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
eq.compute()function to return the calculated quantity.Label : TeX label for the variable
Units : physical units for the variable
Description : description of the variable
Module : where in the code the source is defined (mostly for developers)
Name |
Label |
Units |
Description |
Module |
|---|---|---|---|---|
|
\(\mathbf{e}_{\rho}\) |
meters |
Covariant radial basis vector |
|
|
\(\mathbf{e}_{\theta}\) |
meters |
Covariant poloidal basis vector |
|
|
\(\mathbf{e}_{\zeta}\) |
meters |
Covariant toroidal basis vector |
|
|
\(\partial_{\rho} \mathbf{e}_{\rho}\) |
meters |
Covariant radial basis vector, derivative wrt radial coordinate |
|
|
\(\partial_{\theta} \mathbf{e}_{\rho}\) |
meters |
Covariant radial basis vector, derivative wrt poloidal angle |
|
|
\(\partial_{\zeta} \mathbf{e}_{\rho}\) |
meters |
Covariant radial basis vector, derivative wrt toroidal angle |
|
|
\(\partial_{\rho} \mathbf{e}_{\theta}\) |
meters |
Covariant poloidal basis vector, derivative wrt radial coordinate |
|
|
\(\partial_{\theta} \mathbf{e}_{\theta}\) |
meters |
Covariant poloidal basis vector, derivative wrt poloidal angle |
|
|
\(\partial_{\zeta} \mathbf{e}_{\theta}\) |
meters |
Covariant poloidal basis vector, derivative wrt toroidal angle |
|
|
\(\partial_{\rho} \mathbf{e}_{\zeta}\) |
meters |
Covariant toroidal basis vector, derivative wrt radial coordinate |
|
|
\(\partial_{\theta} \mathbf{e}_{\zeta}\) |
meters |
Covariant toroidal basis vector, derivative wrt poloidal angle |
|
|
\(\partial_{\zeta} \mathbf{e}_{\zeta}\) |
meters |
Covariant toroidal basis vector, derivative wrt toroidal angle |
|
|
\(\partial_{\rho \rho} \mathbf{e}_{\rho}\) |
meters |
Covariant radial basis vector, second derivative wrt radial coordinate |
|
|
\(\partial_{\theta \theta} \mathbf{e}_{\rho}\) |
meters |
Covariant radial basis vector, second derivative wrt poloidal angle |
|
|
\(\partial_{\zeta \zeta} \mathbf{e}_{\rho}\) |
meters |
Covariant radial basis vector, second derivative wrt toroidal angle |
|
|
\(\partial_{\rho \theta} \mathbf{e}_{\rho}\) |
meters |
Covariant radial basis vector, second derivative wrt radial coordinate and poloidal angle |
|
|
\(\partial_{\rho \zeta} \mathbf{e}_{\rho}\) |
meters |
Covariant radial basis vector, second derivative wrt radial coordinate and toroidal angle |
|
|
\(\partial_{\theta \zeta} \mathbf{e}_{\rho}\) |
meters |
Covariant radial basis vector, second derivative wrt poloidal and toroidal angles |
|
|
\(\partial_{\rho \rho} \mathbf{e}_{\theta}\) |
meters |
Covariant poloidal basis vector, second derivative wrt radial coordinate |
|
|
\(\partial_{\theta \theta} \mathbf{e}_{\theta}\) |
meters |
Covariant poloidal basis vector, second derivative wrt poloidal angle |
|
|
\(\partial_{\zeta \zeta} \mathbf{e}_{\theta}\) |
meters |
Covariant poloidal basis vector, second derivative wrt toroidal angle |
|
|
\(\partial_{\rho \theta} \mathbf{e}_{\theta}\) |
meters |
Covariant poloidal basis vector, second derivative wrt radial coordinate and poloidal angle |
|
|
\(\partial_{\rho \zeta} \mathbf{e}_{\theta}\) |
meters |
Covariant poloidal basis vector, second derivative wrt radial coordinate and toroidal angle |
|
|
\(\partial_{\theta \zeta} \mathbf{e}_{\theta}\) |
meters |
Covariant poloidal basis vector, second derivative wrt poloidal and toroidal angles |
|
|
\(\partial_{\rho \rho} \mathbf{e}_{\zeta}\) |
meters |
Covariant toroidal basis vector, second derivative wrt radial coordinate |
|
|
\(\partial_{\theta \theta} \mathbf{e}_{\zeta}\) |
meters |
Covariant toroidal basis vector, second derivative wrt poloidal angle |
|
|
\(\partial_{\zeta \zeta} \mathbf{e}_{\zeta}\) |
meters |
Covariant toroidal basis vector, second derivative wrt toroidal angle |
|
|
\(\partial_{\rho \theta} \mathbf{e}_{\zeta}\) |
meters |
Covariant toroidal basis vector, second derivative wrt radial coordinate and poloidal angle |
|
|
\(\partial_{\rho \zeta} \mathbf{e}_{\zeta}\) |
meters |
Covariant toroidal basis vector, second derivative wrt radial coordinate and toroidal angle |
|
|
\(\partial_{\theta \zeta} \mathbf{e}_{\zeta}\) |
meters |
Covariant toroidal basis vector, second derivative wrt poloidal and toroidal angles |
|
|
\(\mathbf{e}_{\theta_{PEST}}\) |
meters |
Covariant straight field line poloidal basis vector |
|
|
\(\mathbf{e}^{\rho}\) |
inverse meters |
Contravariant radial basis vector |
|
|
\(\mathbf{e}^{\theta}\) |
inverse meters |
Contravariant poloidal basis vector |
|
|
\(\mathbf{e}^{\zeta}\) |
inverse meters |
Contravariant toroidal basis vector |
|
|
\(\hat{b}\) |
None |
Unit vector along magnetic field |
|
|
\(\hat{n}\) |
None |
Unit vector normal to flux surface |
|
|
\(\nabla \alpha\) |
Inverse meters |
Unit vector normal to flux surface |
|
|
\(1 - \frac{3}{4} \langle B^2 \rangle \int_0^{1/Bmax} \frac{\lambda\; d\lambda}{\langle \sqrt{1 - \lambda B} \rangle}\) |
None |
Neoclassical effective trapped particle fraction |
|
|
\(\langle\mathbf{J}\cdot\mathbf{B}\rangle_{Redl}\) |
Tesla Ampere / meter^2 |
Bootstrap current profile, Redl model for quasisymmetry |
|
|
\(0\) |
None |
Zeros |
|
|
\(\rho\) |
None |
Radial coordinate, proportional to the square root of the toroidal flux |
|
|
\(\partial_{\rho} \rho\) |
None |
Radial coordinate, proportional to the square root of the toroidal flux, derivative wrt radial coordinate |
|
|
\(\partial_{\theta} \rho\) |
None |
Radial coordinate, proportional to the square root of the toroidal flux, derivative wrt poloidal coordinate |
|
|
\(\partial_{\zeta} \rho\) |
None |
Radial coordinate, proportional to the square root of the toroidal flux, derivative wrt toroidal coordinate |
|
|
\(\theta\) |
radians |
Poloidal angular coordinate (geometric, not magnetic) |
|
|
\(\partial_{\rho} \theta\) |
radians |
Poloidal angular coordinate (geometric, not magnetic), derivative wrt radial coordinate |
|
|
\(\partial_{\theta} \theta\) |
radians |
Poloidal angular coordinate (geometric, not magnetic), derivative wrt poloidal coordinate |
|
|
\(\partial_{\zeta} \theta\) |
radians |
Poloidal angular coordinate (geometric, not magnetic), derivative wrt toroidal coordinate |
|
|
\(\zeta\) |
radians |
Toroidal angular coordinate |
|
|
\(\partial_{\rho} \zeta\) |
radians |
Toroidal angular coordinate derivative, wrt radial coordinate |
|
|
\(\partial_{\theta} \zeta\) |
radians |
Toroidal angular coordinate, derivative wrt poloidal coordinate |
|
|
\(\partial_{\zeta} \zeta\) |
radians |
Toroidal angular coordinate, derivative wrt toroidal coordinate |
|
|
\(\vartheta\) |
radians |
PEST straight field line poloidal angular coordinate |
|
|
\(\partial_{\rho} \vartheta\) |
radians |
PEST straight field line poloidal angular coordinate, derivative wrt radial coordinate |
|
|
\(\partial_{\theta} \vartheta\) |
radians |
PEST straight field line poloidal angular coordinate, derivative wrt poloidal coordinate |
|
|
\(\partial_{\zeta} \vartheta\) |
radians |
PEST straight field line poloidal angular coordinate, derivative wrt toroidal coordinate |
|
|
\(\alpha\) |
None |
Field line label |
|
|
\(\partial_\rho \alpha\) |
None |
Field line label, derivative wrt radial coordinate |
|
|
\(\partial_\theta \alpha\) |
None |
Field line label, derivative wrt poloidal coordinate |
|
|
\(\partial_\zeta \alpha\) |
None |
Field line label, derivative wrt toroidal coordinate |
|
|
\(R\) |
meters |
Major radius in lab frame |
|
|
\(\partial_{\rho} R\) |
meters |
Major radius in lab frame, first radial derivative |
|
|
\(\partial_{\theta} R\) |
meters |
Major radius in lab frame, first poloidal derivative |
|
|
\(\partial_{\zeta} R\) |
meters |
Major radius in lab frame, first toroidal derivative |
|
|
\(\partial_{\rho \rho} R\) |
meters |
Major radius in lab frame, second radial derivative |
|
|
\(\partial_{\theta \theta} R\) |
meters |
Major radius in lab frame, second poloidal derivative |
|
|
\(\partial_{\zeta \zeta} R\) |
meters |
Major radius in lab frame, second toroidal derivative |
|
|
\(\partial_{\rho \theta} R\) |
meters |
Major radius in lab frame, second derivative wrt radius and poloidal angle |
|
|
\(\partial_{\rho \zeta} R\) |
meters |
Major radius in lab frame, second derivative wrt radius and toroidal angle |
|
|
\(\partial_{\theta \zeta} R\) |
meters |
Major radius in lab frame, second derivative wrt poloidal and toroidal angles |
|
|
\(\partial_{ ho \rho \rho} R\) |
meters |
Major radius in lab frame, third radial derivative |
|
|
\(\partial_{\theta \theta \theta} R\) |
meters |
Major radius in lab frame, third poloidal derivative |
|
|
\(\partial_{\zeta \zeta \zeta} R\) |
meters |
Major radius in lab frame, third toroidal derivative |
|
|
\(\partial_{\rho \rho \theta} R\) |
meters |
Major radius in lab frame, third derivative, wrt radius twice and poloidal angle |
|
|
\(\partial_{\rho \theta \theta} R\) |
meters |
Major radius in lab frame, third derivative wrt radius and poloidal angle twice |
|
|
\(\partial_{\rho \rho \zeta} R\) |
meters |
Major radius in lab frame, third derivative, wrt radius twice and toroidal angle |
|
|
\(\partial_{\rho \zeta \zeta} R\) |
meters |
Major radius in lab frame, third derivative wrt radius and toroidal angle twice |
|
|
\(\partial_{\theta \theta \zeta} R\) |
meters |
Major radius in lab frame, third derivative wrt poloidal angle twice and toroidal angle |
|
|
\(\partial_{\theta \zeta \zeta} R\) |
meters |
Major radius in lab frame, third derivative wrt poloidal angle and toroidal angle twice |
|
|
\(\partial_{\rho \theta \zeta} R\) |
meters |
Major radius in lab frame, third derivative wrt radius, poloidal angle, and toroidal angle |
|
|
\(Z\) |
meters |
Vertical coordinate in lab frame |
|
|
\(\partial_{\rho} Z\) |
meters |
Vertical coordinate in lab frame, first radial derivative |
|
|
\(\partial_{\theta} Z\) |
meters |
Vertical coordinate in lab frame, first poloidal derivative |
|
|
\(\partial_{\zeta} Z\) |
meters |
Vertical coordinate in lab frame, first toroidal derivative |
|
|
\(\partial_{\rho \rho} Z\) |
meters |
Vertical coordinate in lab frame, second radial derivative |
|
|
\(\partial_{\theta \theta} Z\) |
meters |
Vertical coordinate in lab frame, second poloidal derivative |
|
|
\(\partial_{\zeta \zeta} Z\) |
meters |
Vertical coordinate in lab frame, second toroidal derivative |
|
|
\(\partial_{\rho \theta} Z\) |
meters |
Vertical coordinate in lab frame, second derivative wrt radius and poloidal angle |
|
|
\(\partial_{\rho \zeta} Z\) |
meters |
Vertical coordinate in lab frame, second derivative wrt radius and toroidal angle |
|
|
\(\partial_{\theta \zeta} Z\) |
meters |
Vertical coordinate in lab frame, second derivative wrt poloidal and toroidal angles |
|
|
\(\partial_{ ho \rho \rho} Z\) |
meters |
Vertical coordinate in lab frame, third radial derivative |
|
|
\(\partial_{\theta \theta \theta} Z\) |
meters |
Vertical coordinate in lab frame, third poloidal derivative |
|
|
\(\partial_{\zeta \zeta \zeta} Z\) |
meters |
Vertical coordinate in lab frame, third toroidal derivative |
|
|
\(\partial_{\rho \rho \theta} Z\) |
meters |
Vertical coordinate in lab frame, third derivative, wrt radius twice and poloidal angle |
|
|
\(\partial_{\rho \theta \theta} Z\) |
meters |
Vertical coordinate in lab frame, third derivative wrt radius and poloidal angle twice |
|
|
\(\partial_{\rho \rho \zeta} Z\) |
meters |
Vertical coordinate in lab frame, third derivative, wrt radius twice and toroidal angle |
|
|
\(\partial_{\rho \zeta \zeta} Z\) |
meters |
Vertical coordinate in lab frame, third derivative wrt radius and toroidal angle twice |
|
|
\(\partial_{\theta \theta \zeta} Z\) |
meters |
Vertical coordinate in lab frame, third derivative wrt poloidal angle twice and toroidal angle |
|
|
\(\partial_{\theta \zeta \zeta} Z\) |
meters |
Vertical coordinate in lab frame, third derivative wrt poloidal angle and toroidal angle twice |
|
|
\(\partial_{\rho \theta \zeta} Z\) |
meters |
Vertical coordinate in lab frame, third derivative wrt radius, poloidal angle, and toroidal angle |
|
|
\(\phi\) |
radians |
Toroidal angle in lab frame |
|
|
\(\partial_{\rho} \phi\) |
radians |
Toroidal angle in lab frame, derivative wrt radial coordinate |
|
|
\(\partial_{\theta} \phi\) |
radians |
Toroidal angle in lab frame, derivative wrt poloidal coordinate |
|
|
\(\partial_{\zeta} \phi\) |
radians |
Toroidal angle in lab frame, derivative wrt toroidal coordinate |
|
|
\(\partial_{\rho \rho} \phi\) |
radians |
Toroidal angle in lab frame, second derivative wrt radial coordinate |
|
|
\(\partial_{\rho \theta} \phi\) |
radians |
Toroidal angle in lab frame, second derivative wrt radial and poloidal coordinate |
|
|
\(\partial_{\rho \zeta} \phi\) |
radians |
Toroidal angle in lab frame, second derivative wrt radial and toroidal coordinate |
|
|
\(\partial_{\theta \theta} \phi\) |
radians |
Toroidal angle in lab frame, second derivative wrt poloidal coordinate |
|
|
\(\partial_{\theta \zeta} \phi\) |
radians |
Toroidal angle in lab frame, second derivative wrt poloidal and toroidal coordinate |
|
|
\(\partial_{\zeta \zeta} \phi\) |
radians |
Toroidal angle in lab frame, second derivative wrt toroidal coordinate |
|
|
\(X = R \cos{\phi}\) |
meters |
Cartesian X coordinate |
|
|
\(\partial_{\rho} X\) |
meters |
Cartesian X coordinate, derivative wrt radial coordinate |
|
|
\(\partial_{\theta} X\) |
meters |
Cartesian X coordinate, derivative wrt poloidal coordinate |
|
|
\(\partial_{\zeta} X\) |
meters |
Cartesian X coordinate, derivative wrt toroidal coordinate |
|
|
\(Y = R \sin{\phi}\) |
meters |
Cartesian Y coordinate |
|
|
\(\partial_{\rho} Y\) |
meters |
Cartesian Y coordinate, derivative wrt radial coordinate |
|
|
\(\partial_{\theta} Y\) |
meters |
Cartesian Y coordinate, derivative wrt poloidal coordinate |
|
|
\(\partial_{\zeta} Y\) |
meters |
Cartesian Y coordinate, derivative wrt toroidal coordinate |
|
|
\(\lambda\) |
radians |
Poloidal stream function |
|
|
\(\partial_{\rho} \lambda\) |
radians |
Poloidal stream function, first radial derivative |
|
|
\(\partial_{\theta} \lambda\) |
radians |
Poloidal stream function, first poloidal derivative |
|
|
\(\partial_{\zeta} \lambda\) |
radians |
Poloidal stream function, first toroidal derivative |
|
|
\(\partial_{\rho \rho} \lambda\) |
radians |
Poloidal stream function, second radial derivative |
|
|
\(\partial_{\theta \theta} \lambda\) |
radians |
Poloidal stream function, second poloidal derivative |
|
|
\(\partial_{\zeta \zeta} \lambda\) |
radians |
Poloidal stream function, second toroidal derivative |
|
|
\(\partial_{\rho \theta} \lambda\) |
radians |
Poloidal stream function, second derivative wrt radius and poloidal angle |
|
|
\(\partial_{\rho \zeta} \lambda\) |
radians |
Poloidal stream function, second derivative wrt radius and toroidal angle |
|
|
\(\partial_{\theta \zeta} \lambda\) |
radians |
Poloidal stream function, second derivative wrt poloidal and toroidal angles |
|
|
\(\partial_{ ho \rho \rho} \lambda\) |
radians |
Poloidal stream function, third radial derivative |
|
|
\(\partial_{\theta \theta \theta} \lambda\) |
radians |
Poloidal stream function, third poloidal derivative |
|
|
\(\partial_{\zeta \zeta \zeta} \lambda\) |
radians |
Poloidal stream function, third toroidal derivative |
|
|
\(\partial_{\rho \rho \theta} \lambda\) |
radians |
Poloidal stream function, third derivative, wrt radius twice and poloidal angle |
|
|
\(\partial_{\rho \theta \theta} \lambda\) |
radians |
Poloidal stream function, third derivative wrt radius and poloidal angle twice |
|
|
\(\partial_{\rho \rho \zeta} \lambda\) |
radians |
Poloidal stream function, third derivative, wrt radius twice and toroidal angle |
|
|
\(\partial_{\rho \zeta \zeta} \lambda\) |
radians |
Poloidal stream function, third derivative wrt radius and toroidal angle twice |
|
|
\(\partial_{\theta \theta \zeta} \lambda\) |
radians |
Poloidal stream function, third derivative wrt poloidal angle twice and toroidal angle |
|
|
\(\partial_{\theta \zeta \zeta} \lambda\) |
radians |
Poloidal stream function, third derivative wrt poloidal angle and toroidal angle twice |
|
|
\(\partial_{\rho \theta \zeta} \lambda\) |
radians |
Poloidal stream function, third derivative wrt radius, poloidal angle, and toroidal angle |
|
|
\(J^{\rho}\) |
Amperes / cubic meter |
Contravariant radial component of plasma current density |
|
|
\(J^{\theta}\) |
Amperes / cubic meter |
Contravariant poloidal component of plasma current density |
|
|
\(J^{\zeta}\) |
Amperes / cubic meter |
Contravariant toroidal component of plasma current density |
|
|
\(\mathbf{J}\) |
Amperes / square meter |
Plasma current density |
|
|
\(J_{R}\) |
Amperes / square meter |
Radial componenet of plasma current density in lab frame |
|
|
\(J_{\phi}\) |
Amperes / square meter |
Toroidal componenet of plasma current density in lab frame |
|
|
\(J_{Z}\) |
Amperes / square meter |
Vertical componenet of plasma current density in lab frame |
|
|
\(|\mathbf{J}|\) |
Amperes / square meter |
Magnitue of plasma current density |
|
|
\(J_{\rho}\) |
Amperes / meter |
Covariant radial component of plasma current density |
|
|
\(J_{\theta}\) |
Amperes / meter |
Covariant poloidal component of plasma current density |
|
|
\(J_{\zeta}\) |
Amperes / meter |
Covariant toroidal component of plasma current density |
|
|
\(\mathbf{J} \cdot \mathbf{B}\) |
Newtons / cubic meter |
Current density parallel to magnetic field, times field strength (note units are not Amperes) |
|
|
\(\langle \mathbf{J} \cdot \mathbf{B} \rangle\) |
Newtons / cubic meter |
Flux surface average of current density dotted into magnetic field |
|
|
\(\mathbf{J} \cdot \hat{\mathbf{b}}\) |
Amperes / square meter |
Plasma current density parallel to magnetic field |
|
|
\(F_{\rho}\) |
Newtons / square meter |
Covariant radial component of force balance error |
|
|
\(F_{\theta}\) |
Newtons / square meter |
Covariant poloidal component of force balance error |
|
|
\(F_{\zeta}\) |
Newtons / square meter |
Covariant toroidal component of force balance error |
|
|
\(F_{helical}\) |
Newtons / square meter |
Covariant helical component of force balance error |
|
|
\(\mathbf{J} \times \mathbf{B} - \nabla p\) |
Newtons / cubic meter |
Force balance error |
|
|
\(|\mathbf{J} \times \mathbf{B} - \nabla p|\) |
Newtons / cubic meter |
Magnitude of force balance error |
|
|
\(\langle |\mathbf{J} \times \mathbf{B} - \nabla p| \rangle_{vol}\) |
Newtons / cubic meter |
Volume average of magnitude of force balance error |
|
|
\(B^{\theta} \nabla \zeta - B^{\zeta} \nabla \theta\) |
Tesla / square meter |
Helical basis vector |
|
|
\(|B^{\theta} \nabla \zeta - B^{\zeta} \nabla \theta|\) |
Tesla / square meter |
Magnitude of helical basis vector |
|
|
\(W_B\) |
Joules |
Plasma magnetic energy |
|
|
\(W_{B,pol}\) |
Joules |
Plasma magnetic energy in poloidal field |
|
|
\(W_{B,tor}\) |
Joules |
Plasma magnetic energy in toroidal field |
|
|
\(W_p\) |
Joules |
Plasma thermodynamic energy |
|
|
\(W\) |
Joules |
Plasma total energy |
|
|
\(\langle \beta \rangle_{vol}\) |
None |
Normalized plasma pressure |
|
|
\(\langle \beta_{pol} \rangle_{vol}\) |
None |
Normalized poloidal plasma pressure |
|
|
\(\langle \beta_{tor} \rangle_{vol}\) |
None |
Normalized toroidal plasma pressure |
|
|
\(\partial_{\rho} \psi / \sqrt{g}\) |
Tesla / meter |
|
|
|
\(B^{\rho}\) |
Tesla / meter |
Contravariant radial component of magnetic field |
|
|
\(B^{\theta}\) |
Tesla / meter |
Contravariant poloidal component of magnetic field |
|
|
\(B^{\zeta}\) |
Tesla / meter |
Contravariant toroidal component of magnetic field |
|
|
\(B\) |
Tesla |
Magnetic field |
|
|
\(B_{R}\) |
Tesla |
Radial component of magnetic field in lab frame |
|
|
\(B_{\phi}\) |
Tesla |
Toroidal component of magnetic field in lab frame |
|
|
\(B_{Z}\) |
Tesla |
Vertical component of magnetic field in lab frame |
|
|
\(\partial_{\rho \rho} \psi / \sqrt{g} - \partial_{\rho} \psi \partial_{\rho} \sqrt{g} / g\) |
Tesla / meter |
|
|
|
\(\partial_{\rho} B^{\theta}\) |
Tesla / meter |
Contravariant poloidal component of magnetic field, derivative wrt radial coordinate |
|
|
\(\partial_{\rho} B^{\zeta}\) |
Tesla / meter |
Contravariant toroidal component of magnetic field, derivative wrt radial coordinate |
|
|
\(\partial_{\rho} \mathbf{B}\) |
Tesla |
Magnetic field, derivative wrt radial coordinate |
|
|
\(-\partial_{\rho} \psi \partial_{\theta} \sqrt{g} / g\) |
Tesla / meter |
|
|
|
\(\partial_{\theta} B^{\theta}\) |
Tesla / meter |
Contravariant poloidal component of magnetic field, derivative wrt poloidal angle |
|
|
\(\partial_{\theta} B^{\zeta}\) |
Tesla / meter |
Contravariant toroidal component of magnetic field, derivative wrt poloidal angle |
|
|
\(\partial_{\theta} \mathbf{B}\) |
Tesla |
Magnetic field, derivative wrt poloidal angle |
|
|
\(-\partial_{\rho} \psi \partial_{\zeta} \sqrt{g} / g\) |
Tesla / meter |
|
|
|
\(\partial_{\zeta} B^{\theta}\) |
Tesla / meter |
Contravariant poloidal component of magnetic field, derivative wrt toroidal angle |
|
|
\(\partial_{\zeta} B^{\zeta}\) |
Tesla / meter |
Contravariant toroidal component of magnetic field, derivative wrt toroidal angle |
|
|
\(\partial_{\zeta} \mathbf{B}\) |
Tesla |
Magnetic field, derivative wrt toroidal angle |
|
|
\(\psi''' / \sqrt{g} - 2 \psi'' \partial_{\rho} \sqrt{g} / g - \psi' \partial_{\rho\rho} \sqrt{g} / g + 2 \psi' (\partial_{\rho} \sqrt{g})^2 / (\sqrt{g})^3\) |
Tesla / meters |
|
|
|
\(\partial_{\rho\rho} B^{\theta}\) |
Tesla / meters |
Contravariant poloidal component of magnetic field, second derivative wrt radial coordinate |
|
|
\(\partial_{\rho\rho} B^{\zeta}\) |
Tesla / meters |
Contravariant toroidal component of magnetic field, second derivative wrt radial coordinate |
|
|
\(\partial_{\rho\rho} \mathbf{B}\) |
Tesla |
Magnetic field, second derivative wrt radial coordinate |
|
|
\(-\partial_{\rho} \psi \partial_{\theta\theta} \sqrt{g} / g + 2 \partial_{\rho} \psi (\partial_{\theta} \sqrt{g})^2 / (\sqrt{g})^{3}\) |
Tesla / meter |
|
|
|
\(\partial_{\theta\theta} B^{\theta}\) |
Tesla / meter |
Contravariant poloidal component of magnetic field, second derivative wrt poloidal angle |
|
|
\(\partial_{\theta\theta} B^{\zeta}\) |
Tesla / meter |
Contravariant toroidal component of magnetic field, second derivative wrt poloidal angle |
|
|
\(\partial_{\theta\theta} \mathbf{B}\) |
Tesla |
Magnetic field, second derivative wrt poloidal angle |
|
|
\(-\partial_{\rho} \psi \partial_{\zeta\zeta} \sqrt{g} / g + 2 \partial_{\rho} \psi (\partial_{\zeta} \sqrt{g})^2 / (\sqrt{g})^{3}\) |
Tesla / meter |
|
|
|
\(\partial_{\zeta\zeta} B^{\theta}\) |
Tesla / meter |
Contravariant poloidal component of magnetic field, second derivative wrt toroidal angle |
|
|
\(\partial_{\zeta\zeta} B^{\zeta}\) |
Tesla / meter |
Contravariant toroidal component of magnetic field, second derivative wrt toroidal angle |
|
|
\(\partial_{\zeta\zeta} \mathbf{B}\) |
Tesla |
Magnetic field, second derivative wrt toroidal angle |
|
|
\(\psi'' \partial_{\theta} \sqrt{g} / g + \psi' \partial_{\rho\theta} \sqrt{g} / g + 2 \psi' \partial_{\rho} \sqrt{g} \partial_{\theta} \sqrt{g} / (\sqrt{g})^3\) |
Tesla / meters |
|
|
|
\(\partial_{\rho\theta} B^{\theta}\) |
Tesla / meters |
Contravariant poloidal component of magnetic field, second derivative wrt radial coordinate and poloidal angle |
|
|
\(\partial_{\rho\theta} B^{\zeta}\) |
Tesla / meters |
Contravariant toroidal component of magnetic field, second derivative wrt radial coordinate and poloidal angle |
|
|
\(\partial_{\rho\theta} \mathbf{B}\) |
Tesla |
Magnetic field, second derivative wrt radial coordinate and poloidal angle |
|
|
\(-\partial_{\rho} \psi \partial_{\theta\zeta} \sqrt{g} / g + 2 \partial_{\rho} \psi \partial_{\theta} \sqrt{g} \partial_{\zeta} \sqrt{g} / (\sqrt{g})^{3}\) |
Tesla / meter |
|
|
|
\(\partial_{\theta\zeta} B^{\theta}\) |
Tesla / meter |
Contravariant poloidal component of magnetic field, second derivative wrt poloidal and toroidal angles |
|
|
\(\partial_{\theta\zeta} B^{\zeta}\) |
Tesla / meter |
Contravariant toroidal component of magnetic field, second derivative wrt poloidal and toroidal angles |
|
|
\(\partial_{\theta\zeta} \mathbf{B}\) |
Tesla |
Magnetic field, second derivative wrt poloidal and toroidal angles |
|
|
\(\psi'' \partial_{\zeta} \sqrt{g} / g + \psi' \partial_{\rho\zeta} \sqrt{g} / g + 2 \psi' \partial_{\rho} \sqrt{g} \partial_{\zeta} \sqrt{g} / (\sqrt{g})^3\) |
Tesla / meters |
|
|
|
\(\partial_{\rho\zeta} B^{\theta}\) |
Tesla / meters |
Contravariant poloidal component of magnetic field, second derivative wrt radial coordinate and toroidal angle |
|
|
\(\partial_{\rho\zeta} B^{\zeta}\) |
Tesla / meters |
Contravariant toroidal component of magnetic field, second derivative wrt radial coordinate and toroidal angle |
|
|
\(\partial_{\rho\zeta} \mathbf{B}\) |
Tesla |
Magnetic field, second derivative wrt radial coordinate and toroidal angle |
|
|
\(B_{\rho}\) |
Tesla * meters |
Covariant radial component of magnetic field |
|
|
\(B_{\theta}\) |
Tesla * meters |
Covariant poloidal component of magnetic field |
|
|
\(B_{\zeta}\) |
Tesla * meters |
Covariant toroidal component of magnetic field |
|
|
\(\partial_{\rho} B_{\rho}\) |
Tesla * meters |
Covariant radial component of magnetic field, derivative wrt radial coordinate |
|
|
\(\partial_{\rho} B_{\theta}\) |
Tesla * meters |
Covariant poloidal component of magnetic field, derivative wrt radial coordinate |
|
|
\(\partial_{\rho} B_{\zeta}\) |
Tesla * meters |
Covariant toroidal component of magnetic field, derivative wrt radial coordinate |
|
|
\(\partial_{\theta} B_{\rho}\) |
Tesla * meters |
Covariant radial component of magnetic field, derivative wrt poloidal angle |
|
|
\(\partial_{\theta} B_{\theta}\) |
Tesla * meters |
Covariant poloidal component of magnetic field, derivative wrt poloidal angle |
|
|
\(\partial_{\theta} B_{\zeta}\) |
Tesla * meters |
Covariant toroidal component of magnetic field, derivative wrt poloidal angle |
|
|
\(\partial_{\zeta} B_{\rho}\) |
Tesla * meters |
Covariant radial component of magnetic field, derivative wrt toroidal angle |
|
|
\(\partial_{\zeta} B_{\theta}\) |
Tesla * meters |
Covariant poloidal component of magnetic field, derivative wrt toroidal angle |
|
|
\(\partial_{\zeta} B_{\zeta}\) |
Tesla * meters |
Covariant toroidal component of magnetic field, derivative wrt toroidal angle |
|
|
\(\partial_{\rho\rho} B_{\rho}\) |
Tesla * meters |
Covariant radial component of magnetic field, second derivative wrt radial coordinate |
|
|
\(\partial_{\rho\rho} B_{\theta}\) |
Tesla * meters |
Covariant poloidal component of magnetic field, second derivative wrt radial coordinate |
|
|
\(\partial_{\rho\rho} B_{\zeta}\) |
Tesla * meters |
Covariant toroidal component of magnetic field, second derivative wrt radial coordinate |
|
|
\(\partial_{\theta\theta} B_{\rho}\) |
Tesla * meters |
Covariant radial component of magnetic field, second derivative wrt poloidal angle |
|
|
\(\partial_{\theta\theta} B_{\theta}\) |
Tesla * meters |
Covariant poloidal component of magnetic field, second derivative wrt poloidal angle |
|
|
\(\partial_{\theta\theta} B_{\zeta}\) |
Tesla * meters |
Covariant toroidal component of magnetic field, second derivative wrt poloidal angle |
|
|
\(\partial_{\zeta\zeta} B_{\rho}\) |
Tesla * meters |
Covariant radial component of magnetic field, second derivative wrt toroidal angle |
|
|
\(\partial_{\zeta\zeta} B_{\theta}\) |
Tesla * meters |
Covariant poloidal component of magnetic field, second derivative wrt toroidal angle |
|
|
\(\partial_{\zeta\zeta} B_{\zeta}\) |
Tesla * meters |
Covariant toroidal component of magnetic field, second derivative wrt toroidal angle |
|
|
\(\partial_{\rho\theta} B_{\rho}\) |
Tesla * meters |
Covariant radial component of magnetic field, second derivative wrt radial coordinate and poloidal angle |
|
|
\(\partial_{\rho\theta} B_{\theta}\) |
Tesla * meters |
Covariant poloidal component of magnetic field, second derivative wrt radial coordinate and poloidal angle |
|
|
\(\partial_{\rho\theta} B_{\zeta}\) |
Tesla * meters |
Covariant toroidal component of magnetic field, second derivative wrt radial coordinate and poloidal angle |
|
|
\(\partial_{\theta\zeta} B_{\rho}\) |
Tesla * meters |
Covariant radial component of magnetic field, second derivative wrt poloidal and toroidal angles |
|
|
\(\partial_{\theta\zeta} B_{\theta}\) |
Tesla * meters |
Covariant poloidal component of magnetic field, second derivative wrt poloidal and toroidal angles |
|
|
\(\partial_{\theta\zeta} B_{\zeta}\) |
Tesla * meters |
Covariant toroidal component of magnetic field, second derivative wrt poloidal and toroidal angles |
|
|
\(\partial_{\rho\zeta} B_{\rho}\) |
Tesla * meters |
Covariant radial component of magnetic field, second derivative wrt radial coordinate and toroidal angle |
|
|
\(\partial_{\rho\zeta} B_{\theta}\) |
Tesla * meters |
Covariant poloidal component of magnetic field, second derivative wrt radial coordinate and toroidal angle |
|
|
\(\partial_{\rho\zeta} B_{\zeta}\) |
Tesla * meters |
Covariant toroidal component of magnetic field, second derivative wrt radial coordinate and toroidal angle |
|
|
\(|\mathbf{B}|^{2}\) |
Tesla squared |
Magnitude of magnetic field, squared |
|
|
\(|\mathbf{B}|\) |
Tesla |
Magnitude of magnetic field |
|
|
\(\partial_{\rho} |\mathbf{B}|\) |
Tesla |
Magnitude of magnetic field, derivative wrt radial coordinate |
|
|
\(\partial_{\theta} |\mathbf{B}|\) |
Tesla |
Magnitude of magnetic field, derivative wrt poloidal angle |
|
|
\(\partial_{\zeta} |\mathbf{B}|\) |
Tesla |
Magnitude of magnetic field, derivative wrt toroidal angle |
|
|
\(\partial_{\rho\rho} |\mathbf{B}|\) |
Tesla |
Magnitude of magnetic field, second derivative wrt radial coordinate |
|
|
\(\partial_{\theta\theta} |\mathbf{B}|\) |
Tesla |
Magnitude of magnetic field, second derivative wrt poloidal angle |
|
|
\(\partial_{\zeta\zeta} |\mathbf{B}|\) |
Tesla |
Magnitude of magnetic field, second derivative wrt toroidal angle |
|
|
\(\partial_{\rho\theta} |\mathbf{B}|\) |
Tesla |
Magnitude of magnetic field, derivative wrt radial coordinate and poloidal angle |
|
|
\(\partial_{\theta\zeta} |\mathbf{B}|\) |
Tesla |
Magnitude of magnetic field, derivative wrt poloidal and toroidal angles |
|
|
\(\partial_{\rho\zeta} |\mathbf{B}|\) |
Tesla |
Magnitude of magnetic field, derivative wrt radial coordinate and toroidal angle |
|
|
\(\nabla |\mathbf{B}|\) |
Tesla / meters |
Gradient of magnetic field magnitude |
|
|
\(\langle |B| \rangle_{vol}\) |
Tesla |
Volume average magnetic field |
|
|
\(\langle |B| \rangle_{rms}\) |
Tesla |
Volume average magnetic field, root mean square |
|
|
\(\langle |B| \rangle\) |
Tesla |
Flux surface average magnetic field |
|
|
\(\langle B^2 \rangle\) |
Tesla squared |
Flux surface average magnetic field squared |
|
|
\(\langle 1/B \rangle\) |
1 / Tesla |
Flux surface averaged inverse field strength |
|
|
\(\partial_{\rho} \langle B^2 \rangle\) |
Tesla squared |
Flux surface average magnetic field squared, radial derivative |
|
|
\((\nabla B^{2})_{\rho}\) |
Tesla squared |
Covariant radial component of magnetic pressure gradient |
|
|
\((\nabla B^{2})_{\theta}\) |
Tesla squared |
Covariant poloidal component of magnetic pressure gradient |
|
|
\((\nabla B^{2})_{\zeta}\) |
Tesla squared |
Covariant toroidal component of magnetic pressure gradient |
|
|
\(\nabla B^{2}\) |
Tesla squared / meters |
Magnetic pressure gradient |
|
|
\(|\nabla B^{2}/(2\mu_0)|\) |
Newton / cubic meter |
Magnitude of magnetic pressure gradient |
|
|
\(\langle |\nabla B^{2}/(2\mu_0)| \rangle_{vol}\) |
Newtons per cubic meter |
Volume average of magnitude of magnetic pressure gradient |
|
|
\(((\nabla \times \mathbf{B}) \times \mathbf{B})_{\rho}\) |
Tesla squared |
Covariant radial component of Lorentz force |
|
|
\(((\nabla \times \mathbf{B}) \times \mathbf{B})_{\theta}\) |
Tesla squared |
Covariant poloidal component of Lorentz force |
|
|
\(((\nabla \times \mathbf{B}) \times \mathbf{B})_{\zeta}\) |
Tesla squared |
Covariant toroidal component of Lorentz force |
|
|
\((\nabla \times \mathbf{B}) \times \mathbf{B}\) |
Tesla squared / meters |
Lorentz force |
|
|
\((\mathbf{B} \cdot \nabla) \mathbf{B}\) |
Tesla squared / meters |
Magnetic tension |
|
|
\(((\mathbf{B} \cdot \nabla) \mathbf{B})_{\rho}\) |
Tesla squared |
Covariant radial component of magnetic tension |
|
|
\(((\mathbf{B} \cdot \nabla) \mathbf{B})_{\theta}\) |
Tesla squared |
Covariant poloidal component of magnetic tension |
|
|
\(((\mathbf{B} \cdot \nabla) \mathbf{B})_{\zeta}\) |
Tesla squared |
Covariant toroidal component of magnetic tension |
|
|
\(|(\mathbf{B} \cdot \nabla) \mathbf{B}|\) |
Tesla squared / meters |
Magnitude of magnetic tension |
|
|
\(\langle |(\mathbf{B} \cdot \nabla) \mathbf{B}| \rangle_{vol}\) |
Tesla squared / meters |
Volume average magnetic tension magnitude |
|
|
\(\mathbf{B} \cdot \nabla B\) |
Tesla squared / meters |
|
|
|
\(\partial_{\theta} (\mathbf{B} \cdot \nabla B)\) |
Tesla squared / meters |
|
|
|
\(\partial_{\zeta} (\mathbf{B} \cdot \nabla B)\) |
Tesla squared / meters |
|
|
|
\(\max_{\theta \zeta} |B|\) |
Tesla |
Maximum field strength on each flux surface |
|
|
\(\min_{\theta \zeta} |B|\) |
Tesla |
Minimum field strength on each flux surface |
|
|
\((r / R_0)_{effective}\) |
None |
Effective local inverse aspect ratio, based on max and min |B| |
|
|
\(\kappa\) |
Inverse meters |
Curvature vector of magnetic field lines |
|
|
\(\kappa_n\) |
Inverse meters |
Normal curvature vector of magnetic field lines |
|
|
\(\kappa_g\) |
Inverse meters |
Geodesic curvature vector of magnetic field lines |
|
|
\(\nabla \mathbf{B}\) |
Tesla / meter |
Gradient of magnetic field vector |
|
|
\(|\nabla \mathbf{B}|\) |
Tesla / meter |
Frobenius norm of gradient of magnetic field vector |
|
|
\(L_{\nabla \mathbf{B}} = \frac{\sqrt{2}|B|}{|\nabla \mathbf{B}|}\) |
meters |
Magnetic field length scale based on Frobenius norm of gradient of magnetic field vector |
|
|
\(V\) |
cubic meters |
Volume |
|
|
\(V(\rho)\) |
cubic meters |
Volume enclosed by flux surfaces |
|
|
\(\partial_{\rho} V(\rho)\) |
cubic meters |
Volume enclosed by flux surfaces, derivative wrt radial coordinate |
|
|
\(\partial_{\rho\rho} V(\rho)\) |
cubic meters |
Volume enclosed by flux surfaces, second derivative wrt radial coordinate |
|
|
\(A\) |
square meters |
Average cross-sectional area |
|
|
\(S(\rho)\) |
square meters |
Surface area of flux surfaces |
|
|
\(R_{0}\) |
meters |
Average major radius |
|
|
\(a\) |
meters |
Average minor radius |
|
|
\(R_{0} / a\) |
None |
Aspect ratio |
|
|
\(a_{major} / a_{minor}\) |
None |
Maximum elongation |
|
|
\(\hat{\mathbf{n}}_{\rho}\) |
None |
Unit normal vector to constant rho surface |
|
|
\(L_{sff}\) |
meters |
L coefficient of second fundamental form |
|
|
\(M_{sff}\) |
meters |
M coefficient of second fundamental form |
|
|
\(N_{sff}\) |
meters |
N coefficient of second fundamental form |
|
|
\(k_{1}\) |
Inverse meters |
First principle curvature of flux surfaces |
|
|
\(k_{2}\) |
Inverse meters |
Second principle curvature of flux surfaces |
|
|
\(K\) |
meters squared |
Gaussian curvature of flux surfaces |
|
|
\(H\) |
meters |
Mean curvature of flux surfaces |
|
|
\(\sqrt{g}\) |
cubic meters |
Jacobian determinant of flux coordinate system |
|
|
\(\sqrt{g}_{PEST}\) |
cubic meters |
Jacobian determinant of PEST flux coordinate system |
|
|
\(|e_{\theta} \times e_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface |
|
|
\(|e_{\zeta} \times e_{\rho}|\) |
square meters |
2D Jacobian determinant for constant theta surface |
|
|
\(|e_{\rho} \times e_{\theta}|\) |
square meters |
2D Jacobian determinant for constant zeta surface |
|
|
\(\partial_{\rho} \sqrt{g}\) |
cubic meters |
Jacobian determinant of flux coordinate system, derivative wrt radial coordinate |
|
|
\(\partial_{\theta} \sqrt{g}\) |
cubic meters |
Jacobian determinant of flux coordinate system, derivative wrt poloidal angle |
|
|
\(\partial_{\zeta} \sqrt{g}\) |
cubic meters |
Jacobian determinant of flux coordinate system, derivative wrt toroidal angle |
|
|
\(\partial_{\rho\rho} \sqrt{g}\) |
cubic meters |
Jacobian determinant of flux coordinate system, second derivative wrt radial coordinate |
|
|
\(\partial_{\theta\theta} \sqrt{g}\) |
cubic meters |
Jacobian determinant of flux coordinate system, second derivative wrt poloidal angle |
|
|
\(\partial_{\zeta\zeta} \sqrt{g}\) |
cubic meters |
Jacobian determinant of flux coordinate system, second derivative wrt toroidal angle |
|
|
\(\partial_{\rho\theta} \sqrt{g}\) |
cubic meters |
Jacobian determinant of flux coordinate system, second derivative wrt radial coordinate and poloidal angle |
|
|
\(\partial_{\theta\zeta} \sqrt{g}\) |
cubic meters |
Jacobian determinant of flux coordinate system, second derivative wrt poloidal and toroidal angles |
|
|
\(\partial_{\rho\zeta} \sqrt{g}\) |
cubic meters |
Jacobian determinant of flux coordinate system, second derivative wrt radial coordinate and toroidal angle |
|
|
\(g_{\rho\rho}\) |
square meters |
Radial/Radial element of covariant metric tensor |
|
|
\(g_{\theta\theta}\) |
square meters |
Poloidal/Poloidal element of covariant metric tensor |
|
|
\(g_{\zeta\zeta}\) |
square meters |
Toroidal/Toroidal element of covariant metric tensor |
|
|
\(g_{\rho\theta}\) |
square meters |
Radial/Poloidal element of covariant metric tensor |
|
|
\(g_{\rho\zeta}\) |
square meters |
Radial/Toroidal element of covariant metric tensor |
|
|
\(g_{\theta\zeta}\) |
square meters |
Poloidal/Toroidal element of covariant metric tensor |
|
|
\(\partial_{\rho} g_{\theta\theta}\) |
square meters |
Poloidal/Poloidal element of covariant metric tensor, derivative wrt rho |
|
|
\(\partial_{\rho} g_{\theta\zeta}\) |
square meters |
Poloidal/Toroidal element of covariant metric tensor, derivative wrt rho |
|
|
\(\partial_{\rho\rho} g_{\theta\theta}\) |
square meters |
Poloidal/Poloidal element of covariant metric tensor, second derivative wrt rho |
|
|
\(\partial_{\rho\rho} g_{\theta\zeta}\) |
square meters |
Poloidal/Toroidal element of covariant metric tensor, second derivative wrt rho |
|
|
\(g^{\rho\rho}\) |
inverse square meters |
Radial/Radial element of contravariant metric tensor |
|
|
\(g^{\theta\theta}\) |
inverse square meters |
Poloidal/Poloidal element of contravariant metric tensor |
|
|
\(g^{\zeta\zeta}\) |
inverse square meters |
Toroidal/Toroidal element of contravariant metric tensor |
|
|
\(g^{\rho\theta}\) |
inverse square meters |
Radial/Poloidal element of contravariant metric tensor |
|
|
\(g^{\rho\zeta}\) |
inverse square meters |
Radial/Toroidal element of contravariant metric tensor |
|
|
\(g^{\theta\zeta}\) |
inverse square meters |
Poloidal/Toroidal element of contravariant metric tensor |
|
|
\(g^{\rho}{\rho}_{\rho}\) |
inverse square meters |
Radial/Radial element of contravariant metric tensor, first radial derivative |
|
|
\(g^{\rho}{\theta}_{\rho}\) |
inverse square meters |
Radial/Poloidal element of contravariant metric tensor, first radial derivative |
|
|
\(g^{\rho}{\zeta}_{\rho}\) |
inverse square meters |
Radial/Toroidal element of contravariant metric tensor, first radial derivative |
|
|
\(g^{\theta}{\theta}_{\rho}\) |
inverse square meters |
Poloidal/Poloidal element of contravariant metric tensor, first radial derivative |
|
|
\(g^{\theta}{\zeta}_{\rho}\) |
inverse square meters |
Poloidal/Toroidal element of contravariant metric tensor, first radial derivative |
|
|
\(g^{\zeta}{\zeta}_{\rho}\) |
inverse square meters |
Toroidal/Toroidal element of contravariant metric tensor, first radial derivative |
|
|
\(g^{\rho}{\rho}_{\theta}\) |
inverse square meters |
Radial/Radial element of contravariant metric tensor, first poloidal derivative |
|
|
\(g^{\rho}{\theta}_{\theta}\) |
inverse square meters |
Radial/Poloidal element of contravariant metric tensor, first poloidal derivative |
|
|
\(g^{\rho}{\zeta}_{\theta}\) |
inverse square meters |
Radial/Toroidal element of contravariant metric tensor, first poloidal derivative |
|
|
\(g^{\theta}{\theta}_{\theta}\) |
inverse square meters |
Poloidal/Poloidal element of contravariant metric tensor, first poloidal derivative |
|
|
\(g^{\theta}{\zeta}_{\theta}\) |
inverse square meters |
Poloidal/Toroidal element of contravariant metric tensor, first poloidal derivative |
|
|
\(g^{\zeta}{\zeta}_{\theta}\) |
inverse square meters |
Toroidal/Toroidal element of contravariant metric tensor, first poloidal derivative |
|
|
\(g^{\rho}{\rho}_{\zeta}\) |
inverse square meters |
Radial/Radial element of contravariant metric tensor, first toroidal derivative |
|
|
\(g^{\rho}{\theta}_{\zeta}\) |
inverse square meters |
Radial/Poloidal element of contravariant metric tensor, first toroidal derivative |
|
|
\(g^{\rho}{\zeta}_{\zeta}\) |
inverse square meters |
Radial/Toroidal element of contravariant metric tensor, first toroidal derivative |
|
|
\(g^{\theta}{\theta}_{\zeta}\) |
inverse square meters |
Poloidal/Poloidal element of contravariant metric tensor, first toroidal derivative |
|
|
\(g^{\theta}{\zeta}_{\zeta}\) |
inverse square meters |
Poloidal/Toroidal element of contravariant metric tensor, first toroidal derivative |
|
|
\(g^{\zeta}{\zeta}_{\zeta}\) |
inverse square meters |
Toroidal/Toroidal element of contravariant metric tensor, first toroidal derivative |
|
|
\(|\nabla \rho|\) |
inverse meters |
Magnitude of contravariant radial basis vector |
|
|
\(|\nabla \theta|\) |
inverse meters |
Magnitude of contravariant poloidal basis vector |
|
|
\(|\nabla \zeta|\) |
inverse meters |
Magnitude of contravariant toroidal basis vector |
|
|
\(\psi = \Psi / (2 \pi)\) |
Webers |
Toroidal flux (normalized by 2pi) |
|
|
\(\partial_{\rho} \psi = \partial_{\rho} \Psi / (2 \pi)\) |
Webers |
Toroidal flux (normalized by 2pi), first radial derivative |
|
|
\(\partial_{\rho\rho} \psi = \partial_{\rho\rho} \Psi / (2 \pi)\) |
Webers |
Toroidal flux (normalized by 2pi), second radial derivative |
|
|
\(\partial_{\rho\rho\rho} \psi = \partial_{\rho\rho\rho} \Psi / (2 \pi)\) |
Webers |
Toroidal flux (normalized by 2pi), third radial derivative |
|
|
\(\nabla\psi\) |
Webers per meter |
Toroidal flux gradient (normalized by 2pi) |
|
|
\(|\nabla\psi|^{2}\) |
Webers squared per square meter |
Toroidal flux gradient (normalized by 2pi) magnitude squared |
|
|
\(|\nabla\psi|\) |
Webers per meter |
Toroidal flux gradient (normalized by 2pi) magnitude |
|
|
\(\partial_{\rho} \chi\) |
Webers |
Poloidal flux (normalized by 2pi), first radial derivative |
|
|
\(\chi\) |
Webers |
Poloidal flux (normalized by 2pi) |
|
|
\(T_e\) |
electron-Volts |
Electron temperature |
|
|
\(\partial_{\rho} T_e\) |
electron-Volts |
Electron temperature, first radial derivative |
|
|
\(n_e\) |
1 / cubic meters |
Electron density |
|
|
\(\partial_{\rho} n_e\) |
1 / cubic meters |
Electron density, first radial derivative |
|
|
\(T_i\) |
electron-Volts |
Ion temperature |
|
|
\(\partial_{\rho} T_i\) |
electron-Volts |
Ion temperature, first radial derivative |
|
|
\(Z_{eff}\) |
None |
Effective atomic number |
|
|
\(\partial_{\rho} Z_{eff}\) |
None |
Effective atomic number, first radial derivative |
|
|
\(p\) |
Pascals |
Pressure |
|
|
\(\partial_{\rho} p\) |
Pascals |
Pressure, first radial derivative |
|
|
\(\nabla p\) |
Newtons / cubic meter |
Pressure gradient |
|
|
\(|\nabla p|^{2}\) |
Newtons per cubic meter squared |
Magnitude of pressure gradient squared |
|
|
\(|\nabla p|\) |
Newtons per cubic meter |
Magnitude of pressure gradient |
|
|
\(\langle |\nabla p| \rangle_{vol}\) |
Newtons per cubic meter |
Volume average of magnitude of pressure gradient |
|
|
\(\iota\) |
None |
Rotational transform (normalized by 2pi) |
|
|
\(\partial_{\rho} \iota\) |
None |
Rotational transform (normalized by 2pi), first radial derivative |
|
|
\(\partial_{\rho\rho} \iota\) |
None |
Rotational transform (normalized by 2pi), second radial derivative |
|
|
\(\iota_{0} numerator\) |
inverse meters |
Zero toroidal current rotational transform numerator |
|
|
\(\partial_{\rho} \iota_{0} numerator\) |
inverse meters |
Zero toroidal current rotational transform numerator, first radial derivative |
|
|
\(\partial_{\rho\rho} \iota_{0} numerator\) |
inverse meters |
Zero toroidal current rotational transform numerator, second radial derivative |
|
|
\(\iota_{0} denominator\) |
inverse meters |
Zero toroidal current rotational transform denominator |
|
|
\(\partial_{\rho} \iota_{0} denominator\) |
inverse meters |
Zero toroidal current rotational transform denominator, first radial derivative |
|
|
\(\partial_{\rho\rho} \iota_{0} denominator\) |
inverse meters |
Zero toroidal current rotational transform denominator, second radial derivative |
|
|
\(q = 1/\iota\) |
None |
Safety factor ‘q’, inverse of rotational transform. |
|
|
\(I\) |
Tesla * meters |
Covariant poloidal component of magnetic field in Boozer coordinates (proportional to toroidal current) |
|
|
\(\partial_{\rho} I\) |
Tesla * meters |
Covariant poloidal component of magnetic field in Boozer coordinates (proportional to toroidal current), derivative wrt radial coordinate |
|
|
\(\partial_{\rho\rho} I\) |
Tesla * meters |
Boozer toroidal current enclosed by flux surfaces, second derivative wrt radial coordinate |
|
|
\(G\) |
Tesla * meters |
Covariant toroidal component of magnetic field in Boozer coordinates (proportional to poloidal current) |
|
|
\(\partial_{\rho} G\) |
Tesla * meters |
Covariant toroidal component of magnetic field in Boozer coordinates (proportional to poloidal current), derivative wrt radial coordinate |
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\(\partial_{\rho\rho} G\) |
Tesla * meters |
Boozer poloidal current enclosed by flux surfaces, second derivative wrt radial coordinate |
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\(\frac{2\pi}{\mu_0} I\) |
Amperes |
Net toroidal current enclosed by flux surfaces |
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\(\frac{2\pi}{\mu_0} \partial_{\rho} I\) |
Amperes |
Net toroidal current enclosed by flux surfaces, derivative wrt radial coordinate |
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\(\frac{2\pi}{\mu_0} \partial_{\rho\rho} I\) |
Amperes |
Net toroidal current enclosed by flux surfaces, second derivative wrt radial coordinate |
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\(B_{\theta, m, n}\) |
Tesla * meters |
Fourier coefficients for covariant poloidal component of magnetic field |
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\(B_{\zeta, m, n}\) |
Tesla * meters |
Fourier coefficients for covariant toroidal component of magnetic field |
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\(w_{Boozer,m,n}\) |
Tesla * meters |
RHS of eq 10 in Hirshman 1995 ‘Transformation from VMEC to Boozer Coordinates’ |
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\(w_{Boozer}\) |
Tesla * meters |
Inverse Fourier transform of RHS of eq 10 in Hirshman 1995 ‘Transformation from VMEC to Boozer Coordinates’ |
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\(\partial_{\theta} w_{Boozer}\) |
Tesla * meters |
Inverse Fourier transform of RHS of eq 10 in Hirshman 1995 ‘Transformation from VMEC to Boozer Coordinates’, poloidal derivative |
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\(\partial_{\zeta} w_{Boozer}\) |
Tesla * meters |
Inverse Fourier transform of RHS of eq 10 in Hirshman 1995 ‘Transformation from VMEC to Boozer Coordinates’, toroidal derivative |
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\(\nu = \zeta_{B} - \zeta\) |
radians |
Boozer toroidal stream function |
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\(\partial_{\theta} \nu\) |
radians |
Boozer toroidal stream function, derivative wrt poloidal angle |
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\(\partial_{\zeta} \nu\) |
radians |
Boozer toroidal stream function, derivative wrt toroidal angle |
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\(\theta_{B}\) |
radians |
Boozer poloidal angular coordinate |
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\(\zeta_{B}\) |
radians |
Boozer toroidal angular coordinate |
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\(\sqrt{g}_{B}\) |
None |
Jacobian determinant of Boozer coordinates |
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\(B_{mn}^{Boozer}\) |
Tesla |
Boozer harmonics of magnetic field |
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\(Boozer modes\) |
None |
Boozer harmonics |
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\((M \iota - N) (\mathbf{B} \times \nabla \psi) \cdot \nabla B - (M G + N I) \mathbf{B} \cdot \nabla B\) |
Tesla cubed |
Two-term quasisymmetry metric |
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\(\nabla \psi \times \nabla B \cdot \nabla (\mathbf{B} \cdot \nabla B)\) |
Tesla quarted / square meters |
Triple product quasisymmetry metric |
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\(1/B^2 (\mathbf{b} \times \nabla B) \cdot \nabla \psi\) |
None |
Measure of cross field drift at each point, unweighted by particle energy |
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\(D_{shear}\) |
Inverse Webers squared |
Mercier stability criterion magnetic shear term |
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\(D_{current}\) |
Inverse Webers squared |
Mercier stability criterion toroidal current term |
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\(D_{well}\) |
Inverse Webers squared |
Mercier stability criterion magnetic well term |
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\(D_{geodesic}\) |
Inverse Webers squared |
Mercier stability criterion geodesic curvature term |
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\(D_{Mercier}\) |
Inverse Webers squared |
Mercier stability criterion (positive/negative value denotes stability/instability) |
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\(Magnetic Well\) |
None |
Magnetic well proxy for MHD stability (positive/negative value denotes stability/instability) |
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