Quantities for Postprocessing

GVEC provides a number of built-in quantities for postprocessing an equilibrium. These can be used for example with the compute, evaluate and evaluate_sfl functions, or the plotting utilities. The table_of_quantities function can be used to generate a table of available quantities.

See the derivations in the developer guide for more details on the definitions of the quantities listed below.

Solution variables

label	long name	symbol
X1	first reference coordinate	\(X^1\)
X2	second reference coordinate	\(X^2\)
LA	straight field line potential	\(\lambda\)
dX1_dr	radial derivative of the first reference coordinate	\(\frac{\partial X^1}{\partial \rho}\)
dX1_dt	poloidal derivative of the first reference coordinate	\(\frac{\partial X^1}{\partial \theta}\)
dX1_dz	toroidal derivative of the first reference coordinate	\(\frac{\partial X^1}{\partial \zeta}\)
dX1_drr	second radial derivative of the first reference coordinate	\(\frac{\partial^2 X^1}{\partial \rho^2}\)
dX1_drt	radial-poloidal derivative of the first reference coordinate	\(\frac{\partial^2 X^1}{\partial \rho\partial \theta}\)
dX1_drz	radial-toroidal derivative of the first reference coordinate	\(\frac{\partial^2 X^1}{\partial \rho\partial \zeta}\)
dX1_dtt	second poloidal derivative of the first reference coordinate	\(\frac{\partial^2 X^1}{\partial \theta^2}\)
dX1_dtz	poloidal-toroidal derivative of the first reference coordinate	\(\frac{\partial^2 X^1}{\partial \theta\partial \zeta}\)
dX1_dzz	second toroidal derivative of the first reference coordinate	\(\frac{\partial^2 X^1}{\partial \zeta^2}\)
dX2_dr	radial derivative of the second reference coordinate	\(\frac{\partial X^2}{\partial \rho}\)
dX2_dt	poloidal derivative of the second reference coordinate	\(\frac{\partial X^2}{\partial \theta}\)
dX2_dz	toroidal derivative of the second reference coordinate	\(\frac{\partial X^2}{\partial \zeta}\)
dX2_drr	second radial derivative of the second reference coordinate	\(\frac{\partial^2 X^2}{\partial \rho^2}\)
dX2_drt	radial-poloidal derivative of the second reference coordinate	\(\frac{\partial^2 X^2}{\partial \rho\partial \theta}\)
dX2_drz	radial-toroidal derivative of the second reference coordinate	\(\frac{\partial^2 X^2}{\partial \rho\partial \zeta}\)
dX2_dtt	second poloidal derivative of the second reference coordinate	\(\frac{\partial^2 X^2}{\partial \theta^2}\)
dX2_dtz	poloidal-toroidal derivative of the second reference coordinate	\(\frac{\partial^2 X^2}{\partial \theta\partial \zeta}\)
dX2_dzz	second toroidal derivative of the second reference coordinate	\(\frac{\partial^2 X^2}{\partial \zeta^2}\)
dLA_dr	radial derivative of the straight field line potential	\(\frac{\partial \lambda}{\partial \rho}\)
dLA_dt	poloidal derivative of the straight field line potential	\(\frac{\partial \lambda}{\partial \theta}\)
dLA_dz	toroidal derivative of the straight field line potential	\(\frac{\partial \lambda}{\partial \zeta}\)
dLA_drr	second radial derivative of the straight field line potential	\(\frac{\partial^2 \lambda}{\partial \rho^2}\)
dLA_drt	radial-poloidal derivative of the straight field line potential	\(\frac{\partial^2 \lambda}{\partial \rho\partial \theta}\)
dLA_drz	radial-toroidal derivative of the straight field line potential	\(\frac{\partial^2 \lambda}{\partial \rho\partial \zeta}\)
dLA_dtt	second poloidal derivative of the straight field line potential	\(\frac{\partial^2 \lambda}{\partial \theta^2}\)
dLA_dtz	poloidal-toroidal derivative of the straight field line potential	\(\frac{\partial^2 \lambda}{\partial \theta\partial \zeta}\)
dLA_dzz	second toroidal derivative of the straight field line potential	\(\frac{\partial^2 \lambda}{\partial \zeta^2}\)

Additional solution variables for the Boozer transform

Note

If a Boozer transform is performed (e.g. evaluate_sfl(..., sfl="boozer")), the variables NU_B, dNU_B_dr, … dNU_B_dzz are available instead of those given below.

label	long name	symbol
dNU_B_dt	poloidal derivative of the Boozer potential computed from the magnetic field	\(\left.\frac{\partial \nu_B}{\partial \theta}\right|_\text{def.}\)
dNU_B_dz	toroidal derivative of the Boozer potential computed from the magnetic field	\(\left.\frac{\partial \nu_B}{\partial \zeta}\right|_\text{def.}\)

Curvilinear coordinates

label	long name	symbol
Jac_l	logical Jacobian determinant	\(\mathcal{J}_l\)
Jac	Jacobian determinant	\(\mathcal{J}\)
e_rho	radial tangent basis vector	\(\mathbf{e}_\rho\)
e_theta	poloidal tangent basis vector	\(\mathbf{e}_\theta\)
e_zeta	toroidal tangent basis vector	\(\mathbf{e}_\zeta\)
grad_rho	radial reciprocal basis vector	\(\nabla\rho\)
grad_theta	poloidal reciprocal basis vector	\(\nabla\theta\)
grad_zeta	toroidal reciprocal basis vector	\(\nabla\zeta\)
g_rr	rr component of the metric tensor	\(g_{\rho\rho}\)
g_rt	rt component of the metric tensor	\(g_{\rho\theta}\)
g_rz	rz component of the metric tensor	\(g_{\rho\zeta}\)
g_tt	tt component of the metric tensor	\(g_{\theta\theta}\)
g_tz	tz component of the metric tensor	\(g_{\theta\zeta}\)
g_zz	zz component of the metric tensor	\(g_{\zeta\zeta}\)
k_rr	rr logical curvature vector	\(\mathbf{k}_{\rho\rho}\)
k_rt	rt logical curvature vector	\(\mathbf{k}_{\rho\theta}\)
k_rz	rz logical curvature vector	\(\mathbf{k}_{\rho\zeta}\)
k_tt	tt logical curvature vector	\(\mathbf{k}_{\theta\theta}\)
k_tz	tz logical curvature vector	\(\mathbf{k}_{\theta\zeta}\)
k_zz	zz logical curvature vector	\(\mathbf{k}_{\zeta\zeta}\)
II_tt	poloidal component of the second fundamental form	\(\mathrm{II}_{\theta\theta}\)
II_tz	poloidal-toroidal component of the second fundamental form	\(\mathrm{II}_{\theta\zeta}\)
II_zz	toroidal component of the second fundamental form	\(\mathrm{II}_{\zeta\zeta}\)
mod_e_rho	modulus of the radial tangent basis vector	\(\left|\mathbf{e}_\rho\right|\)
mod_e_theta	modulus of the poloidal tangent basis vector	\(\left|\mathbf{e}_\theta\right|\)
mod_e_zeta	modulus of the toroidal tangent basis vector	\(\left|\mathbf{e}_\zeta\right|\)
mod_grad_rho	modulus of the radial reciprocal basis vector	\(\left|\nabla\rho\right|\)
mod_grad_theta	modulus of the poloidal reciprocal basis vector	\(\left|\nabla\theta\right|\)
mod_grad_zeta	modulus of the toroidal reciprocal basis vector	\(\left|\nabla\zeta\right|\)
dJac_l_dr	radial derivative of the logical Jacobian determinant	\(\frac{\partial \mathcal{J}_l}{\partial \rho}\)
dJac_l_dt	poloidal derivative of the logical Jacobian determinant	\(\frac{\partial \mathcal{J}_l}{\partial \theta}\)
dJac_l_dz	toroidal derivative of the logical Jacobian determinant	\(\frac{\partial \mathcal{J}_l}{\partial \zeta}\)
dJac_dr	radial derivative of the Jacobian determinant	\(\frac{\partial \mathcal{J}}{\partial \rho}\)
dJac_dt	poloidal derivative of the Jacobian determinant	\(\frac{\partial \mathcal{J}}{\partial \theta}\)
dJac_dz	toroidal derivative of the Jacobian determinant	\(\frac{\partial \mathcal{J}}{\partial \zeta}\)
dg_rr_dr	radial derivative of the rr component of the metric tensor	\(\frac{\partial g_{\rho\rho}}{\partial \rho}\)
dg_rr_dt	poloidal derivative of the rr component of the metric tensor	\(\frac{\partial g_{\rho\rho}}{\partial \theta}\)
dg_rr_dz	toroidal derivative of the rr component of the metric tensor	\(\frac{\partial g_{\rho\rho}}{\partial \zeta}\)
dg_rt_dr	radial derivative of the rt component of the metric tensor	\(\frac{\partial g_{\rho\theta}}{\partial \rho}\)
dg_rt_dt	poloidal derivative of the rt component of the metric tensor	\(\frac{\partial g_{\rho\theta}}{\partial \theta}\)
dg_rt_dz	toroidal derivative of the rt component of the metric tensor	\(\frac{\partial g_{\rho\theta}}{\partial \zeta}\)
dg_rz_dr	radial derivative of the rz component of the metric tensor	\(\frac{\partial g_{\rho\zeta}}{\partial \rho}\)
dg_rz_dt	poloidal derivative of the rz component of the metric tensor	\(\frac{\partial g_{\rho\zeta}}{\partial \theta}\)
dg_rz_dz	toroidal derivative of the rz component of the metric tensor	\(\frac{\partial g_{\rho\zeta}}{\partial \zeta}\)
dg_tt_dr	radial derivative of the tt component of the metric tensor	\(\frac{\partial g_{\theta\theta}}{\partial \rho}\)
dg_tt_dt	poloidal derivative of the tt component of the metric tensor	\(\frac{\partial g_{\theta\theta}}{\partial \theta}\)
dg_tt_dz	toroidal derivative of the tt component of the metric tensor	\(\frac{\partial g_{\theta\theta}}{\partial \zeta}\)
dg_tz_dr	radial derivative of the tz component of the metric tensor	\(\frac{\partial g_{\theta\zeta}}{\partial \rho}\)
dg_tz_dt	poloidal derivative of the tz component of the metric tensor	\(\frac{\partial g_{\theta\zeta}}{\partial \theta}\)
dg_tz_dz	toroidal derivative of the tz component of the metric tensor	\(\frac{\partial g_{\theta\zeta}}{\partial \zeta}\)
dg_zz_dr	radial derivative of the zz component of the metric tensor	\(\frac{\partial g_{\zeta\zeta}}{\partial \rho}\)
dg_zz_dt	poloidal derivative of the zz component of the metric tensor	\(\frac{\partial g_{\zeta\zeta}}{\partial \theta}\)
dg_zz_dz	toroidal derivative of the zz component of the metric tensor	\(\frac{\partial g_{\zeta\zeta}}{\partial \zeta}\)

Boozer coordinates

label	long name	symbol
Jac_B	Jacobian determinant in Boozer coordinates	\(\mathcal{J}_B\)
e_rho_B	radial tangent basis vector in Boozer coordinates	\(\mathbf{e}_{\rho_B}\)
e_theta_B	poloidal tangent basis vector in Boozer coordinates	\(\mathbf{e}_{\theta_B}\)
e_zeta_B	toroidal tangent basis vector in Boozer coordinates	\(\mathbf{e}_{\zeta_B}\)
grad_theta_B	poloidal reciprocal basis vector in Boozer coordinates	\(\nabla\theta_B\)
grad_zeta_B	toroidal reciprocal basis vector in Boozer coordinates	\(\nabla\zeta_B\)
g_rr_B	rr component of the metric tensor in Boozer coordinates	\(g_{\rho_B \rho_B}\)
g_rt_B	rt component of the metric tensor in Boozer coordinates	\(g_{\rho_B \theta_B}\)
g_rz_B	rz component of the metric tensor in Boozer coordinates	\(g_{\rho_B \zeta_B}\)
g_tt_B	tt component of the metric tensor in Boozer coordinates	\(g_{\theta_B \theta_B}\)
g_tz_B	tz component of the metric tensor in Boozer coordinates	\(g_{\theta_B \zeta_B}\)
g_zz_B	zz component of the metric tensor in Boozer coordinates	\(g_{\zeta_B \zeta_B}\)
k_tt_B	tt boozer curvature vector	\(\mathbf{k}_{\theta_B \theta_B}\)
k_tz_B	tz boozer curvature vector	\(\mathbf{k}_{\theta_B \zeta_B}\)
k_zz_B	zz boozer curvature vector	\(\mathbf{k}_{\zeta_B \zeta_B}\)
II_tt_B	t,t component of the second fundamental form in Boozer coordinates	\(\mathrm{II}_{\theta_B \theta_B}\)
II_tz_B	t,z component of the second fundamental form in Boozer coordinates	\(\mathrm{II}_{\theta_B \zeta_B}\)
II_zz_B	z,z component of the second fundamental form in Boozer coordinates	\(\mathrm{II}_{\zeta_B \zeta_B}\)

PEST coordinates

label	long name	symbol
theta_P	poloidal angle in PEST coordinates	\(\theta_P\)
Jac_P	Jacobian determinant in PEST coordinates	\(\mathcal{J}_P\)
e_rho_P	poloidal tangent basis vector in PEST coordinates	\(\mathbf{e}_{\theta_P}\)
e_theta_P	poloidal tangent basis vector in PEST coordinates	\(\mathbf{e}_{\theta_P}\)
e_zeta_P	toroidal tangent basis vector in PEST coordinates	\(\mathbf{e}_{\zeta_P}\)
grad_theta_P	poloidal reciprocal basis vector in PEST coordinates	\(\nabla \theta_P\)
g_rr_P	rr component of the metric tensor in PEST coordinates	\(g_{\rho_P \rho_P}\)
g_rt_P	rt component of the metric tensor in PEST coordinates	\(g_{\rho_P \theta_P}\)
g_rz_P	rz component of the metric tensor in PEST coordinates	\(g_{\rho_P \zeta_P}\)
g_tt_P	tt component of the metric tensor in PEST coordinates	\(g_{\theta_P \theta_P}\)
g_tz_P	tz component of the metric tensor in PEST coordinates	\(g_{\theta_P \zeta_P}\)
g_zz_P	zz component of the metric tensor in PEST coordinates	\(g_{\zeta_P \zeta_P}\)
k_tt_P	tt PEST curvature vector	\(\mathbf{k}_{\theta_P \theta_P}\)
k_tz_P	tz PEST curvature vector	\(\mathbf{k}_{\theta_P \zeta_P}\)
k_zz_P	zz PEST curvature vector	\(\mathbf{k}_{\zeta_P \zeta_P}\)
II_tt_P	t,t component of the second fundamental form in PEST coordinates	\(\mathrm{II}_{\theta_P \theta_P}\)
II_tz_P	t,z component of the second fundamental form in PEST coordinates	\(\mathrm{II}_{\theta_P \zeta_P}\)
II_zz_P	z,z component of the second fundamental form in PEST coordinates	\(\mathrm{II}_{\zeta_P \zeta_P}\)

Reference coordinates

Also called the coordinate frame or \(h\)-map.

label	long name	symbol
Jac_h	reference Jacobian determinant	\(\mathcal{J}_h\)
N_FP	number of field periods	\(N_\text{FP}\)
e_q1	first reference tangent basis vector	\(\mathbf{e}_{q^1}\)
e_q2	second reference tangent basis vector	\(\mathbf{e}_{q^2}\)
e_q3	toroidal reference tangent basis vector	\(\mathbf{e}_{q^3}\)
k_q1q1	q1-q1 reference curvature vector	\(k_{q^1q^1}\)
k_q1q2	q1-q2 reference curvature vector	\(k_{q^1q^2}\)
k_q1q3	q1-q3 reference curvature vector	\(k_{q^1q^3}\)
k_q2q2	q2-q2 reference curvature vector	\(k_{q^2q^2}\)
k_q2q3	q2-q3 reference curvature vector	\(k_{q^2q^3}\)
k_q3q3	q3-q3 reference curvature vector	\(k_{q^3q^3}\)
dJac_h_dr	radial derivative of the reference Jacobian determinant	\(\frac{\partial \mathcal{J}_h}{\partial \rho}\)
dJac_h_dt	poloidal derivative of the reference Jacobian determinant	\(\frac{\partial \mathcal{J}_h}{\partial \theta}\)
dJac_h_dz	toroidal derivative of the reference Jacobian determinant	\(\frac{\partial \mathcal{J}_h}{\partial \zeta}\)

Geometric quantities

label	long name	symbol
pos	position vector	\(\mathbf{x}\)
normal	surface normal	\(\mathbf{n}\)
dA	differential area element	\(dA\)
V	volume	\(V\)
L_axis	length of the magnetic axis	\(L_\text{axis}\)
A_surface	surface area	\(A_\text{surface}\)
r_major	effective major radius	\(r_\text{major,eff}\)
r_minor	effective minor radius	\(r_\text{minor,eff}\)
aspect_ratio	effective aspect ratio	\(a_\text{eff}\)
elongation	effective elongation	\(E_\text{eff}\)
dV_dPhi_n	derivative of the plasma volume w.r.t. normalized toroidal magnetic flux	\(\frac{dV}{d\Phi_n}\)
dV_dPhi_n2	second derivative of the plasma volume w.r.t. normalized toroidal magnetic flux	\(\frac{d^2V}{d\Phi_n^2}\)

Magnetic flux

label	long name	symbol
Phi_edge	toroidal magnetic flux at the edge	\(\Phi_0\)
Phi	toroidal magnetic flux	\(\Phi\)
dPhi_dr	toroidal magnetic flux gradient	\(\frac{d\Phi}{d\rho}\)
dPhi_drr	toroidal magnetic flux curvature	\(\frac{d^2\Phi}{d\rho^2}\)
chi	poloidal magnetic flux	\(\chi\)
dchi_dr	poloidal magnetic flux gradient	\(\frac{d\chi}{d\rho}\)
dchi_drr	poloidal magnetic flux curvature	\(\frac{d^2\chi}{d\rho^2}\)
iota	rotational transform	\(\iota\)
diota_dr	rotational transform gradient	\(\frac{d\iota}{d\rho}\)
diota_drr	rotational transform curvature	\(\frac{d^2\iota}{d\rho^2}\)
iota_avg	average rotational transform	\(\overline{\iota}\)
iota_avg2	rotational transform averaged over rho^2	\(\overline{\iota}_2\)
shear	global magnetic shear	\(s_g\)
shear_avg	average global magnetic shear	\(\overline{s_g}\)
shear_avg2	global magnetic shear averaged over rho^2	\(\overline{s_g}_2\)
iota_0	geometric contribution to the rotational transform	\(\iota_0\)
iota_curr	toroidal current contribution to the rotational transform	\(\iota_\text{curr}\)
iota_curr_0	factor to the toroidal current contribution to the rotational transform	\(\iota_{\text{curr},0}\)

Current profiles

label	long name	symbol
I_tor	toroidal current enclosed by flux surface	\(I_\text{tor}\)
I_pol	poloidal current, relative to the magnetic axis	\(I_\text{pol}\)
dI_tor_dr	derivative of the toroidal current enclosed by the flux surface	\(\frac{dI_\text{tor}}{d\rho}\)

Pressure

label	long name	symbol
p	pressure	\(p\)
dp_dr	pressure gradient	\(\frac{dp}{d\rho}\)
dp_drr	pressure curvature	\(\frac{d^2p}{d\rho^2}\)
beta_avg	volume-averaged plasma beta	\(\overline{\beta}\)

Magnetic field

label	long name	symbol
B	magnetic field	\(\mathbf{B}\)
B_contra_t	poloidal component of the magnetic field	\(B^\theta\)
B_contra_z	toroidal component of the magnetic field	\(B^\zeta\)
B_theta_avg	flux-surface averaged poloidal magnetic field	\(\overline{B_\theta}\)
B_zeta_avg	flux-surface averaged toroidal magnetic field	\(\overline{B_\zeta}\)
mod_B	modulus of the magnetic field	\(\left|\mathbf{B}\right|\)
grad_mod_B	gradient of the modulus of the magnetic field	\(\nabla\left|\mathbf{B}\right|\)
dB_contra_t_dr	radial derivative of the poloidal magnetic field	\(\frac{\partial B^\theta}{\partial \rho}\)
dB_contra_t_dt	poloidal derivative of the poloidal magnetic field	\(\frac{\partial B^\theta}{\partial \theta}\)
dB_contra_t_dz	toroidal derivative of the poloidal magnetic field	\(\frac{\partial B^\theta}{\partial \zeta}\)
dB_contra_z_dr	radial derivative of the toroidal magnetic field	\(\frac{\partial B^\zeta}{\partial \rho}\)
dB_contra_z_dt	poloidal derivative of the toroidal magnetic field	\(\frac{\partial B^\zeta}{\partial \theta}\)
dB_contra_z_dz	toroidal derivative of the toroidal magnetic field	\(\frac{\partial B^\zeta}{\partial \zeta}\)
dmod_B_dr	radial derivative of the modulus of the magnetic field	\(\frac{\partial \left|\mathbf{B}\right|}{\partial \rho}\)
dmod_B_dt	poloidal derivative of the modulus of the magnetic field	\(\frac{\partial \left|\mathbf{B}\right|}{\partial \theta}\)
dmod_B_dz	toroidal derivative of the modulus of the magnetic field	\(\frac{\partial \left|\mathbf{B}\right|}{\partial \zeta}\)
dB_theta_avg_dr	derivative of the flux-surface averaged poloidal magnetic field	\(\frac{d\overline{B_\theta}}{d\rho}\)
dB_dr	radial derivative of the magnetic field	\(\frac{\partial \mathbf{B}}{\partial \rho}\)
dB_dt	poloidal derivative of the magnetic field	\(\frac{\partial \mathbf{B}}{\partial \theta}\)
dB_dz	toroidal derivative of the magnetic field	\(\frac{\partial \mathbf{B}}{\partial \zeta}\)
db_dr	radial derivative of the normalized magnetic field	\(\frac{\partial \mathbf{b}}{\partial \rho}\)
db_dt	poloidal derivative of the normalized magnetic field	\(\frac{\partial \mathbf{b}}{\partial \theta}\)
db_dz	toroidal derivative of the normalized magnetic field	\(\frac{\partial \mathbf{b}}{\partial \zeta}\)

Boozer magnetic field

label	long name	symbol
B_contra_t_B	contravariant \(\theta\) component of the magnetic field in Boozer coordinates	\(B^{\theta_B}\)
B_contra_z_B	contravariant \(\zeta\) component of the magnetic field in Boozer coordinates	\(B^{\zeta_B}\)
B_rho_B	\(\rho\) component of the magnetic field in Boozer coordinates	\(B_{\rho_B}\)
B_theta_B	\(\theta\) component of the magnetic field in Boozer coordinates	\(B_{\theta_B}\)
B_zeta_B	\(\zeta\) component of the magnetic field in Boozer coordinates	\(B_{\zeta_B}\)
dmod_B_dr_B	radial Boozer derivative of the modulus of the magnetic field	\(\frac{\partial\left|\mathbf{B}\right|}{\partial \rho_B}\)
dmod_B_dt_B	poloidal Boozer derivative of the modulus of the magnetic field	\(\frac{\partial\left|\mathbf{B}\right|}{\partial \theta_B}\)
dmod_B_dz_B	toroidal Boozer derivative of the modulus of the magnetic field	\(\frac{\partial\left|\mathbf{B}\right|}{\partial \zeta_B}\)

PEST magnetic field

label	long name	symbol
B_contra_t_P	contravariant \(\theta\) component of the magnetic field in PEST coordinates	\(B^{\theta_P}\)
B_rho_P	\(\rho\) component of the magnetic field in PEST coordinates	\(B_{\rho_P}\)
B_theta_P	\(\theta\) component of the magnetic field in PEST coordinates	\(B_{\theta_P}\)
B_zeta_P	\(\zeta\) component of the magnetic field in PEST coordinates	\(B_{\zeta_P}\)
dmod_B_dr_P	radial PEST-like derivative of the modulus of the magnetic field	\(\frac{\partial\left|\mathbf{B}\right|}{\partial \rho_P}\)
dmod_B_dt_P	poloidal PEST-like derivative of the modulus of the magnetic field	\(\frac{\partial\left|\mathbf{B}\right|}{\partial \vartheta_P}\)
dmod_B_dz_P	toroidal PEST-like derivative of the modulus of the magnetic field	\(\frac{\partial\left|\mathbf{B}\right|}{\partial \zeta_P}\)

Current density

label	long name	symbol
J	current density	\(\mathbf{J}\)
J_contra_r	contravariant radial current density	\(J^{\rho}\)
J_contra_t	contravariant poloidal current density	\(J^{\theta}\)
J_contra_z	contravariant toroidal current density	\(J^{\zeta}\)
mod_J	modulus of the current density	\(\left|\mathbf{J}\right|\)

Boozer current density

label	long name	symbol
J_contra_t_B	contravariant \(\theta\) component of the current density in Boozer coordinates	\(J^{\theta_B}\)
J_contra_z_B	contravariant \(\zeta\) component of the current density in Boozer coordinates	\(J^{\zeta_B}\)
J_rho_B	\(\rho\) component of the current density in Boozer coordinates	\(J_{\rho_B}\)
J_theta_B	\(\theta\) component of the current density in Boozer coordinates	\(J_{\theta_B}\)
J_zeta_B	\(\zeta\) component of the current density in Boozer coordinates	\(J_{\zeta_B}\)

PEST current density

label	long name	symbol
J_contra_t_P	contravariant \(\theta\) component of the current density in PEST coordinates	\(J^{\theta_P}\)
J_rho_P	\(\rho\) component of the current density in PEST coordinates	\(J_{\rho_P}\)
J_theta_P	\(\theta\) component of the current density in PEST coordinates	\(J_{\theta_P}\)
J_zeta_P	\(\zeta\) component of the current density in PEST coordinates	\(J_{\zeta_P}\)

MHD Force

label	long name	symbol
W_MHD	total MHD energy	\(W_\text{MHD}\)
F	MHD force	\(F\)
mod_F	modulus of the MHD force	\(\left|F\right|\)
F_r_avg	radial force balance	\(\overline{F_\rho}\)

Derived quantities of interest

label	long name	symbol
mirror_ratio	mirror ratio	\(\Delta_\text{mirror}\)
L_gradB	magnetic gradient scale length	\(L_{\nabla\mathbf{B}}\)
vacuum_magnetic_well_depth	vacuum magnetic well depth	\(d_\text{well}\)

Mercier stability criterion

label	long name	symbol
D_Merc	Mercier criterion	\(D_\text{Merc}\)
D_Merc_Curr	Current contribution to the Mercier criterion	\(D_\text{M,Curr}\)
D_Merc_Geod	Geodesic contribution to the Mercier criterion	\(D_\text{M,Geod}\)
D_Merc_Shear	Shear contribution to the Mercier criterion	\(D_\text{M,Shear}\)
D_Merc_Well	Magnetic well contribution to the Mercier criterion	\(D_\text{M,Well}\)

Geodesic curvature

Added in version 1.4.0: Experimental! See the derivation for details.

label	long name	symbol
kappa_B	field line curvature	\(\mathbf{\kappa}_B\)
kappa_G	geodesic curvature	\(\kappa_G\)

Others

label	long name	symbol
gamma	adiabatic index	\(\gamma\)
mu0	magnetic constant	\(\mu_0\)
xyz	cartesian vector components	\((x,y,z)\)