Quantities for Postprocessing#
GVEC provides a number of built-in quantities for postprocessing an equilibrium. These can be used with the compute, evaluate and evaluate_sfl functions.
Table of built-in quantities#
label |
long name |
symbol |
|---|---|---|
|
surface area |
\(A_\text{surface}\) |
|
magnetic field |
\(\mathbf{B}\) |
|
poloidal component of the magnetic field |
\(B^\theta\) |
|
contravariant \(\theta\) component of the magnetic field in Boozer coordinates |
\(B^{\theta_B}\) |
|
contravariant \(\theta\) component of the magnetic field in PEST coordinates |
\(B^{\theta_P}\) |
|
toroidal component of the magnetic field |
\(B^\zeta\) |
|
contravariant \(\zeta\) component of the magnetic field in Boozer coordinates |
\(B^{\zeta_B}\) |
|
\(\rho\) component of the magnetic field in Boozer coordinates |
\(B_{\rho_B}\) |
|
\(\rho\) component of the magnetic field in PEST coordinates |
\(B_{\rho_P}\) |
|
\(\theta\) component of the magnetic field in Boozer coordinates |
\(B_{\theta_B}\) |
|
\(\theta\) component of the magnetic field in PEST coordinates |
\(B_{\theta_P}\) |
|
flux-surface averaged poloidal magnetic field |
\(\overline{B_\theta}\) |
|
\(\zeta\) component of the magnetic field in Boozer coordinates |
\(B_{\zeta_B}\) |
|
\(\zeta\) component of the magnetic field in PEST coordinates |
\(B_{\zeta_P}\) |
|
flux-surface averaged toroidal magnetic field |
\(\overline{B_\zeta}\) |
|
Mercier criterion |
\(D_\text{Merc}\) |
|
Current contribution to the Mercier criterion |
\(D_\text{M,Curr}\) |
|
Geodesic contribution to the Mercier criterion |
\(D_\text{M,Geod}\) |
|
Shear contribution to the Mercier criterion |
\(D_\text{M,Shear}\) |
|
Magnetic well contribution to the Mercier criterion |
\(D_\text{M,Well}\) |
|
MHD force |
\(F\) |
|
radial force balance |
\(\overline{F_\rho}\) |
|
poloidal component of the second fundamental form |
\(\mathrm{II}_{\theta\theta}\) |
|
t,t component of the second fundamental form in Boozer coordinates |
\(\mathrm{II}_{\theta_B \theta_B}\) |
|
t,t component of the second fundamental form in PEST coordinates |
\(\mathrm{II}_{\theta_P \theta_P}\) |
|
poloidal-toroidal component of the second fundamental form |
\(\mathrm{II}_{\theta\zeta}\) |
|
t,z component of the second fundamental form in Boozer coordinates |
\(\mathrm{II}_{\theta_B \zeta_B}\) |
|
t,z component of the second fundamental form in PEST coordinates |
\(\mathrm{II}_{\theta_P \zeta_P}\) |
|
toroidal component of the second fundamental form |
\(\mathrm{II}_{\zeta\zeta}\) |
|
z,z component of the second fundamental form in Boozer coordinates |
\(\mathrm{II}_{\zeta_B \zeta_B}\) |
|
z,z component of the second fundamental form in PEST coordinates |
\(\mathrm{II}_{\zeta_P \zeta_P}\) |
|
poloidal current, relative to the magnetic axis |
\(I_\text{pol}\) |
|
toroidal current enclosed by flux surface |
\(I_\text{tor}\) |
|
current density |
\(\mathbf{J}\) |
|
contravariant radial current density |
\(J^{\rho}\) |
|
contravariant poloidal current density |
\(J^{\theta}\) |
|
contravariant \(\theta\) component of the current density in Boozer coordinates |
\(J^{\theta_B}\) |
|
contravariant \(\theta\) component of the current density in PEST coordinates |
\(J^{\theta_P}\) |
|
contravariant toroidal current density |
\(J^{\zeta}\) |
|
contravariant \(\zeta\) component of the current density in Boozer coordinates |
\(J^{\zeta_B}\) |
|
\(\rho\) component of the current density in Boozer coordinates |
\(J_{\rho_B}\) |
|
\(\rho\) component of the current density in PEST coordinates |
\(J_{\rho_P}\) |
|
\(\theta\) component of the current density in Boozer coordinates |
\(J_{\theta_B}\) |
|
\(\theta\) component of the current density in PEST coordinates |
\(J_{\theta_P}\) |
|
\(\zeta\) component of the current density in Boozer coordinates |
\(J_{\zeta_B}\) |
|
\(\zeta\) component of the current density in PEST coordinates |
\(J_{\zeta_P}\) |
|
Jacobian determinant |
\(\mathcal{J}\) |
|
Jacobian determinant in Boozer coordinates |
\(\mathcal{J}_B\) |
|
Jacobian determinant in PEST coordinates |
\(\mathcal{J}_P\) |
|
reference Jacobian determinant |
\(\mathcal{J}_h\) |
|
logical Jacobian determinant |
\(\mathcal{J}_l\) |
|
straight field line potential |
\(\lambda\) |
|
length of the magnetic axis |
\(L_\text{axis}\) |
|
magnetic gradient scale length |
\(L_{\nabla\mathbf{B}}\) |
|
number of field periods |
\(N_\text{FP}\) |
|
toroidal magnetic flux |
\(\Phi\) |
|
toroidal magnetic flux at the edge |
\(\Phi_0\) |
|
volume |
\(V\) |
|
total MHD energy |
\(W_\text{MHD}\) |
|
first reference coordinate |
\(X^1\) |
|
second reference coordinate |
\(X^2\) |
|
effective aspect ratio |
\(a_\text{eff}\) |
|
volume-averaged plasma beta |
\(\overline{\beta}\) |
|
poloidal magnetic flux |
\(\chi\) |
|
differential area element |
\(dA\) |
|
radial derivative of the poloidal magnetic field |
\(\frac{\partial B^\theta}{\partial \rho}\) |
|
poloidal derivative of the poloidal magnetic field |
\(\frac{\partial B^\theta}{\partial \theta}\) |
|
toroidal derivative of the poloidal magnetic field |
\(\frac{\partial B^\theta}{\partial \zeta}\) |
|
radial derivative of the toroidal magnetic field |
\(\frac{\partial B^\zeta}{\partial \rho}\) |
|
poloidal derivative of the toroidal magnetic field |
\(\frac{\partial B^\zeta}{\partial \theta}\) |
|
toroidal derivative of the toroidal magnetic field |
\(\frac{\partial B^\zeta}{\partial \zeta}\) |
|
radial derivative of the magnetic field |
\(\frac{\partial \mathbf{B}}{\partial \rho}\) |
|
poloidal derivative of the magnetic field |
\(\frac{\partial \mathbf{B}}{\partial \theta}\) |
|
toroidal derivative of the magnetic field |
\(\frac{\partial \mathbf{B}}{\partial \zeta}\) |
|
derivative of the flux-surface averaged poloidal magnetic field |
\(\frac{d\overline{B_\theta}}{d\rho}\) |
|
derivative of the toroidal current enclosed by the flux surface |
\(\frac{dI_\text{tor}}{d\rho}\) |
|
radial derivative of the Jacobian determinant |
\(\frac{\partial \mathcal{J}}{\partial \rho}\) |
|
poloidal derivative of the Jacobian determinant |
\(\frac{\partial \mathcal{J}}{\partial \theta}\) |
|
toroidal derivative of the Jacobian determinant |
\(\frac{\partial \mathcal{J}}{\partial \zeta}\) |
|
radial derivative of the reference Jacobian determinant |
\(\frac{\partial \mathcal{J}_h}{\partial \rho}\) |
|
poloidal derivative of the reference Jacobian determinant |
\(\frac{\partial \mathcal{J}_h}{\partial \theta}\) |
|
toroidal derivative of the reference Jacobian determinant |
\(\frac{\partial \mathcal{J}_h}{\partial \zeta}\) |
|
radial derivative of the logical Jacobian determinant |
\(\frac{\partial \mathcal{J}_l}{\partial \rho}\) |
|
poloidal derivative of the logical Jacobian determinant |
\(\frac{\partial \mathcal{J}_l}{\partial \theta}\) |
|
toroidal derivative of the logical Jacobian determinant |
\(\frac{\partial \mathcal{J}_l}{\partial \zeta}\) |
|
radial derivative of the straight field line potential |
\(\frac{\partial \lambda}{\partial \rho}\) |
|
second radial derivative of the straight field line potential |
\(\frac{\partial^2 \lambda}{\partial \rho^2}\) |
|
radial-poloidal derivative of the straight field line potential |
\(\frac{\partial^2 \lambda}{\partial \rho\partial \theta}\) |
|
radial-toroidal derivative of the straight field line potential |
\(\frac{\partial^2 \lambda}{\partial \rho\partial \zeta}\) |
|
poloidal derivative of the straight field line potential |
\(\frac{\partial \lambda}{\partial \theta}\) |
|
second poloidal derivative of the straight field line potential |
\(\frac{\partial^2 \lambda}{\partial \theta^2}\) |
|
poloidal-toroidal derivative of the straight field line potential |
\(\frac{\partial^2 \lambda}{\partial \theta\partial \zeta}\) |
|
toroidal derivative of the straight field line potential |
\(\frac{\partial \lambda}{\partial \zeta}\) |
|
second toroidal derivative of the straight field line potential |
\(\frac{\partial^2 \lambda}{\partial \zeta^2}\) |
|
poloidal derivative of the Boozer potential computed from the magnetic field |
\(\left.\frac{\partial \nu_B}{\partial \theta}\right|_\text{def.}\) |
|
toroidal derivative of the Boozer potential computed from the magnetic field |
\(\left.\frac{\partial \nu_B}{\partial \zeta}\right|_\text{def.}\) |
|
toroidal magnetic flux gradient |
\(\frac{d\Phi}{d\rho}\) |
|
toroidal magnetic flux curvature |
\(\frac{d^2\Phi}{d\rho^2}\) |
|
derivative of the plasma volume w.r.t. normalized toroidal magnetic flux |
\(\frac{dV}{d\Phi_n}\) |
|
second derivative of the plasma volume w.r.t. normalized toroidal magnetic flux |
\(\frac{d^2V}{d\Phi_n^2}\) |
|
radial derivative of the first reference coordinate |
\(\frac{\partial X^1}{\partial \rho}\) |
|
second radial derivative of the first reference coordinate |
\(\frac{\partial^2 X^1}{\partial \rho^2}\) |
|
radial-poloidal derivative of the first reference coordinate |
\(\frac{\partial^2 X^1}{\partial \rho\partial \theta}\) |
|
radial-toroidal derivative of the first reference coordinate |
\(\frac{\partial^2 X^1}{\partial \rho\partial \zeta}\) |
|
poloidal derivative of the first reference coordinate |
\(\frac{\partial X^1}{\partial \theta}\) |
|
second poloidal derivative of the first reference coordinate |
\(\frac{\partial^2 X^1}{\partial \theta^2}\) |
|
poloidal-toroidal derivative of the first reference coordinate |
\(\frac{\partial^2 X^1}{\partial \theta\partial \zeta}\) |
|
toroidal derivative of the first reference coordinate |
\(\frac{\partial X^1}{\partial \zeta}\) |
|
second toroidal derivative of the first reference coordinate |
\(\frac{\partial^2 X^1}{\partial \zeta^2}\) |
|
radial derivative of the second reference coordinate |
\(\frac{\partial X^2}{\partial \rho}\) |
|
second radial derivative of the second reference coordinate |
\(\frac{\partial^2 X^2}{\partial \rho^2}\) |
|
radial-poloidal derivative of the second reference coordinate |
\(\frac{\partial^2 X^2}{\partial \rho\partial \theta}\) |
|
radial-toroidal derivative of the second reference coordinate |
\(\frac{\partial^2 X^2}{\partial \rho\partial \zeta}\) |
|
poloidal derivative of the second reference coordinate |
\(\frac{\partial X^2}{\partial \theta}\) |
|
second poloidal derivative of the second reference coordinate |
\(\frac{\partial^2 X^2}{\partial \theta^2}\) |
|
poloidal-toroidal derivative of the second reference coordinate |
\(\frac{\partial^2 X^2}{\partial \theta\partial \zeta}\) |
|
toroidal derivative of the second reference coordinate |
\(\frac{\partial X^2}{\partial \zeta}\) |
|
second toroidal derivative of the second reference coordinate |
\(\frac{\partial^2 X^2}{\partial \zeta^2}\) |
|
poloidal magnetic flux gradient |
\(\frac{d\chi}{d\rho}\) |
|
poloidal magnetic flux curvature |
\(\frac{d^2\chi}{d\rho^2}\) |
|
radial derivative of the rr component of the metric tensor |
\(\frac{\partial g_{\rho\rho}}{\partial \rho}\) |
|
poloidal derivative of the rr component of the metric tensor |
\(\frac{\partial g_{\rho\rho}}{\partial \theta}\) |
|
toroidal derivative of the rr component of the metric tensor |
\(\frac{\partial g_{\rho\rho}}{\partial \zeta}\) |
|
radial derivative of the rt component of the metric tensor |
\(\frac{\partial g_{\rho\theta}}{\partial \rho}\) |
|
poloidal derivative of the rt component of the metric tensor |
\(\frac{\partial g_{\rho\theta}}{\partial \theta}\) |
|
toroidal derivative of the rt component of the metric tensor |
\(\frac{\partial g_{\rho\theta}}{\partial \zeta}\) |
|
radial derivative of the rz component of the metric tensor |
\(\frac{\partial g_{\rho\zeta}}{\partial \rho}\) |
|
poloidal derivative of the rz component of the metric tensor |
\(\frac{\partial g_{\rho\zeta}}{\partial \theta}\) |
|
toroidal derivative of the rz component of the metric tensor |
\(\frac{\partial g_{\rho\zeta}}{\partial \zeta}\) |
|
radial derivative of the tt component of the metric tensor |
\(\frac{\partial g_{\theta\theta}}{\partial \rho}\) |
|
poloidal derivative of the tt component of the metric tensor |
\(\frac{\partial g_{\theta\theta}}{\partial \theta}\) |
|
toroidal derivative of the tt component of the metric tensor |
\(\frac{\partial g_{\theta\theta}}{\partial \zeta}\) |
|
radial derivative of the tz component of the metric tensor |
\(\frac{\partial g_{\theta\zeta}}{\partial \rho}\) |
|
poloidal derivative of the tz component of the metric tensor |
\(\frac{\partial g_{\theta\zeta}}{\partial \theta}\) |
|
toroidal derivative of the tz component of the metric tensor |
\(\frac{\partial g_{\theta\zeta}}{\partial \zeta}\) |
|
radial derivative of the zz component of the metric tensor |
\(\frac{\partial g_{\zeta\zeta}}{\partial \rho}\) |
|
poloidal derivative of the zz component of the metric tensor |
\(\frac{\partial g_{\zeta\zeta}}{\partial \theta}\) |
|
toroidal derivative of the zz component of the metric tensor |
\(\frac{\partial g_{\zeta\zeta}}{\partial \zeta}\) |
|
rotational transform gradient |
\(\frac{d\iota}{d\rho}\) |
|
rotational transform curvature |
\(\frac{d^2\iota}{d\rho^2}\) |
|
radial derivative of the modulus of the magnetic field |
\(\frac{\partial \left|\mathbf{B}\right|}{\partial \rho}\) |
|
radial Boozer derivative of the modulus of the magnetic field |
\(\frac{\partial\left|\mathbf{B}\right|}{\partial \rho_B}\) |
|
poloidal derivative of the modulus of the magnetic field |
\(\frac{\partial \left|\mathbf{B}\right|}{\partial \theta}\) |
|
poloidal Boozer derivative of the modulus of the magnetic field |
\(\frac{\partial\left|\mathbf{B}\right|}{\partial \theta_B}\) |
|
toroidal derivative of the modulus of the magnetic field |
\(\frac{\partial \left|\mathbf{B}\right|}{\partial \zeta}\) |
|
toroidal Boozer derivative of the modulus of the magnetic field |
\(\frac{\partial\left|\mathbf{B}\right|}{\partial \zeta_B}\) |
|
pressure gradient |
\(\frac{dp}{d\rho}\) |
|
pressure curvature |
\(\frac{d^2p}{d\rho^2}\) |
|
first reference tangent basis vector |
\(\mathbf{e}_{q^1}\) |
|
second reference tangent basis vector |
\(\mathbf{e}_{q^2}\) |
|
toroidal reference tangent basis vector |
\(\mathbf{e}_{q^3}\) |
|
radial tangent basis vector |
\(\mathbf{e}_\rho\) |
|
radial tangent basis vector in Boozer coordinates |
\(\mathbf{e}_{\rho_B}\) |
|
poloidal tangent basis vector in PEST coordinates |
\(\mathbf{e}_{\theta_P}\) |
|
poloidal tangent basis vector |
\(\mathbf{e}_\theta\) |
|
poloidal tangent basis vector in Boozer coordinates |
\(\mathbf{e}_{\theta_B}\) |
|
poloidal tangent basis vector in PEST coordinates |
\(\mathbf{e}_{\theta_P}\) |
|
toroidal tangent basis vector |
\(\mathbf{e}_\zeta\) |
|
toroidal tangent basis vector in Boozer coordinates |
\(\mathbf{e}_{\zeta_B}\) |
|
toroidal tangent basis vector in PEST coordinates |
\(\mathbf{e}_{\zeta_P}\) |
|
effective elongation |
\(E_\text{eff}\) |
|
rr component of the metric tensor |
\(g_{\rho\rho}\) |
|
rr component of the metric tensor in Boozer coordinates |
\(g_{\rho_B \rho_B}\) |
|
rr component of the metric tensor in PEST coordinates |
\(g_{\rho_P \rho_P}\) |
|
rt component of the metric tensor |
\(g_{\rho\theta}\) |
|
rt component of the metric tensor in Boozer coordinates |
\(g_{\rho_B \theta_B}\) |
|
rt component of the metric tensor in PEST coordinates |
\(g_{\rho_P \theta_P}\) |
|
rz component of the metric tensor |
\(g_{\rho\zeta}\) |
|
rz component of the metric tensor in Boozer coordinates |
\(g_{\rho_B \zeta_B}\) |
|
rz component of the metric tensor in PEST coordinates |
\(g_{\rho_P \zeta_P}\) |
|
tt component of the metric tensor |
\(g_{\theta\theta}\) |
|
tt component of the metric tensor in Boozer coordinates |
\(g_{\theta_B \theta_B}\) |
|
tt component of the metric tensor in PEST coordinates |
\(g_{\theta_P \theta_P}\) |
|
tz component of the metric tensor |
\(g_{\theta\zeta}\) |
|
tz component of the metric tensor in Boozer coordinates |
\(g_{\theta_B \zeta_B}\) |
|
tz component of the metric tensor in PEST coordinates |
\(g_{\theta_P \zeta_P}\) |
|
zz component of the metric tensor |
\(g_{\zeta\zeta}\) |
|
zz component of the metric tensor in Boozer coordinates |
\(g_{\zeta_B \zeta_B}\) |
|
zz component of the metric tensor in PEST coordinates |
\(g_{\zeta_P \zeta_P}\) |
|
adiabatic index |
\(\gamma\) |
|
gradient of the modulus of the magnetic field |
\(\nabla\left|\mathbf{B}\right|\) |
|
radial reciprocal basis vector |
\(\nabla\rho\) |
|
poloidal reciprocal basis vector |
\(\nabla\theta\) |
|
poloidal reciprocal basis vector in Boozer coordinates |
\(\nabla\theta_B\) |
|
poloidal reciprocal basis vector in PEST coordinates |
\(\nabla \theta_P\) |
|
toroidal reciprocal basis vector |
\(\nabla\zeta\) |
|
toroidal reciprocal basis vector in Boozer coordinates |
\(\nabla\zeta_B\) |
|
rotational transform |
\(\iota\) |
|
geometric contribution to the rotational transform |
\(\iota_0\) |
|
average rotational transform |
\(\overline{\iota}\) |
|
rotational transform averaged over rho^2 |
\(\overline{\iota}_2\) |
|
toroidal current contribution to the rotational transform |
\(\iota_\text{curr}\) |
|
factor to the toroidal current contribution to the rotational transform |
\(\iota_{\text{curr},0}\) |
|
q1-q1 reference curvature vector |
\(k_{q^1q^1}\) |
|
q1-q2 reference curvature vector |
\(k_{q^1q^2}\) |
|
q1-q3 reference curvature vector |
\(k_{q^1q^3}\) |
|
q2-q2 reference curvature vector |
\(k_{q^2q^2}\) |
|
q2-q3 reference curvature vector |
\(k_{q^2q^3}\) |
|
q3-q3 reference curvature vector |
\(k_{q^3q^3}\) |
|
rr logical curvature vector |
\(\mathbf{k}_{\rho\rho}\) |
|
rt logical curvature vector |
\(\mathbf{k}_{\rho\theta}\) |
|
rz logical curvature vector |
\(\mathbf{k}_{\rho\zeta}\) |
|
tt logical curvature vector |
\(\mathbf{k}_{\theta\theta}\) |
|
tt boozer curvature vector |
\(\mathbf{k}_{\theta_B \theta_B}\) |
|
tt PEST curvature vector |
\(\mathbf{k}_{\theta_P \theta_P}\) |
|
tz logical curvature vector |
\(\mathbf{k}_{\theta\zeta}\) |
|
tz boozer curvature vector |
\(\mathbf{k}_{\theta_B \zeta_B}\) |
|
tz PEST curvature vector |
\(\mathbf{k}_{\theta_P \zeta_P}\) |
|
zz logical curvature vector |
\(\mathbf{k}_{\zeta\zeta}\) |
|
zz boozer curvature vector |
\(\mathbf{k}_{\zeta_B \zeta_B}\) |
|
zz PEST curvature vector |
\(\mathbf{k}_{\zeta_P \zeta_P}\) |
|
mirror ratio |
\(\Delta_\text{mirror}\) |
|
modulus of the magnetic field |
\(\left|\mathbf{B}\right|\) |
|
modulus of the MHD force |
\(\left|F\right|\) |
|
modulus of the current density |
\(\left|\mathbf{J}\right|\) |
|
modulus of the radial tangent basis vector |
\(\left|\mathbf{e}_\rho\right|\) |
|
modulus of the poloidal tangent basis vector |
\(\left|\mathbf{e}_\theta\right|\) |
|
modulus of the toroidal tangent basis vector |
\(\left|\mathbf{e}_\zeta\right|\) |
|
modulus of the radial reciprocal basis vector |
\(\left|\nabla\rho\right|\) |
|
modulus of the poloidal reciprocal basis vector |
\(\left|\nabla\theta\right|\) |
|
modulus of the toroidal reciprocal basis vector |
\(\left|\nabla\zeta\right|\) |
|
magnetic constant |
\(\mu_0\) |
|
surface normal |
\(\mathbf{n}\) |
|
pressure |
\(p\) |
|
position vector |
\(\mathbf{x}\) |
|
effective major radius |
\(r_\text{major,eff}\) |
|
effective minor radius |
\(r_\text{minor,eff}\) |
|
global magnetic shear |
\(s_g\) |
|
average global magnetic shear |
\(\overline{s_g}\) |
|
global magnetic shear averaged over rho^2 |
\(\overline{s_g}_2\) |
|
poloidal angle in PEST coordinates |
\(\theta_P\) |
|
vacuum magnetic well depth |
\(d_\text{well}\) |
|
cartesian vector components |
\((x,y,z)\) |