tr
Z_rtt	\(\partial_{\rho \theta \theta} Z\)	meters	Vertical coordinate in lab frame, third derivative wrt radius and poloidal angle twice	Z_trt, Z_ttr
Z_rttt	\(\partial_{\rho \theta \theta \theta} Z\)	meters	Vertical coordinate in lab frame, third derivative wrt radius and poloidal angle thrice	Z_trtt, Z_ttrt, Z_tttr
Z_t	\(\partial_{\theta} Z\)	meters	Vertical coordinate in lab frame, first poloidal derivative
Z_tt	\(\partial_{\theta \theta} Z\)	meters	Vertical coordinate in lab frame, second poloidal derivative
Z_ttt	\(\partial_{\theta \theta \theta} Z\)	meters	Vertical coordinate in lab frame, third poloidal derivative
a_major/a_minor	\(a_{\mathrm{major}} / a_{\mathrm{minor}}\)	None	Elongation at a toroidal cross-section
curvature_H_zeta	\(H_{\zeta}\)	meters	Mean curvature of constant zeta surfaces
curvature_K_zeta	\(K_{\zeta}\)	meters squared	Gaussian curvature of constant zeta surfaces
curvature_k1_zeta	\(k_{1,\zeta}\)	Inverse meters	First principle curvature of constant zeta surfaces
curvature_k2_zeta	\(k_{2,\zeta}\)	Inverse meters	Second principle curvature of constant zeta surfaces
e^theta*sqrt(g)	\(\mathbf{e}^{\theta} \sqrt{g}\)	square meters	Contravariant poloidal basis vector weighted by 3-D volume Jacobian
e_phi	\(\mathbf{e}_{\phi}\)	meters	Covariant cylindrical toroidal basis vector
e_rho	\(\mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector
e_rho_r	\(\partial_{\rho} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, derivative wrt radial coordinate
e_rho_rr	\(\partial_{\rho \rho} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, second derivative wrt radial and radial coordinates
e_rho_rrr	\(\partial_{\rho \rho \rho} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, third derivative wrt radial coordinate
e_rho_rrt	\(\partial_{\rho \rho \theta} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, third derivative wrt radial coordinate twice and poloidal once	e_rho_rtr, e_rho_trr, e_theta_rrr
e_rho_rt	\(\partial_{\rho \theta} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, second derivative wrt radial and poloidal coordinates	e_rho_tr, e_theta_rr, x_rrt, x_rtr, x_trr
e_rho_rtt	\(\partial_{\rho \theta \theta} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, third derivative wrt radial coordinateonce and poloidal twice	e_rho_trt, e_rho_ttr, e_theta_rrt, e_theta_rtr, e_theta_trr
e_rho_t	\(\partial_{\theta} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, derivative wrt poloidal coordinate	e_theta_r
e_rho_tt	\(\partial_{\theta \theta} \mathbf{e}_{\rho}\)	meters	Covariant Radial basis vector, second derivative wrt poloidal and poloidal coordinates	e_theta_rt, e_theta_tr
e_rho_z	\(\partial_{\zeta} \mathbf{e}_{\rho}\)	meters	Covariant radial basis vector, derivative wrt toroidal angle	e_zeta_r
e_theta	\(\mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector
e_theta_rtt	\(\partial_{\rho \theta \theta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, third derivative wrt radial coordinate once and poloidal twice	e_rho_ttt, e_theta_trt, e_theta_ttr
e_theta_t	\(\partial_{\theta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, derivative wrt poloidal coordinate
e_theta_tt	\(\partial_{\theta \theta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, second derivative wrt poloidal and poloidal coordinates
e_theta_z	\(\partial_{\zeta} \mathbf{e}_{\theta}\)	meters	Covariant poloidal basis vector, derivative wrt toroidal angle	e_zeta_t
e_theta|r,p	\(\mathbf{e}_{\theta} |_{\rho, \phi}\)	meters	Covariant poloidal basis vector in (ρ,θ,ϕ) coordinates. ϕ increases counterclockwise when viewed from above (cylindrical R,ϕ plane with Z out of page).
e_zeta	\(\mathbf{e}_{\zeta}\)	meters	Covariant toroidal basis vector
e_zeta_rr	\(\partial_{\rho \rho} \mathbf{e}_{\zeta}\)	meters	Covariant toroidal basis vector, second derivative wrt radial coordinate	e_rho_rz, e_rho_zr
e_zeta_z	\(\partial_{\zeta} \mathbf{e}_{\zeta}\)	meters	Covariant toroidal basis vector, derivative wrt toroidal angle
g_rr	\(g_{\rho\rho}\)	square meters	Radial/Radial element of covariant metric tensor
g_rt	\(g_{\rho\theta}\)	square meters	Radial/Poloidal element of covariant metric tensor	g_tr
g_rz	\(g_{\rho\zeta}\)	square meters	Radial/Toroidal element of covariant metric tensor	g_zr
g_tt	\(g_{\theta\theta}\)	square meters	Poloidal/Poloidal element of covariant metric tensor
g_tt_r	\(\partial_{\rho} g_{\theta\theta}\)	square meters	Poloidal/Poloidal element of covariant metric tensor, derivative wrt rho
g_tz	\(g_{\theta\zeta}\)	square meters	Poloidal/Toroidal element of covariant metric tensor	g_zt
g_tz_r	\(\partial_{\rho} g_{\theta\zeta}\)	square meters	Poloidal/Toroidal element of covariant metric tensor, derivative wrt rho
g_zz	\(g_{\zeta\zeta}\)	square meters	Toroidal/Toroidal element of covariant metric tensor
n_rho	\(\hat{\mathbf{n}}_{\rho}\)	None	Unit vector normal to constant rho surface (direction of e^rho)
n_rho_z	\(\partial_{\zeta}\hat{\mathbf{n}}_{\rho}\)	None	Unit vector normal to constant rho surface (direction of e^rho), derivative wrt toroidal angle
n_theta	\(\hat{\mathbf{n}}_{\theta}\)	None	Unit vector normal to constant theta surface (direction of e^theta)
n_zeta	\(\hat{\mathbf{n}}_{\zeta}\)	None	Unit vector normal to constant zeta surface (direction of e^zeta)
omega	\(\omega\)	radians	Toroidal stream function
omega_r	\(\partial_{\rho} \omega\)	radians	Toroidal stream function, first radial derivative
omega_rr	\(\partial_{\rho \rho} \omega\)	radians	Toroidal stream function, second radial derivative
omega_rrr	\(\partial_{\rho \rho \rho} \omega\)	radians	Toroidal stream function, third radial derivative
omega_rrrr	\(\partial_{\rho \rho \rho \rho} \omega\)	radians	Toroidal stream function, fourth radial derivative
omega_rrrt	\(\partial_{\rho \rho \rho \theta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radial coordinate thrice and poloidal once	omega_rrtr, omega_rtrr, omega_trrr
omega_rrrz	\(\partial_{\rho \rho \rho \zeta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radial coordinate thrice and toroidal once	omega_rrzr, omega_rzrr, omega_zrrr
omega_rrt	\(\partial_{\rho \rho \theta} \omega\)	radians	Toroidal stream function, third derivative, wrt radius twice and poloidal angle	omega_rtr, omega_trr
omega_rrtt	\(\partial_{\rho \rho \theta \theta} \omega\)	radians	Toroidal stream function, fourth derivative, wrt radius twice and poloidal angle twice	omega_rttr, omega_trrt, omega_ttrr
omega_rrtz	\(\partial_{\rho \theta \zeta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radius twice, poloidal angle, and toroidal angle	omega_rtzr, omega_tzrr, omega_zrrt
omega_rrz	\(\partial_{\rho \rho \zeta} \omega\)	radians	Toroidal stream function, third derivative, wrt radius twice and toroidal angle	omega_rzr, omega_zrr
omega_rrzz	\(\partial_{\rho \rho \zeta \zeta} \omega\)	radians	Toroidal stream function, fourth derivative, wrt radius twice and toroidal angle twice	omega_rzzr, omega_zrrz, omega_zzrr
omega_rt	\(\partial_{\rho \theta} \omega\)	radians	Toroidal stream function, second derivative wrt radius and poloidal angle	omega_tr
omega_rtt	\(\partial_{\rho \theta \theta} \omega\)	radians	Toroidal stream function, third derivative wrt radius and poloidal angle twice	omega_trt, omega_ttr
omega_rttt	\(\partial_{\rho \theta \theta \theta} \omega\)	radians	Toroidal stream function, third derivative wrt radius and poloidal angle thrice	omega_trtt, omega_ttrt, omega_tttr
omega_rttz	\(\partial_{\rho \theta \theta \zeta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radius once, poloidal angle twice, and toroidal angle once	omega_ttzr, omega_tzrt, omega_zrtt
omega_rtz	\(\partial_{\rho \theta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt radius, poloidal angle, and toroidal angle	omega_tzr, omega_zrt
omega_rtzz	\(\partial_{\rho \theta \zeta \zeta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radius, poloidal angle, and toroidal angle twice	omega_tzzr, omega_zrtz, omega_zzrt
omega_rz	\(\partial_{\rho \zeta} \omega\)	radians	Toroidal stream function, second derivative wrt radius and toroidal angle	omega_zr
omega_rzz	\(\partial_{\rho \zeta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt radius and toroidal angle twice	omega_zrz, omega_zzr
omega_rzzz	\(\partial_{\rho \zeta \zeta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt radius and toroidal angle thrice	omega_zrzz, omega_zzrz, omega_zzzr
omega_t	\(\partial_{\theta} \omega\)	radians	Toroidal stream function, first poloidal derivative
omega_tt	\(\partial_{\theta \theta} \omega\)	radians	Toroidal stream function, second poloidal derivative
omega_ttt	\(\partial_{\theta \theta \theta} \omega\)	radians	Toroidal stream function, third poloidal derivative
omega_ttz	\(\partial_{\theta \theta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt poloidal angle twice and toroidal angle	omega_tzt, omega_ztt
omega_tz	\(\partial_{\theta \zeta} \omega\)	radians	Toroidal stream function, second derivative wrt poloidal and toroidal angles	omega_zt
omega_tzz	\(\partial_{\theta \zeta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt poloidal angle and toroidal angle twice	omega_ztz, omega_zzt
omega_z	\(\partial_{\zeta} \omega\)	radians	Toroidal stream function, first toroidal derivative
omega_zz	\(\partial_{\zeta \zeta} \omega\)	radians	Toroidal stream function, second toroidal derivative
omega_zzz	\(\partial_{\zeta \zeta \zeta} \omega\)	radians	Toroidal stream function, third toroidal derivative
perimeter(z)	\(P(\zeta)\)	meters	Perimeter of enclosed cross-section (enclosed constant phi surface), scaled by max(ρ)⁻¹, as function of zeta
phi	\(\phi\)	radians	Toroidal phi position along surface
phi_r	\(\partial_{\rho} \phi\)	radians	Toroidal angle in lab frame, derivative wrt radial coordinate
phi_t	\(\partial_{\theta} \phi\)	radians	Toroidal angle in lab frame, derivative wrt poloidal coordinate
phi_z	\(\partial_{\zeta} \phi\)	radians	Toroidal angle in lab frame, derivative wrt toroidal coordinate
rho	\(\rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux
rho_r	\(\partial_{\rho} \rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux, derivative wrt radial coordinate
rho_t	\(\partial_{\theta} \rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux, derivative wrt poloidal coordinate
rho_z	\(\partial_{\zeta} \rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux, derivative wrt toroidal coordinate
theta	\(\theta\)	radians	Poloidal angular coordinate (geometric, not magnetic)
theta_r	\(\partial_{\rho} \theta\)	radians	Poloidal angular coordinate (geometric, not magnetic), derivative wrt radial coordinate
theta_t	\(\partial_{\theta} \theta\)	radians	Poloidal angular coordinate (geometric, not magnetic), derivative wrt poloidal coordinate
theta_z	\(\partial_{\zeta} \theta\)	radians	Poloidal angular coordinate (geometric, not magnetic), derivative wrt toroidal coordinate
x	\(\mathbf{r}\)	meters	Position vector along surface
zeta	\(\zeta\)	radians	Toroidal angular coordinate
zeta_r	\(\partial_{\rho} \zeta\)	radians	Toroidal angular coordinate derivative, wrt radial coordinate
zeta_t	\(\partial_{\theta} \zeta\)	radians	Toroidal angular coordinate, derivative wrt poloidal coordinate
zeta_z	\(\partial_{\zeta} \zeta\)	radians	Toroidal angular coordinate, derivative wrt toroidal coordinate
|e_rho x e_theta|	\(|\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\)	square meters	2D Jacobian determinant for constant zeta surface
|e_rho x e_theta|_r	\(\partial_{\rho} |\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\)	square meters	2D Jacobian determinant for constant zeta surface derivative wrt radial coordinate
|e_rho x e_theta|_rr	\(\partial_{\rho \rho} |\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\)	square meters	2D Jacobian determinant for constant zeta surface second derivative wrt radial coordinate
|e_theta x e_zeta|	\(|\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\)	square meters	2D Jacobian determinant for constant rho surface
|e_theta x e_zeta|_r	\(\partial_{\rho} |\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\)	square meters	2D Jacobian determinant for constant rho surface derivative wrt radial coordinate
|e_theta x e_zeta|_rr	\(\partial_{\rho\rho} |\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\)	square meters	2D Jacobian determinant for constant rho surface second derivative wrt radial coordinate
|e_theta x e_zeta|_z	\(\partial_{\zeta}|e_{\theta} \times e_{\zeta}|\)	square meters	2D Jacobian determinant for constant rho surface,derivative wrt toroidal angle
|e_zeta x e_rho|	\(|\mathbf{e}_{\zeta} \times \mathbf{e}_{\rho}|\)	square meters	2D Jacobian determinant for constant theta surface

desc.coils.FourierRZCoil

List of Variables: desc.coils.FourierRZCoil

Name	Label	Units	Description	Aliases	kwargs
0	\(0\)	None	Zeros
R	\(R\)	meters	Cylindrical radial position along curve
X	\(X\)	meters	Cartesian X coordinate.
Y	\(Y\)	meters	Cartesian Y coordinate.
Z	\(Z\)	meters	Cylindrical vertical position along curve
center	\(\langle\mathbf{x}\rangle\)	meters	Centroid of the curve
curvature	\(\kappa\)	Inverse meters	Scalar curvature of the curve, with the sign denoting the convexity/concavity relative to the center of the curve (a circle has positive curvature)
ds	\(ds\)	None	Spacing of curve parameter
frenet_binormal	\(\mathbf{B}_{\mathrm{Frenet-Serret}}\)	None	Binormal unit vector to curve in Frenet-Serret frame
frenet_normal	\(\mathbf{N}_{\mathrm{Frenet-Serret}}\)	None	Normal unit vector to curve in Frenet-Serret frame
frenet_tangent	\(\mathbf{T}_{\mathrm{Frenet-Serret}}\)	None	Tangent unit vector to curve in Frenet-Serret frame
length	\(L\)	meters	Length of the curve
phi	\(\phi\)	radians	Toroidal phi position along curve
s	\(s\)	None	Curve parameter, on [0, 2pi)
torsion	\(\tau\)	Inverse meters	Scalar torsion of the curve
x	\(\mathbf{x}\)	meters	Position vector along curve
x_s	\(\partial_{s} \mathbf{x}\)	meters	Position vector along curve, first derivative
x_ss	\(\partial_{ss} \mathbf{x}\)	meters	Position vector along curve, second derivative
x_sss	\(\partial_{sss} \mathbf{x}\)	meters	Position vector along curve, third derivative

desc.coils.FourierXYZCoil

List of Variables: desc.coils.FourierXYZCoil

Name	Label	Units	Description	Aliases	kwargs
0	\(0\)	None	Zeros
R	\(R\)	meters	Cylindrical radial position along curve
X	\(X\)	meters	Cartesian X coordinate.
Y	\(Y\)	meters	Cartesian Y coordinate.
Z	\(Z\)	meters	Cylindrical vertical position along curve
center	\(\langle\mathbf{x}\rangle\)	meters	Centroid of the curve
curvature	\(\kappa\)	Inverse meters	Scalar curvature of the curve, with the sign denoting the convexity/concavity relative to the center of the curve (a circle has positive curvature)
ds	\(ds\)	None	Spacing of curve parameter
frenet_binormal	\(\mathbf{B}_{\mathrm{Frenet-Serret}}\)	None	Binormal unit vector to curve in Frenet-Serret frame
frenet_normal	\(\mathbf{N}_{\mathrm{Frenet-Serret}}\)	None	Normal unit vector to curve in Frenet-Serret frame
frenet_tangent	\(\mathbf{T}_{\mathrm{Frenet-Serret}}\)	None	Tangent unit vector to curve in Frenet-Serret frame
length	\(L\)	meters	Length of the curve
phi	\(\phi\)	radians	Toroidal phi position along curve
s	\(s\)	None	Curve parameter, on [0, 2pi)
torsion	\(\tau\)	Inverse meters	Scalar torsion of the curve
x	\(\mathbf{x}\)	meters	Position vector along curve
x_s	\(\partial_{s} \mathbf{x}\)	meters	Position vector along curve, first derivative
x_ss	\(\partial_{ss} \mathbf{x}\)	meters	Position vector along curve, second derivative
x_sss	\(\partial_{sss} \mathbf{x}\)	meters	Position vector along curve, third derivative

desc.coils.FourierPlanarCoil

List of Variables: desc.coils.FourierPlanarCoil

Name	Label	Units	Description	Aliases	kwargs
0	\(0\)	None	Zeros
R	\(R\)	meters	Cylindrical radial position along curve
X	\(X\)	meters	Cartesian X coordinate.
Y	\(Y\)	meters	Cartesian Y coordinate.
Z	\(Z\)	meters	Cylindrical vertical position along curve
center	\(\langle\mathbf{x}\rangle\)	meters	Centroid of the curve		basis_in
curvature	\(\kappa\)	Inverse meters	Scalar curvature of the curve, with the sign denoting the convexity/concavity relative to the center of the curve (a circle has positive curvature)
ds	\(ds\)	None	Spacing of curve parameter
frenet_binormal	\(\mathbf{B}_{\mathrm{Frenet-Serret}}\)	None	Binormal unit vector to curve in Frenet-Serret frame
frenet_normal	\(\mathbf{N}_{\mathrm{Frenet-Serret}}\)	None	Normal unit vector to curve in Frenet-Serret frame
frenet_tangent	\(\mathbf{T}_{\mathrm{Frenet-Serret}}\)	None	Tangent unit vector to curve in Frenet-Serret frame
length	\(L\)	meters	Length of the curve
phi	\(\phi\)	radians	Toroidal phi position along curve
s	\(s\)	None	Curve parameter, on [0, 2pi)
torsion	\(\tau\)	Inverse meters	Scalar torsion of the curve
x	\(\mathbf{x}\)	meters	Position vector along curve		basis_in
x_s	\(\partial_{s} \mathbf{x}\)	meters	Position vector along curve, first derivative		basis_in
x_ss	\(\partial_{ss} \mathbf{x}\)	meters	Position vector along curve, second derivative		basis_in
x_sss	\(\partial_{sss} \mathbf{x}\)	meters	Position vector along curve, third derivative		basis_in

desc.magnetic_fields._current_potential.CurrentPotentialField

List of Variables: desc.magnetic_fields._current_potential.CurrentPotentialField

Name	Label	Units	Description	Aliases	kwargs
0	\(0\)	None	Zeros
A	\(A\)	square meters	Average cross-sectional area
A(z)	\(A(\zeta)\)	square meters	Area of enclosed cross-section (enclosed constant phi surface), scaled by max(ρ)⁻², as function of zeta
K	\(\mathbf{K}\)	Amperes per meter	Surface current density, defined as thesurface normal vector cross the gradient of the current potential.
L_sff_rho	\(L_{\mathrm{SFF},\rho}\)	meters	L coefficient of second fundamental form of constant rho surface
M_sff_rho	\(M_{\mathrm{SFF},\rho}\)	meters	M coefficient of second fundamental form of constant rho surface
N_sff_rho	\(N_{\mathrm{SFF},\rho}\)	meters	N coefficient of second fundamental form of constant rho surface
Phi	\(\Phi\)	Amperes	Surface current potential
Phi_t	\(\partial_{\theta}\Phi\)	Amperes	Surface current potential, poloidal derivative
Phi_z	\(\partial_{\zeta}\Phi\)	Amperes	Surface current potential, toroidal derivative
R	\(R\)	meters	Cylindrical radial position along surface
R0	\(R_{0}\)	meters	Average major radius
R0/a	\(R_{0} / a\)	None	Aspect ratio
R_t	\(\partial_{\theta} R\)	meters	Major radius in lab frame, first poloidal derivative
R_tt	\(\partial_{\theta \theta} R\)	meters	Major radius in lab frame, second poloidal derivative
R_ttt	\(\partial_{\theta \theta \theta} R\)	meters	Major radius in lab frame, third poloidal derivative
R_ttz	\(\partial_{\theta \theta \zeta} R\)	meters	Major radius in lab frame, third derivative wrt poloidal angle twice and toroidal angle	R_tzt, R_ztt
R_tz	\(\partial_{\theta \zeta} R\)	meters	Major radius in lab frame, second derivative wrt poloidal and toroidal angles	R_zt
R_tzz	\(\partial_{\theta \zeta \zeta} R\)	meters	Major radius in lab frame, third derivative wrt poloidal angle and toroidal angle twice	R_ztz, R_zzt
R_z	\(\partial_{\zeta} R\)	meters	Major radius in lab frame, first toroidal derivative
R_zz	\(\partial_{\zeta \zeta} R\)	meters	Major radius in lab frame, second toroidal derivative
R_zzz	\(\partial_{\zeta \zeta \zeta} R\)	meters	Major radius in lab frame, third toroidal derivative
S	\(S\)	square meters	Surface area of outermost flux surface
V	\(V\)	cubic meters	Volume
X	\(X\)	meters	Cartesian X coordinate.
Y	\(Y\)	meters	Cartesian Y coordinate.
Z	\(Z\)	meters	Cylindrical vertical position along surface
Z_t	\(\partial_{\theta} Z\)	meters	Vertical coordinate in lab frame, first poloidal derivative
Z_tt	\(\partial_{\theta \theta} Z\)	meters	Vertical coordinate in lab frame, second poloidal derivative
Z_ttt	\(\partial_{\theta \theta \theta} Z\)	meters	Vertical coordinate in lab frame, third poloidal derivative
Z_ttz	\(\partial_{\theta \theta \zeta} Z\)	meters	Vertical coordinate in lab frame, third derivative wrt poloidal angle twice and toroidal angle	Z_tzt, Z_ztt
Z_tz	\(\partial_{\theta \zeta} Z\)	meters	Vertical coordinate in lab frame, second derivative wrt poloidal and toroidal angles	Z_zt
Z_tzz	\(\partial_{\theta \zeta \zeta} Z\)	meters	Vertical coordinate in lab frame, third derivative wrt poloidal angle and toroidal angle twice	Z_ztz, Z_zzt
Z_z	\(\partial_{\zeta} Z\)	meters	Vertical coordinate in lab frame, first toroidal derivative
Z_zz	\(\partial_{\zeta \zeta} Z\)	meters	Vertical coordinate in lab frame, second toroidal derivative
Z_zzz	\(\partial_{\zeta \zeta \zeta} Z\)	meters	Vertical coordinate in lab frame, third toroidal derivative
a	\(a\)	meters	Average minor radius
a_major/a_minor	\(a_{\mathrm{major}} / a_{\mathrm{minor}}\)	None	Elongation at a toroidal cross-section
curvature_H_rho	\(H_{\rho}\)	meters	Mean curvature of constant rho surfaces
curvature_K_rho	\(K_{\rho}\)	meters squared	Gaussian curvature of constant rho surfaces
curvature_k1_rho	\(k_{1,\rho}\)	Inverse meters	First principle curvature of constant rho surfaces
curvature_k2_rho	\(k_{2,\rho}\)	Inverse meters	Second principle curvature of constant rho surfaces
e^theta*sqrt(g)	\(\mathbf{e}^{\theta} \sqrt{g}\)	square meters	Contravariant poloidal basis vector weighted by 3-D volume Jacobian
e_phi	\(\mathbf{e}_{\phi}\)	meters	Covariant cylindrical toroidal basis vector
e_rho	\(\mathbf{e}_{\rho}\)	meters	Covariant radial basis vector
e_rho_r	\(\partial_{\rho} \mathbf{e}_{\rho}\)	meters	Covariant radial basis vector, derivative wrt radial coordinate
e_rho_rr	\(\partial_{\rho \rho} \mathbf{e}_{\rho}\)	meters	Covariant radial basis vector, second derivative wrt radial coordinate
e_rho_t	\(\partial_{\theta} \mathbf{e}_{\rho}\)	meters	Covariant radial basis vector, derivative wrt poloidal angle	e_theta_r
e_rho_z	\(\partial_{\zeta} \mathbf{e}_{\rho}\)	meters	Covariant radial basis vector, derivative wrt toroidal angle	e_zeta_r
e_theta	\(\mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector
e_theta_rr	\(\partial_{\rho \rho} \mathbf{e}_{\theta}\)	meters	Covariant poloidal basis vector, second derivative wrt radial coordinate	e_rho_rt, e_rho_tr
e_theta_t	\(\partial_{\theta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, derivative wrt poloidal coordinate
e_theta_tt	\(\partial_{\theta \theta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, second derivative wrt poloidal and poloidal coordinates
e_theta_tz	\(\partial_{\theta \zeta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, second derivative wrt poloidal and toroidal coordinates	e_theta_zt, e_zeta_tt
e_theta_z	\(\partial_{\zeta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, derivative wrt toroidal coordinate	e_zeta_t
e_theta_zz	\(\partial_{\zeta \zeta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, second derivative wrt toroidal and toroidal coordinates	e_zeta_tz, e_zeta_zt
e_theta|r,p	\(\mathbf{e}_{\theta} |_{\rho, \phi}\)	meters	Covariant poloidal basis vector in (ρ,θ,ϕ) coordinates. ϕ increases counterclockwise when viewed from above (cylindrical R,ϕ plane with Z out of page).
e_zeta	\(\mathbf{e}_{\zeta}\)	meters	Covariant Toroidal basis vector
e_zeta_rr	\(\partial_{\rho \rho} \mathbf{e}_{\zeta}\)	meters	Covariant toroidal basis vector, second derivative wrt radial coordinate	e_rho_rz, e_rho_zr
e_zeta_z	\(\partial_{\zeta} \mathbf{e}_{\zeta}\)	meters	Covariant Toroidal basis vector, derivative wrt toroidal coordinate
e_zeta_zz	\(\partial_{\zeta \zeta} \mathbf{e}_{\zeta}\)	meters	Covariant Toroidal basis vector, second derivative wrt toroidal and toroidal coordinates
g_rr	\(g_{\rho\rho}\)	square meters	Radial/Radial element of covariant metric tensor
g_rt	\(g_{\rho\theta}\)	square meters	Radial/Poloidal element of covariant metric tensor	g_tr
g_rz	\(g_{\rho\zeta}\)	square meters	Radial/Toroidal element of covariant metric tensor	g_zr
g_tt	\(g_{\theta\theta}\)	square meters	Poloidal/Poloidal element of covariant metric tensor
g_tt_r	\(\partial_{\rho} g_{\theta\theta}\)	square meters	Poloidal/Poloidal element of covariant metric tensor, derivative wrt rho
g_tz	\(g_{\theta\zeta}\)	square meters	Poloidal/Toroidal element of covariant metric tensor	g_zt
g_tz_r	\(\partial_{\rho} g_{\theta\zeta}\)	square meters	Poloidal/Toroidal element of covariant metric tensor, derivative wrt rho
g_zz	\(g_{\zeta\zeta}\)	square meters	Toroidal/Toroidal element of covariant metric tensor
n_rho	\(\hat{\mathbf{n}}_{\rho}\)	None	Unit vector normal to constant rho surface (direction of e^rho)
n_rho_z	\(\partial_{\zeta}\hat{\mathbf{n}}_{\rho}\)	None	Unit vector normal to constant rho surface (direction of e^rho), derivative wrt toroidal angle
n_theta	\(\hat{\mathbf{n}}_{\theta}\)	None	Unit vector normal to constant theta surface (direction of e^theta)
n_zeta	\(\hat{\mathbf{n}}_{\zeta}\)	None	Unit vector normal to constant zeta surface (direction of e^zeta)
omega	\(\omega\)	radians	Toroidal stream function
omega_r	\(\partial_{\rho} \omega\)	radians	Toroidal stream function, first radial derivative
omega_rr	\(\partial_{\rho \rho} \omega\)	radians	Toroidal stream function, second radial derivative
omega_rrr	\(\partial_{\rho \rho \rho} \omega\)	radians	Toroidal stream function, third radial derivative
omega_rrrr	\(\partial_{\rho \rho \rho \rho} \omega\)	radians	Toroidal stream function, fourth radial derivative
omega_rrrt	\(\partial_{\rho \rho \rho \theta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radial coordinate thrice and poloidal once	omega_rrtr, omega_rtrr, omega_trrr
omega_rrrz	\(\partial_{\rho \rho \rho \zeta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radial coordinate thrice and toroidal once	omega_rrzr, omega_rzrr, omega_zrrr
omega_rrt	\(\partial_{\rho \rho \theta} \omega\)	radians	Toroidal stream function, third derivative, wrt radius twice and poloidal angle	omega_rtr, omega_trr
omega_rrtt	\(\partial_{\rho \rho \theta \theta} \omega\)	radians	Toroidal stream function, fourth derivative, wrt radius twice and poloidal angle twice	omega_rttr, omega_trrt, omega_ttrr
omega_rrtz	\(\partial_{\rho \theta \zeta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radius twice, poloidal angle, and toroidal angle	omega_rtzr, omega_tzrr, omega_zrrt
omega_rrz	\(\partial_{\rho \rho \zeta} \omega\)	radians	Toroidal stream function, third derivative, wrt radius twice and toroidal angle	omega_rzr, omega_zrr
omega_rrzz	\(\partial_{\rho \rho \zeta \zeta} \omega\)	radians	Toroidal stream function, fourth derivative, wrt radius twice and toroidal angle twice	omega_rzzr, omega_zrrz, omega_zzrr
omega_rt	\(\partial_{\rho \theta} \omega\)	radians	Toroidal stream function, second derivative wrt radius and poloidal angle	omega_tr
omega_rtt	\(\partial_{\rho \theta \theta} \omega\)	radians	Toroidal stream function, third derivative wrt radius and poloidal angle twice	omega_trt, omega_ttr
omega_rttt	\(\partial_{\rho \theta \theta \theta} \omega\)	radians	Toroidal stream function, third derivative wrt radius and poloidal angle thrice	omega_trtt, omega_ttrt, omega_tttr
omega_rttz	\(\partial_{\rho \theta \theta \zeta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radius once, poloidal angle twice, and toroidal angle once	omega_ttzr, omega_tzrt, omega_zrtt
omega_rtz	\(\partial_{\rho \theta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt radius, poloidal angle, and toroidal angle	omega_tzr, omega_zrt
omega_rtzz	\(\partial_{\rho \theta \zeta \zeta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radius, poloidal angle, and toroidal angle twice	omega_tzzr, omega_zrtz, omega_zzrt
omega_rz	\(\partial_{\rho \zeta} \omega\)	radians	Toroidal stream function, second derivative wrt radius and toroidal angle	omega_zr
omega_rzz	\(\partial_{\rho \zeta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt radius and toroidal angle twice	omega_zrz, omega_zzr
omega_rzzz	\(\partial_{\rho \zeta \zeta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt radius and toroidal angle thrice	omega_zrzz, omega_zzrz, omega_zzzr
omega_t	\(\partial_{\theta} \omega\)	radians	Toroidal stream function, first poloidal derivative
omega_tt	\(\partial_{\theta \theta} \omega\)	radians	Toroidal stream function, second poloidal derivative
omega_ttt	\(\partial_{\theta \theta \theta} \omega\)	radians	Toroidal stream function, third poloidal derivative
omega_ttz	\(\partial_{\theta \theta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt poloidal angle twice and toroidal angle	omega_tzt, omega_ztt
omega_tz	\(\partial_{\theta \zeta} \omega\)	radians	Toroidal stream function, second derivative wrt poloidal and toroidal angles	omega_zt
omega_tzz	\(\partial_{\theta \zeta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt poloidal angle and toroidal angle twice	omega_ztz, omega_zzt
omega_z	\(\partial_{\zeta} \omega\)	radians	Toroidal stream function, first toroidal derivative
omega_zz	\(\partial_{\zeta \zeta} \omega\)	radians	Toroidal stream function, second toroidal derivative
omega_zzz	\(\partial_{\zeta \zeta \zeta} \omega\)	radians	Toroidal stream function, third toroidal derivative
perimeter(z)	\(P(\zeta)\)	meters	Perimeter of enclosed cross-section (enclosed constant phi surface), scaled by max(ρ)⁻¹, as function of zeta
phi	\(\phi\)	radians	Toroidal phi position along surface
phi_r	\(\partial_{\rho} \phi\)	radians	Toroidal angle in lab frame, derivative wrt radial coordinate
phi_t	\(\partial_{\theta} \phi\)	radians	Toroidal angle in lab frame, derivative wrt poloidal coordinate
phi_z	\(\partial_{\zeta} \phi\)	radians	Toroidal angle in lab frame, derivative wrt toroidal coordinate
rho	\(\rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux
rho_r	\(\partial_{\rho} \rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux, derivative wrt radial coordinate
rho_t	\(\partial_{\theta} \rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux, derivative wrt poloidal coordinate
rho_z	\(\partial_{\zeta} \rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux, derivative wrt toroidal coordinate
theta	\(\theta\)	radians	Poloidal angular coordinate (geometric, not magnetic)
theta_r	\(\partial_{\rho} \theta\)	radians	Poloidal angular coordinate (geometric, not magnetic), derivative wrt radial coordinate
theta_t	\(\partial_{\theta} \theta\)	radians	Poloidal angular coordinate (geometric, not magnetic), derivative wrt poloidal coordinate
theta_z	\(\partial_{\zeta} \theta\)	radians	Poloidal angular coordinate (geometric, not magnetic), derivative wrt toroidal coordinate
x	\(\mathbf{r}\)	meters	Position vector along surface
zeta	\(\zeta\)	radians	Toroidal angular coordinate
zeta_r	\(\partial_{\rho} \zeta\)	radians	Toroidal angular coordinate derivative, wrt radial coordinate
zeta_t	\(\partial_{\theta} \zeta\)	radians	Toroidal angular coordinate, derivative wrt poloidal coordinate
zeta_z	\(\partial_{\zeta} \zeta\)	radians	Toroidal angular coordinate, derivative wrt toroidal coordinate
|e_rho x e_theta|	\(|\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\)	square meters	2D Jacobian determinant for constant zeta surface
|e_rho x e_theta|_r	\(\partial_{\rho} |\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\)	square meters	2D Jacobian determinant for constant zeta surface derivative wrt radial coordinate
|e_rho x e_theta|_rr	\(\partial_{\rho \rho} |\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\)	square meters	2D Jacobian determinant for constant zeta surface second derivative wrt radial coordinate
|e_theta x e_zeta|	\(|\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\)	square meters	2D Jacobian determinant for constant rho surface
|e_theta x e_zeta|_r	\(\partial_{\rho} |\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\)	square meters	2D Jacobian determinant for constant rho surface derivative wrt radial coordinate
|e_theta x e_zeta|_rr	\(\partial_{\rho\rho} |\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\)	square meters	2D Jacobian determinant for constant rho surface second derivative wrt radial coordinate
|e_theta x e_zeta|_z	\(\partial_{\zeta}|e_{\theta} \times e_{\zeta}|\)	square meters	2D Jacobian determinant for constant rho surface,derivative wrt toroidal angle
|e_zeta x e_rho|	\(|\mathbf{e}_{\zeta} \times \mathbf{e}_{\rho}|\)	square meters	2D Jacobian determinant for constant theta surface

desc.magnetic_fields._current_potential.FourierCurrentPotentialField

List of Variables: desc.magnetic_fields._current_potential.FourierCurrentPotentialField

Name	Label	Units	Description	Aliases	kwargs
0	\(0\)	None	Zeros
A	\(A\)	square meters	Average cross-sectional area
A(z)	\(A(\zeta)\)	square meters	Area of enclosed cross-section (enclosed constant phi surface), scaled by max(ρ)⁻², as function of zeta
K	\(\mathbf{K}\)	Amperes per meter	Surface current density, defined as thesurface normal vector cross the gradient of the current potential.
L_sff_rho	\(L_{\mathrm{SFF},\rho}\)	meters	L coefficient of second fundamental form of constant rho surface
M_sff_rho	\(M_{\mathrm{SFF},\rho}\)	meters	M coefficient of second fundamental form of constant rho surface
N_sff_rho	\(N_{\mathrm{SFF},\rho}\)	meters	N coefficient of second fundamental form of constant rho surface
Phi	\(\Phi\)	Amperes	Surface current potential
Phi_t	\(\partial_{\theta}\Phi\)	Amperes	Surface current potential, poloidal derivative
Phi_z	\(\partial_{\zeta}\Phi\)	Amperes	Surface current potential, toroidal derivative
R	\(R\)	meters	Cylindrical radial position along surface
R0	\(R_{0}\)	meters	Average major radius
R0/a	\(R_{0} / a\)	None	Aspect ratio
R_t	\(\partial_{\theta} R\)	meters	Major radius in lab frame, first poloidal derivative
R_tt	\(\partial_{\theta \theta} R\)	meters	Major radius in lab frame, second poloidal derivative
R_ttt	\(\partial_{\theta \theta \theta} R\)	meters	Major radius in lab frame, third poloidal derivative
R_ttz	\(\partial_{\theta \theta \zeta} R\)	meters	Major radius in lab frame, third derivative wrt poloidal angle twice and toroidal angle	R_tzt, R_ztt
R_tz	\(\partial_{\theta \zeta} R\)	meters	Major radius in lab frame, second derivative wrt poloidal and toroidal angles	R_zt
R_tzz	\(\partial_{\theta \zeta \zeta} R\)	meters	Major radius in lab frame, third derivative wrt poloidal angle and toroidal angle twice	R_ztz, R_zzt
R_z	\(\partial_{\zeta} R\)	meters	Major radius in lab frame, first toroidal derivative
R_zz	\(\partial_{\zeta \zeta} R\)	meters	Major radius in lab frame, second toroidal derivative
R_zzz	\(\partial_{\zeta \zeta \zeta} R\)	meters	Major radius in lab frame, third toroidal derivative
S	\(S\)	square meters	Surface area of outermost flux surface
V	\(V\)	cubic meters	Volume
X	\(X\)	meters	Cartesian X coordinate.
Y	\(Y\)	meters	Cartesian Y coordinate.
Z	\(Z\)	meters	Cylindrical vertical position along surface
Z_t	\(\partial_{\theta} Z\)	meters	Vertical coordinate in lab frame, first poloidal derivative
Z_tt	\(\partial_{\theta \theta} Z\)	meters	Vertical coordinate in lab frame, second poloidal derivative
Z_ttt	\(\partial_{\theta \theta \theta} Z\)	meters	Vertical coordinate in lab frame, third poloidal derivative
Z_ttz	\(\partial_{\theta \theta \zeta} Z\)	meters	Vertical coordinate in lab frame, third derivative wrt poloidal angle twice and toroidal angle	Z_tzt, Z_ztt
Z_tz	\(\partial_{\theta \zeta} Z\)	meters	Vertical coordinate in lab frame, second derivative wrt poloidal and toroidal angles	Z_zt
Z_tzz	\(\partial_{\theta \zeta \zeta} Z\)	meters	Vertical coordinate in lab frame, third derivative wrt poloidal angle and toroidal angle twice	Z_ztz, Z_zzt
Z_z	\(\partial_{\zeta} Z\)	meters	Vertical coordinate in lab frame, first toroidal derivative
Z_zz	\(\partial_{\zeta \zeta} Z\)	meters	Vertical coordinate in lab frame, second toroidal derivative
Z_zzz	\(\partial_{\zeta \zeta \zeta} Z\)	meters	Vertical coordinate in lab frame, third toroidal derivative
a	\(a\)	meters	Average minor radius
a_major/a_minor	\(a_{\mathrm{major}} / a_{\mathrm{minor}}\)	None	Elongation at a toroidal cross-section
curvature_H_rho	\(H_{\rho}\)	meters	Mean curvature of constant rho surfaces
curvature_K_rho	\(K_{\rho}\)	meters squared	Gaussian curvature of constant rho surfaces
curvature_k1_rho	\(k_{1,\rho}\)	Inverse meters	First principle curvature of constant rho surfaces
curvature_k2_rho	\(k_{2,\rho}\)	Inverse meters	Second principle curvature of constant rho surfaces
e^theta*sqrt(g)	\(\mathbf{e}^{\theta} \sqrt{g}\)	square meters	Contravariant poloidal basis vector weighted by 3-D volume Jacobian
e_phi	\(\mathbf{e}_{\phi}\)	meters	Covariant cylindrical toroidal basis vector
e_rho	\(\mathbf{e}_{\rho}\)	meters	Covariant radial basis vector
e_rho_r	\(\partial_{\rho} \mathbf{e}_{\rho}\)	meters	Covariant radial basis vector, derivative wrt radial coordinate
e_rho_rr	\(\partial_{\rho \rho} \mathbf{e}_{\rho}\)	meters	Covariant radial basis vector, second derivative wrt radial coordinate
e_rho_t	\(\partial_{\theta} \mathbf{e}_{\rho}\)	meters	Covariant radial basis vector, derivative wrt poloidal angle	e_theta_r
e_rho_z	\(\partial_{\zeta} \mathbf{e}_{\rho}\)	meters	Covariant radial basis vector, derivative wrt toroidal angle	e_zeta_r
e_theta	\(\mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector
e_theta_rr	\(\partial_{\rho \rho} \mathbf{e}_{\theta}\)	meters	Covariant poloidal basis vector, second derivative wrt radial coordinate	e_rho_rt, e_rho_tr
e_theta_t	\(\partial_{\theta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, derivative wrt poloidal coordinate
e_theta_tt	\(\partial_{\theta \theta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, second derivative wrt poloidal and poloidal coordinates
e_theta_tz	\(\partial_{\theta \zeta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, second derivative wrt poloidal and toroidal coordinates	e_theta_zt, e_zeta_tt
e_theta_z	\(\partial_{\zeta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, derivative wrt toroidal coordinate	e_zeta_t
e_theta_zz	\(\partial_{\zeta \zeta} \mathbf{e}_{\theta}\)	meters	Covariant Poloidal basis vector, second derivative wrt toroidal and toroidal coordinates	e_zeta_tz, e_zeta_zt
e_theta|r,p	\(\mathbf{e}_{\theta} |_{\rho, \phi}\)	meters	Covariant poloidal basis vector in (ρ,θ,ϕ) coordinates. ϕ increases counterclockwise when viewed from above (cylindrical R,ϕ plane with Z out of page).
e_zeta	\(\mathbf{e}_{\zeta}\)	meters	Covariant Toroidal basis vector
e_zeta_rr	\(\partial_{\rho \rho} \mathbf{e}_{\zeta}\)	meters	Covariant toroidal basis vector, second derivative wrt radial coordinate	e_rho_rz, e_rho_zr
e_zeta_z	\(\partial_{\zeta} \mathbf{e}_{\zeta}\)	meters	Covariant Toroidal basis vector, derivative wrt toroidal coordinate
e_zeta_zz	\(\partial_{\zeta \zeta} \mathbf{e}_{\zeta}\)	meters	Covariant Toroidal basis vector, second derivative wrt toroidal and toroidal coordinates
g_rr	\(g_{\rho\rho}\)	square meters	Radial/Radial element of covariant metric tensor
g_rt	\(g_{\rho\theta}\)	square meters	Radial/Poloidal element of covariant metric tensor	g_tr
g_rz	\(g_{\rho\zeta}\)	square meters	Radial/Toroidal element of covariant metric tensor	g_zr
g_tt	\(g_{\theta\theta}\)	square meters	Poloidal/Poloidal element of covariant metric tensor
g_tt_r	\(\partial_{\rho} g_{\theta\theta}\)	square meters	Poloidal/Poloidal element of covariant metric tensor, derivative wrt rho
g_tz	\(g_{\theta\zeta}\)	square meters	Poloidal/Toroidal element of covariant metric tensor	g_zt
g_tz_r	\(\partial_{\rho} g_{\theta\zeta}\)	square meters	Poloidal/Toroidal element of covariant metric tensor, derivative wrt rho
g_zz	\(g_{\zeta\zeta}\)	square meters	Toroidal/Toroidal element of covariant metric tensor
n_rho	\(\hat{\mathbf{n}}_{\rho}\)	None	Unit vector normal to constant rho surface (direction of e^rho)
n_rho_z	\(\partial_{\zeta}\hat{\mathbf{n}}_{\rho}\)	None	Unit vector normal to constant rho surface (direction of e^rho), derivative wrt toroidal angle
n_theta	\(\hat{\mathbf{n}}_{\theta}\)	None	Unit vector normal to constant theta surface (direction of e^theta)
n_zeta	\(\hat{\mathbf{n}}_{\zeta}\)	None	Unit vector normal to constant zeta surface (direction of e^zeta)
omega	\(\omega\)	radians	Toroidal stream function
omega_r	\(\partial_{\rho} \omega\)	radians	Toroidal stream function, first radial derivative
omega_rr	\(\partial_{\rho \rho} \omega\)	radians	Toroidal stream function, second radial derivative
omega_rrr	\(\partial_{\rho \rho \rho} \omega\)	radians	Toroidal stream function, third radial derivative
omega_rrrr	\(\partial_{\rho \rho \rho \rho} \omega\)	radians	Toroidal stream function, fourth radial derivative
omega_rrrt	\(\partial_{\rho \rho \rho \theta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radial coordinate thrice and poloidal once	omega_rrtr, omega_rtrr, omega_trrr
omega_rrrz	\(\partial_{\rho \rho \rho \zeta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radial coordinate thrice and toroidal once	omega_rrzr, omega_rzrr, omega_zrrr
omega_rrt	\(\partial_{\rho \rho \theta} \omega\)	radians	Toroidal stream function, third derivative, wrt radius twice and poloidal angle	omega_rtr, omega_trr
omega_rrtt	\(\partial_{\rho \rho \theta \theta} \omega\)	radians	Toroidal stream function, fourth derivative, wrt radius twice and poloidal angle twice	omega_rttr, omega_trrt, omega_ttrr
omega_rrtz	\(\partial_{\rho \theta \zeta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radius twice, poloidal angle, and toroidal angle	omega_rtzr, omega_tzrr, omega_zrrt
omega_rrz	\(\partial_{\rho \rho \zeta} \omega\)	radians	Toroidal stream function, third derivative, wrt radius twice and toroidal angle	omega_rzr, omega_zrr
omega_rrzz	\(\partial_{\rho \rho \zeta \zeta} \omega\)	radians	Toroidal stream function, fourth derivative, wrt radius twice and toroidal angle twice	omega_rzzr, omega_zrrz, omega_zzrr
omega_rt	\(\partial_{\rho \theta} \omega\)	radians	Toroidal stream function, second derivative wrt radius and poloidal angle	omega_tr
omega_rtt	\(\partial_{\rho \theta \theta} \omega\)	radians	Toroidal stream function, third derivative wrt radius and poloidal angle twice	omega_trt, omega_ttr
omega_rttt	\(\partial_{\rho \theta \theta \theta} \omega\)	radians	Toroidal stream function, third derivative wrt radius and poloidal angle thrice	omega_trtt, omega_ttrt, omega_tttr
omega_rttz	\(\partial_{\rho \theta \theta \zeta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radius once, poloidal angle twice, and toroidal angle once	omega_ttzr, omega_tzrt, omega_zrtt
omega_rtz	\(\partial_{\rho \theta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt radius, poloidal angle, and toroidal angle	omega_tzr, omega_zrt
omega_rtzz	\(\partial_{\rho \theta \zeta \zeta} \omega\)	radians	Toroidal stream function, fourth derivative wrt radius, poloidal angle, and toroidal angle twice	omega_tzzr, omega_zrtz, omega_zzrt
omega_rz	\(\partial_{\rho \zeta} \omega\)	radians	Toroidal stream function, second derivative wrt radius and toroidal angle	omega_zr
omega_rzz	\(\partial_{\rho \zeta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt radius and toroidal angle twice	omega_zrz, omega_zzr
omega_rzzz	\(\partial_{\rho \zeta \zeta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt radius and toroidal angle thrice	omega_zrzz, omega_zzrz, omega_zzzr
omega_t	\(\partial_{\theta} \omega\)	radians	Toroidal stream function, first poloidal derivative
omega_tt	\(\partial_{\theta \theta} \omega\)	radians	Toroidal stream function, second poloidal derivative
omega_ttt	\(\partial_{\theta \theta \theta} \omega\)	radians	Toroidal stream function, third poloidal derivative
omega_ttz	\(\partial_{\theta \theta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt poloidal angle twice and toroidal angle	omega_tzt, omega_ztt
omega_tz	\(\partial_{\theta \zeta} \omega\)	radians	Toroidal stream function, second derivative wrt poloidal and toroidal angles	omega_zt
omega_tzz	\(\partial_{\theta \zeta \zeta} \omega\)	radians	Toroidal stream function, third derivative wrt poloidal angle and toroidal angle twice	omega_ztz, omega_zzt
omega_z	\(\partial_{\zeta} \omega\)	radians	Toroidal stream function, first toroidal derivative
omega_zz	\(\partial_{\zeta \zeta} \omega\)	radians	Toroidal stream function, second toroidal derivative
omega_zzz	\(\partial_{\zeta \zeta \zeta} \omega\)	radians	Toroidal stream function, third toroidal derivative
perimeter(z)	\(P(\zeta)\)	meters	Perimeter of enclosed cross-section (enclosed constant phi surface), scaled by max(ρ)⁻¹, as function of zeta
phi	\(\phi\)	radians	Toroidal phi position along surface
phi_r	\(\partial_{\rho} \phi\)	radians	Toroidal angle in lab frame, derivative wrt radial coordinate
phi_t	\(\partial_{\theta} \phi\)	radians	Toroidal angle in lab frame, derivative wrt poloidal coordinate
phi_z	\(\partial_{\zeta} \phi\)	radians	Toroidal angle in lab frame, derivative wrt toroidal coordinate
rho	\(\rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux
rho_r	\(\partial_{\rho} \rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux, derivative wrt radial coordinate
rho_t	\(\partial_{\theta} \rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux, derivative wrt poloidal coordinate
rho_z	\(\partial_{\zeta} \rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux, derivative wrt toroidal coordinate
theta	\(\theta\)	radians	Poloidal angular coordinate (geometric, not magnetic)
theta_r	\(\partial_{\rho} \theta\)	radians	Poloidal angular coordinate (geometric, not magnetic), derivative wrt radial coordinate
theta_t	\(\partial_{\theta} \theta\)	radians	Poloidal angular coordinate (geometric, not magnetic), derivative wrt poloidal coordinate
theta_z	\(\partial_{\zeta} \theta\)	radians	Poloidal angular coordinate (geometric, not magnetic), derivative wrt toroidal coordinate
x	\(\mathbf{r}\)	meters	Position vector along surface
zeta	\(\zeta\)	radians	Toroidal angular coordinate
zeta_r	\(\partial_{\rho} \zeta\)	radians	Toroidal angular coordinate derivative, wrt radial coordinate
zeta_t	\(\partial_{\theta} \zeta\)	radians	Toroidal angular coordinate, derivative wrt poloidal coordinate
zeta_z	\(\partial_{\zeta} \zeta\)	radians	Toroidal angular coordinate, derivative wrt toroidal coordinate
|e_rho x e_theta|	\(|\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\)	square meters	2D Jacobian determinant for constant zeta surface
|e_rho x e_theta|_r	\(\partial_{\rho} |\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\)	square meters	2D Jacobian determinant for constant zeta surface derivative wrt radial coordinate
|e_rho x e_theta|_rr	\(\partial_{\rho \rho} |\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\)	square meters	2D Jacobian determinant for constant zeta surface second derivative wrt radial coordinate
|e_theta x e_zeta|	\(|\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\)	square meters	2D Jacobian determinant for constant rho surface
|e_theta x e_zeta|_r	\(\partial_{\rho} |\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\)	square meters	2D Jacobian determinant for constant rho surface derivative wrt radial coordinate
|e_theta x e_zeta|_rr	\(\partial_{\rho\rho} |\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\)	square meters	2D Jacobian determinant for constant rho surface second derivative wrt radial coordinate
|e_theta x e_zeta|_z	\(\partial_{\zeta}|e_{\theta} \times e_{\zeta}|\)	square meters	2D Jacobian determinant for constant rho surface,derivative wrt toroidal angle
|e_zeta x e_rho|	\(|\mathbf{e}_{\zeta} \times \mathbf{e}_{\rho}|\)	square meters	2D Jacobian determinant for constant theta surface

desc.coils.SplineXYZCoil

List of Variables: desc.coils.SplineXYZCoil

Name	Label	Units	Description	Aliases	kwargs
0	\(0\)	None	Zeros
R	\(R\)	meters	Cylindrical radial position along curve
X	\(X\)	meters	Cartesian X coordinate.
Y	\(Y\)	meters	Cartesian Y coordinate.
Z	\(Z\)	meters	Cylindrical vertical position along curve
center	\(\langle\mathbf{x}\rangle\)	meters	Centroid of the curve
curvature	\(\kappa\)	Inverse meters	Scalar curvature of the curve, with the sign denoting the convexity/concavity relative to the center of the curve (a circle has positive curvature)
ds	\(ds\)	None	Spacing of curve parameter
frenet_binormal	\(\mathbf{B}_{\mathrm{Frenet-Serret}}\)	None	Binormal unit vector to curve in Frenet-Serret frame
frenet_normal	\(\mathbf{N}_{\mathrm{Frenet-Serret}}\)	None	Normal unit vector to curve in Frenet-Serret frame
frenet_tangent	\(\mathbf{T}_{\mathrm{Frenet-Serret}}\)	None	Tangent unit vector to curve in Frenet-Serret frame
length	\(L\)	meters	Length of the curve		method
phi	\(\phi\)	radians	Toroidal phi position along curve
s	\(s\)	None	Curve parameter, on [0, 2pi)
torsion	\(\tau\)	Inverse meters	Scalar torsion of the curve
x	\(\mathbf{x}\)	meters	Position vector along curve		method
x_s	\(\partial_{s} \mathbf{x}\)	meters	Position vector along curve, first derivative		method
x_ss	\(\partial_{ss} \mathbf{x}\)	meters	Position vector along curve, second derivative		method
x_sss	\(\partial_{sss} \mathbf{x}\)	meters	Position vector along curve, third derivative		method

desc.magnetic_fields._core.OmnigenousField

List of Variables: desc.magnetic_fields._core.OmnigenousField

Name	Label	Units	Description	Aliases	kwargs
alpha	\(\alpha\)	radians	Field line label, defined on [0, 2pi)
eta	\(\eta\)	radians	Intermediate omnigenity coordinate along field lines
h	\(h = \theta + (N / M) \zeta\)	radians	Omnigenity symmetry angle
rho	\(\rho\)	None	Radial coordinate, proportional to the square root of the toroidal flux
theta_B	\((\theta_{B},\zeta_{B})\)	radians	Boozer angular coordinates	zeta_B	helicity, iota
|B|	\(|\mathbf{B}|\)	Tesla	Magnitude of omnigenous magnetic field

Optional Keyword arguments

kwargs

Name	Description
M_booz	int: Maximum poloidal mode number for Boozer harmonics. Default 2*eq.M
N_booz	int: Maximum toroidal mode number for Boozer harmonics. Default 2*eq.N
basis_in	{‘rpz’, ‘xyz’}: Basis for input params vectors, Default ‘xyz’
degree	int: Degree of polynomial used for fitting current profile. Default grid.num_rho-1
gamma	float: Adiabatic index. Default 0
helicity	tuple: Type of quasisymmetry, (M,N). Default (1,0)
iota	float: Value of rotational transform on the Omnigenous surface. Default 1.0
method	Interpolation type, Default ‘cubic’. See SplineXYZCurve docs for options.
n_gauss	int: Number of quadrature points to use for estimating trapped fraction. Default 20.