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
Module : where in the code the source is defined (mostly for developers)
Aliases : alternative names of a variable that can be used in the same way as the primary name
desc.equilibrium.equilibrium.Equilibrium
Name |
Label |
Units |
Description |
Module |
Aliases |
|---|---|---|---|---|---|
|
\(\hat{b}\) |
None |
Unit vector along magnetic field |
|
|
|
\(\mathbf{e}^{\rho}\) |
inverse meters |
Contravariant radial basis vector |
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|
|
\(\partial_{\rho} \mathbf{e}^{\rho}\) |
inverse meters |
Contravariant radial basis vector, derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho\rho} \mathbf{e}^{\rho}\) |
inverse square meters |
Contravariant Radial basis vector, 2nd derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho\theta} \mathbf{e}^{\rho}\) |
inverse square meters |
Contravariant Radial basis vector, derivative wrt radial and poloidal coordinate |
|
|
|
\(\partial_{\rho\zeta} \mathbf{e}^{\rho}\) |
inverse square meters |
Contravariant Radial basis vector, derivative wrt radial and toroidal coordinate |
|
|
|
\(\partial_{\theta} \mathbf{e}^{\rho}\) |
inverse meters |
Contravariant radial basis vector, derivative wrt poloidal coordinate |
|
|
|
\(\partial_{\theta\theta} \mathbf{e}^{\rho}\) |
inverse square meters |
Contravariant Radial basis vector, 2nd derivative wrt poloidal coordinate |
|
|
|
\(\partial_{\theta\zeta} \mathbf{e}^{\rho}\) |
inverse square meters |
Contravariant Radial basis vector, derivative wrt poloidal and toroidal coordinate |
|
|
|
\(\partial_{\zeta} \mathbf{e}^{\rho}\) |
inverse meters |
Contravariant radial basis vector, derivative wrt toroidal coordinate |
|
|
|
\(\partial_{\zeta\zeta} \mathbf{e}^{\rho}\) |
inverse square meters |
Contravariant Radial basis vector, 2nd derivative wrt toroidal coordinate |
|
|
|
\(\mathbf{e}^{\theta}\) |
inverse meters |
Contravariant poloidal basis vector |
|
|
|
\(\mathbf{e}^{\theta} \sqrt{g}\) |
square meters |
Contravariant poloidal basis vector weighted by 3-D volume Jacobian |
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|
|
\(\partial_{\rho} \mathbf{e}^{\theta}\) |
inverse meters |
Contravariant poloidal basis vector, derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho\rho} \mathbf{e}^{\theta}\) |
inverse square meters |
Contravariant Poloidal basis vector, 2nd derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho\theta} \mathbf{e}^{\theta}\) |
inverse square meters |
Contravariant Poloidal basis vector, derivative wrt radial and poloidal coordinate |
|
|
|
\(\partial_{\rho\zeta} \mathbf{e}^{\theta}\) |
inverse square meters |
Contravariant Poloidal basis vector, derivative wrt radial and toroidal coordinate |
|
|
|
\(\partial_{\theta} \mathbf{e}^{\theta}\) |
inverse meters |
Contravariant poloidal basis vector, derivative wrt poloidal coordinate |
|
|
|
\(\partial_{\theta\theta} \mathbf{e}^{\theta}\) |
inverse square meters |
Contravariant Poloidal basis vector, 2nd derivative wrt poloidal coordinate |
|
|
|
\(\partial_{\theta\zeta} \mathbf{e}^{\theta}\) |
inverse square meters |
Contravariant Poloidal basis vector, derivative wrt poloidal and toroidal coordinate |
|
|
|
\(\partial_{\zeta} \mathbf{e}^{\theta}\) |
inverse meters |
Contravariant poloidal basis vector, derivative wrt toroidal coordinate |
|
|
|
\(\partial_{\zeta\zeta} \mathbf{e}^{\theta}\) |
inverse square meters |
Contravariant Poloidal basis vector, 2nd derivative wrt toroidal coordinate |
|
|
|
\(\mathbf{e}^{\zeta}\) |
inverse meters |
Contravariant toroidal basis vector |
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|
|
\(\partial_{\rho} \mathbf{e}^{\zeta}\) |
inverse meters |
Contravariant toroidal basis vector, derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho\rho} \mathbf{e}^{\zeta}\) |
inverse square meters |
Contravariant Toroidal basis vector, 2nd derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho\theta} \mathbf{e}^{\zeta}\) |
inverse square meters |
Contravariant Toroidal basis vector, derivative wrt radial and poloidal coordinate |
|
|
|
\(\partial_{\rho\zeta} \mathbf{e}^{\zeta}\) |
inverse square meters |
Contravariant Toroidal basis vector, derivative wrt radial and toroidal coordinate |
|
|
|
\(\partial_{\theta} \mathbf{e}^{\zeta}\) |
inverse meters |
Contravariant toroidal basis vector, derivative wrt poloidal coordinate |
|
|
|
\(\partial_{\theta\theta} \mathbf{e}^{\zeta}\) |
inverse square meters |
Contravariant Toroidal basis vector, 2nd derivative wrt poloidal coordinate |
|
|
|
\(\partial_{\theta\zeta} \mathbf{e}^{\zeta}\) |
inverse square meters |
Contravariant Toroidal basis vector, derivative wrt poloidal and toroidal coordinate |
|
|
|
\(\partial_{\zeta} \mathbf{e}^{\zeta}\) |
inverse meters |
Contravariant toroidal basis vector, derivative wrt toroidal coordinate |
|
|
|
\(\partial_{\zeta\zeta} \mathbf{e}^{\zeta}\) |
inverse square meters |
Contravariant Toroidal basis vector, 2nd derivative wrt toroidal coordinate |
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|
|
\(\mathbf{e}_{\phi}\) |
meters |
Covariant cylindrical toroidal basis vector |
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|
|
\(\mathbf{e}_{\rho}\) |
meters |
Covariant Radial basis vector |
|
|
|
\(\partial_{\rho} \mathbf{e}_{\rho}\) |
meters |
Covariant Radial basis vector, derivative wrt radial coordinate |
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|
\(\partial_{\rho \rho} \mathbf{e}_{\rho}\) |
meters |
Covariant Radial basis vector, second derivative wrt radial and radial coordinates |
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|
\(\partial_{\rho \rho \rho} \mathbf{e}_{\rho}\) |
meters |
Covariant Radial basis vector, third derivative wrt radial coordinate |
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|
\(\partial_{\rho \rho \theta} \mathbf{e}_{\rho}\) |
meters |
Covariant Radial basis vector, third derivative wrt radial coordinate twice and poloidal once |
|
|
|
\(\partial_{\rho \rho \zeta} \mathbf{e}_{\rho}\) |
meters |
Covariant Radial basis vector, third derivative wrt radial coordinate twice and toroidal once |
|
|
|
\(\partial_{\rho \theta} \mathbf{e}_{\rho}\) |
meters |
Covariant Radial basis vector, second derivative wrt radial and poloidal coordinates |
|
|
|
\(\partial_{\rho \theta \theta} \mathbf{e}_{\rho}\) |
meters |
Covariant Radial basis vector, third derivative wrt radial coordinateonce and poloidal twice |
|
|
|
\(\partial_{\rho \theta \zeta} \mathbf{e}_{\rho}\) |
meters |
Covariant Radial basis vector, third derivative wrt radial, poloidal, and toroidal coordinates |
|
|
|
\(\partial_{\rho \zeta} \mathbf{e}_{\rho}\) |
meters |
Covariant Radial basis vector, second derivative wrt radial and toroidal coordinates |
|
|
|
\(\partial_{\rho \zeta \zeta} \mathbf{e}_{\rho}\) |
meters |
Covariant Radial basis vector, third derivative wrt radial coordinate once and toroidal twice |
|
|
|
\(\partial_{\theta} \mathbf{e}_{\rho}\) |
meters |
Covariant Radial basis vector, derivative wrt poloidal coordinate |
|
|
|
\(\partial_{\theta \theta} \mathbf{e}_{\rho}\) |
meters |
Covariant Radial basis vector, second derivative wrt poloidal and poloidal coordinates |
|
|
|
\(\partial_{\theta \zeta} \mathbf{e}_{\rho}\) |
meters |
Covariant Radial basis vector, second derivative wrt poloidal and toroidal coordinates |
|
|
|
\(\partial_{\zeta} \mathbf{e}_{\rho}\) |
meters |
Covariant Radial basis vector, derivative wrt toroidal coordinate |
|
|
|
\(\partial_{\zeta \zeta} \mathbf{e}_{\rho}\) |
meters |
Covariant Radial basis vector, second derivative wrt toroidal and toroidal coordinates |
|
|
|
\(\mathbf{e}_{\theta}\) |
meters |
Covariant Poloidal basis vector |
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|
|
\(\mathbf{e}_{\theta} / \sqrt{g}\) |
meters |
Covariant Poloidal basis vector divided by 3-D volume Jacobian |
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|
|
\(\mathbf{e}_{\theta_{PEST}}\) |
meters |
Covariant straight field line (PEST) poloidal basis vector |
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|
|
\(\partial_{\rho} \mathbf{e}_{\theta}\) |
meters |
Covariant Poloidal basis vector, derivative wrt radial coordinate |
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|
|
\(\partial_{\rho \rho} \mathbf{e}_{\theta}\) |
meters |
Covariant Poloidal basis vector, second derivative wrt radial and radial coordinates |
|
|
|
\(\partial_{\rho \rho \rho} \mathbf{e}_{\theta}\) |
meters |
Covariant Poloidal basis vector, third derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho \rho \theta} \mathbf{e}_{\theta}\) |
meters |
Covariant Poloidal basis vector, third derivative wrt radial coordinate twice and poloidal once |
|
|
|
\(\partial_{\rho \rho \zeta} \mathbf{e}_{\theta}\) |
meters |
Covariant Poloidal basis vector, third derivative wrt radial coordinate twice and toroidal once |
|
|
|
\(\partial_{\rho \theta} \mathbf{e}_{\theta}\) |
meters |
Covariant Poloidal basis vector, second derivative wrt radial and poloidal coordinates |
|
|
|
\(\partial_{\rho \theta \theta} \mathbf{e}_{\theta}\) |
meters |
Covariant Poloidal basis vector, third derivative wrt radial coordinate once and poloidal twice |
|
|
|
\(\partial_{\rho \theta \zeta} \mathbf{e}_{\theta}\) |
meters |
Covariant Poloidal basis vector, third derivative wrt radial, poloidal, and toroidal coordinates |
|
|
|
\(\partial_{\rho \zeta} \mathbf{e}_{\theta}\) |
meters |
Covariant Poloidal basis vector, second derivative wrt radial and toroidal coordinates |
|
|
|
\(\partial_{\rho \zeta \zeta} \mathbf{e}_{\theta}\) |
meters |
Covariant Poloidal basis vector, third derivative wrt radial coordinate once and toroidal twice |
|
|
|
\(\partial_{\theta} \mathbf{e}_{\theta}\) |
meters |
Covariant Poloidal basis vector, derivative wrt poloidal coordinate |
|
|
|
\(\partial_{\theta \theta} \mathbf{e}_{\theta}\) |
meters |
Covariant Poloidal basis vector, second derivative wrt poloidal and poloidal coordinates |
|
|
|
\(\partial_{\theta \zeta} \mathbf{e}_{\theta}\) |
meters |
Covariant Poloidal basis vector, second derivative wrt poloidal and toroidal coordinates |
|
|
|
\(\partial_{\zeta} \mathbf{e}_{\theta}\) |
meters |
Covariant Poloidal basis vector, derivative wrt toroidal coordinate |
|
|
|
\(\partial_{\zeta \zeta} \mathbf{e}_{\theta}\) |
meters |
Covariant Poloidal basis vector, second derivative wrt toroidal and toroidal coordinates |
|
|
|
\(\mathbf{e}_{\zeta}\) |
meters |
Covariant Toroidal basis vector |
|
|
|
\(\partial_{\rho} \mathbf{e}_{\zeta}\) |
meters |
Covariant Toroidal basis vector, derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho \rho} \mathbf{e}_{\zeta}\) |
meters |
Covariant Toroidal basis vector, second derivative wrt radial and radial coordinates |
|
|
|
\(\partial_{\rho \rho \rho} \mathbf{e}_{\zeta}\) |
meters |
Covariant Toroidal basis vector, third derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho \theta} \mathbf{e}_{\zeta}\) |
meters |
Covariant Toroidal basis vector, third derivative wrt radial coordinate twice and poloidal once |
|
|
|
\(\partial_{\rho \rho \zeta} \mathbf{e}_{\zeta}\) |
meters |
Covariant Toroidal basis vector, third derivative wrt radial coordinate twice and toroidal once |
|
|
|
\(\partial_{\rho \theta} \mathbf{e}_{\zeta}\) |
meters |
Covariant Toroidal basis vector, second derivative wrt radial and poloidal coordinates |
|
|
|
\(\partial_{\rho \theta \theta} \mathbf{e}_{\zeta}\) |
meters |
Covariant Toroidal basis vector, third derivative wrt radial coordinate once and poloidal twice |
|
|
|
\(\partial_{\rho \theta \zeta} \mathbf{e}_{\zeta}\) |
meters |
Covariant Toroidal basis vector, third derivative wrt radial, poloidal, and toroidal coordinates |
|
|
|
\(\partial_{\rho \zeta} \mathbf{e}_{\zeta}\) |
meters |
Covariant Toroidal basis vector, second derivative wrt radial and toroidal coordinates |
|
|
|
\(\partial_{\rho \zeta \zeta} \mathbf{e}_{\zeta}\) |
meters |
Covariant Toroidal basis vector, third derivative wrt radial coordinate once and toroidal twice |
|
|
|
\(\partial_{\theta} \mathbf{e}_{\zeta}\) |
meters |
Covariant Toroidal basis vector, derivative wrt poloidal coordinate |
|
|
|
\(\partial_{\theta \theta} \mathbf{e}_{\zeta}\) |
meters |
Covariant Toroidal basis vector, second derivative wrt poloidal and poloidal coordinates |
|
|
|
\(\partial_{\theta \zeta} \mathbf{e}_{\zeta}\) |
meters |
Covariant Toroidal basis vector, second derivative wrt poloidal and toroidal coordinates |
|
|
|
\(\partial_{\zeta} \mathbf{e}_{\zeta}\) |
meters |
Covariant Toroidal basis vector, derivative wrt toroidal coordinate |
|
|
|
\(\partial_{\zeta \zeta} \mathbf{e}_{\zeta}\) |
meters |
Covariant Toroidal basis vector, second derivative wrt toroidal and toroidal coordinates |
|
|
|
\(\nabla \alpha\) |
Inverse meters |
Unit vector along field line |
|
|
|
\(\nabla\psi\) |
Webers per meter |
Toroidal flux gradient (normalized by 2pi) |
|
|
|
\(\hat{\mathbf{n}}_{\rho}\) |
None |
Unit vector normal to constant rho surface (direction of e^rho) |
|
|
|
\(\partial_{\zeta}\hat{\mathbf{n}}_{\rho}\) |
None |
Unit vector normal to constant rho surface (direction of e^rho), derivative wrt toroidal angle |
|
|
|
\(\hat{\mathbf{n}}_{\theta}\) |
None |
Unit vector normal to constant theta surface (direction of e^theta) |
|
|
|
\(\hat{\mathbf{n}}_{\zeta}\) |
None |
Unit vector normal to constant zeta surface (direction of e^zeta) |
|
|
|
\(1 - \frac{3}{4} \langle |B|^2 \rangle \int_0^{1/Bmax} \frac{\lambda\; d\lambda}{\langle \sqrt{1 - \lambda B} \rangle}\) |
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 |
|
|
|
\(\frac{2\pi}{\mu_0} I_{Redl}\) |
Amperes |
Net toroidal current enclosed by flux surfaces, consistent with bootstrap current from Redl formula |
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|
\(0\) |
None |
Zeros |
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|
\(R\) |
meters |
Major radius in lab frame |
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\(\partial_{\rho} R\) |
meters |
Major radius in lab frame, first radial derivative |
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\(\partial_{\rho \rho} R\) |
meters |
Major radius in lab frame, second radial derivative |
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\(\partial_{\rho \rho \rho} R\) |
meters |
Major radius in lab frame, third radial derivative |
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\(\partial_{\rho \rho \rho \rho} R\) |
meters |
Major radius in lab frame, fourth radial derivative |
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\(\partial_{\rho \rho \rho \theta} R\) |
meters |
Major radius in lab frame, fourth derivative wrt radial coordinate thrice and poloidal once |
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\(\partial_{\rho \rho \rho \zeta} R\) |
meters |
Major radius in lab frame, fourth derivative wrt radial coordinate thrice and toroidal once |
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|
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\(\partial_{\rho \rho \theta} R\) |
meters |
Major radius in lab frame, third derivative, wrt radius twice and poloidal angle |
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|
\(\partial_{\rho \rho \theta \theta} R\) |
meters |
Major radius in lab frame, fourth derivative, wrt radius twice and poloidal angle twice |
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|
\(\partial_{\rho \rho \theta \zeta} R\) |
meters |
Major radius in lab frame, fourth derivative wrt radius twice, poloidal angle, and toroidal angle |
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|
|
\(\partial_{\rho \rho \zeta} R\) |
meters |
Major radius in lab frame, third derivative, wrt radius twice and toroidal angle |
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|
\(\partial_{\rho \rho \zeta \zeta} R\) |
meters |
Major radius in lab frame, fourth derivative, wrt radius twice and toroidal angle twice |
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\(\partial_{\rho \theta} R\) |
meters |
Major radius in lab frame, second derivative wrt radius and poloidal angle |
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\(\partial_{\rho \theta \theta} R\) |
meters |
Major radius in lab frame, third derivative wrt radius and poloidal angle twice |
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|
\(\partial_{\rho \theta \theta \theta} R\) |
meters |
Major radius in lab frame, fourth derivative wrt radius and poloidal angle thrice |
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|
|
\(\partial_{\rho \theta \theta \zeta} R\) |
meters |
Major radius in lab frame, fourth derivative wrt radius once, poloidal angle twice, and toroidal angle once |
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|
|
\(\partial_{\rho \theta \zeta} R\) |
meters |
Major radius in lab frame, third derivative wrt radius, poloidal angle, and toroidal angle |
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|
|
\(\partial_{\rho \theta \zeta \zeta} R\) |
meters |
Major radius in lab frame, fourth derivative wrt radius, poloidal angle, and toroidal angle twice |
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|
|
\(\partial_{\rho \zeta} R\) |
meters |
Major radius in lab frame, second derivative wrt radius and toroidal angle |
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|
|
\(\partial_{\rho \zeta \zeta} R\) |
meters |
Major radius in lab frame, third derivative wrt radius and toroidal angle twice |
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|
|
\(\partial_{\rho \zeta \zeta \zeta} R\) |
meters |
Major radius in lab frame, fourth derivative wrt radius and toroidal angle thrice |
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|
|
\(\partial_{\theta} R\) |
meters |
Major radius in lab frame, first poloidal derivative |
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|
|
\(\partial_{\theta \theta} R\) |
meters |
Major radius in lab frame, second poloidal derivative |
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|
|
\(\partial_{\theta \theta \theta} R\) |
meters |
Major radius in lab frame, third poloidal derivative |
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|
|
\(\partial_{\theta \theta \zeta} R\) |
meters |
Major radius in lab frame, third derivative wrt poloidal angle twice and toroidal angle |
|
|
|
\(\partial_{\theta \zeta} R\) |
meters |
Major radius in lab frame, second derivative wrt poloidal and toroidal angles |
|
|
|
\(\partial_{\theta \zeta \zeta} R\) |
meters |
Major radius in lab frame, third derivative wrt poloidal angle and toroidal angle twice |
|
|
|
\(\partial_{\zeta} R\) |
meters |
Major radius in lab frame, first toroidal derivative |
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|
|
\(\partial_{\zeta \zeta} R\) |
meters |
Major radius in lab frame, second toroidal derivative |
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|
|
\(\partial_{\zeta \zeta \zeta} R\) |
meters |
Major radius in lab frame, third toroidal derivative |
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|
|
\(X = R \cos{\phi}\) |
meters |
Cartesian X coordinate |
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|
|
\(\partial_{\rho} X\) |
meters |
Cartesian X coordinate, derivative wrt radial coordinate |
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|
|
\(\partial_{\theta} X\) |
meters |
Cartesian X coordinate, derivative wrt poloidal coordinate |
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|
|
\(\partial_{\zeta} X\) |
meters |
Cartesian X coordinate, derivative wrt toroidal coordinate |
|
|
|
\(Y = R \sin{\phi}\) |
meters |
Cartesian Y coordinate |
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|
|
\(\partial_{\rho} Y\) |
meters |
Cartesian Y coordinate, derivative wrt radial coordinate |
|
|
|
\(\partial_{\theta} Y\) |
meters |
Cartesian Y coordinate, derivative wrt poloidal coordinate |
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|
|
\(\partial_{\zeta} Y\) |
meters |
Cartesian Y coordinate, derivative wrt toroidal coordinate |
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|
|
\(Z\) |
meters |
Vertical coordinate in lab frame |
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|
|
\(\partial_{\rho} Z\) |
meters |
Vertical coordinate in lab frame, first radial derivative |
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|
|
\(\partial_{\rho \rho} Z\) |
meters |
Vertical coordinate in lab frame, second radial derivative |
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|
|
\(\partial_{\rho \rho \rho} Z\) |
meters |
Vertical coordinate in lab frame, third radial derivative |
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|
|
\(\partial_{\rho \rho \rho \rho} Z\) |
meters |
Vertical coordinate in lab frame, fourth radial derivative |
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|
|
\(\partial_{\rho \rho \rho \theta} Z\) |
meters |
Vertical coordinate in lab frame, fourth derivative wrt radial coordinate thrice and poloidal once |
|
|
|
\(\partial_{\rho \rho \rho \zeta} Z\) |
meters |
Vertical coordinate in lab frame, fourth derivative wrt radial coordinate thrice and toroidal once |
|
|
|
\(\partial_{\rho \rho \theta} Z\) |
meters |
Vertical coordinate in lab frame, third derivative, wrt radius twice and poloidal angle |
|
|
|
\(\partial_{\rho \rho \theta} Z\) |
meters |
Vertical coordinate in lab frame, fourth derivative, wrt radius twice and poloidal angle twice |
|
|
|
\(\partial_{\rho \rho \theta \zeta} Z\) |
meters |
Vertical coordinate in lab frame, fourth derivative wrt radiustwice, poloidal angle, and toroidal angle |
|
|
|
\(\partial_{\rho \rho \zeta} Z\) |
meters |
Vertical coordinate in lab frame, third derivative, wrt radius twice and toroidal angle |
|
|
|
\(\partial_{\rho \rho \zeta \zeta} Z\) |
meters |
Vertical coordinate in lab frame, fourth derivative, wrt radius twice and toroidal angle twice |
|
|
|
\(\partial_{\rho \theta} Z\) |
meters |
Vertical coordinate in lab frame, second derivative wrt radius and poloidal angle |
|
|
|
\(\partial_{\rho \theta \theta} Z\) |
meters |
Vertical coordinate in lab frame, third derivative wrt radius and poloidal angle twice |
|
|
|
\(\partial_{\rho \theta \theta \theta} Z\) |
meters |
Vertical coordinate in lab frame, third derivative wrt radius and poloidal angle thrice |
|
|
|
\(\partial_{\rho \theta \theta \zeta} Z\) |
meters |
Vertical coordinate in lab frame, fourth derivative wrt radius once, poloidal angle twice, and toroidal angle once |
|
|
|
\(\partial_{\rho \theta \zeta} Z\) |
meters |
Vertical coordinate in lab frame, third derivative wrt radius, poloidal angle, and toroidal angle |
|
|
|
\(\partial_{\rho \theta \zeta \zeta} Z\) |
meters |
Vertical coordinate in lab frame, fourth derivative wrt radius, poloidal angle, and toroidal angle twice |
|
|
|
\(\partial_{\rho \zeta} Z\) |
meters |
Vertical coordinate in lab frame, second derivative wrt radius and toroidal angle |
|
|
|
\(\partial_{\rho \zeta \zeta} Z\) |
meters |
Vertical coordinate in lab frame, third derivative wrt radius and toroidal angle twice |
|
|
|
\(\partial_{\rho \zeta \zeta \zeta} Z\) |
meters |
Vertical coordinate in lab frame, third derivative wrt radius and toroidal angle thrice |
|
|
|
\(\partial_{\theta} Z\) |
meters |
Vertical coordinate in lab frame, first poloidal derivative |
|
|
|
\(\partial_{\theta \theta} Z\) |
meters |
Vertical coordinate in lab frame, second poloidal derivative |
|
|
|
\(\partial_{\theta \theta \theta} Z\) |
meters |
Vertical coordinate in lab frame, third poloidal derivative |
|
|
|
\(\partial_{\theta \theta \zeta} Z\) |
meters |
Vertical coordinate in lab frame, third derivative wrt poloidal angle twice and toroidal angle |
|
|
|
\(\partial_{\theta \zeta} Z\) |
meters |
Vertical coordinate in lab frame, second derivative wrt poloidal and toroidal angles |
|
|
|
\(\partial_{\theta \zeta \zeta} Z\) |
meters |
Vertical coordinate in lab frame, third derivative wrt poloidal angle and toroidal angle twice |
|
|
|
\(\partial_{\zeta} Z\) |
meters |
Vertical coordinate in lab frame, first toroidal derivative |
|
|
|
\(\partial_{\zeta \zeta} Z\) |
meters |
Vertical coordinate in lab frame, second toroidal derivative |
|
|
|
\(\partial_{\zeta \zeta \zeta} Z\) |
meters |
Vertical coordinate in lab frame, third toroidal derivative |
|
|
|
\(\alpha\) |
None |
Field line label, defined on [0, 2pi) |
|
|
|
\(\partial_\rho \alpha\) |
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 |
|
|
|
\(\lambda\) |
radians |
Poloidal stream function |
|
|
|
\(\partial_{\rho} \lambda\) |
radians |
Poloidal stream function, first radial derivative |
|
|
|
\(\partial_{\rho \rho} \lambda\) |
radians |
Poloidal stream function, second radial derivative |
|
|
|
\(\partial_{\rho \rho \rho} \lambda\) |
radians |
Poloidal stream function, third radial derivative |
|
|
|
\(\partial_{\rho \rho \rho \theta} \lambda\) |
radians |
Poloidal stream function, third radial derivative and first poloidal derivative |
|
|
|
\(\partial_{\rho \rho \rho \zeta} \lambda\) |
radians |
Poloidal stream function, third radial derivative and first toroidal derivative |
|
|
|
\(\partial_{\rho \rho \theta} \lambda\) |
radians |
Poloidal stream function, third derivative, wrt radius twice and poloidal angle |
|
|
|
\(\partial_{\rho \rho \zeta} \lambda\) |
radians |
Poloidal stream function, third derivative, wrt radius twice and toroidal angle |
|
|
|
\(\partial_{\rho \theta} \lambda\) |
radians |
Poloidal stream function, second derivative wrt radius and poloidal angle |
|
|
|
\(\partial_{\rho \theta \theta} \lambda\) |
radians |
Poloidal stream function, third derivative wrt radius and poloidal angle twice |
|
|
|
\(\partial_{\rho \theta \zeta} \lambda\) |
radians |
Poloidal stream function, third derivative wrt radius, poloidal angle, and toroidal angle |
|
|
|
\(\partial_{\rho \zeta} \lambda\) |
radians |
Poloidal stream function, second derivative wrt radius and toroidal angle |
|
|
|
\(\partial_{\rho \zeta \zeta} \lambda\) |
radians |
Poloidal stream function, third derivative wrt radius and toroidal angle twice |
|
|
|
\(\partial_{\theta} \lambda\) |
radians |
Poloidal stream function, first poloidal derivative |
|
|
|
\(\partial_{\theta \theta} \lambda\) |
radians |
Poloidal stream function, second poloidal derivative |
|
|
|
\(\partial_{\theta \theta \theta} \lambda\) |
radians |
Poloidal stream function, third poloidal derivative |
|
|
|
\(\partial_{\theta \theta \zeta} \lambda\) |
radians |
Poloidal stream function, third derivative wrt poloidal angle twice and toroidal angle |
|
|
|
\(\partial_{\theta \zeta} \lambda\) |
radians |
Poloidal stream function, second derivative wrt poloidal and toroidal angles |
|
|
|
\(\partial_{\theta \zeta \zeta} \lambda\) |
radians |
Poloidal stream function, third derivative wrt poloidal angle and toroidal angle twice |
|
|
|
\(\partial_{\zeta} \lambda\) |
radians |
Poloidal stream function, first toroidal derivative |
|
|
|
\(\partial_{\zeta \zeta} \lambda\) |
radians |
Poloidal stream function, second toroidal derivative |
|
|
|
\(\partial_{\zeta \zeta \zeta} \lambda\) |
radians |
Poloidal stream function, third toroidal derivative |
|
|
|
\(\omega\) |
radians |
Toroidal stream function |
|
|
|
\(\partial_{\rho} \omega\) |
radians |
Toroidal stream function, first radial derivative |
|
|
|
\(\partial_{\rho \rho} \omega\) |
radians |
Toroidal stream function, second radial derivative |
|
|
|
\(\partial_{\rho \rho \rho} \omega\) |
radians |
Toroidal stream function, third radial derivative |
|
|
|
\(\partial_{\rho \rho \rho \rho} \omega\) |
radians |
Toroidal stream function, fourth radial derivative |
|
|
|
\(\partial_{\rho \rho \rho \theta} \omega\) |
radians |
Toroidal stream function, fourth derivative wrt radial coordinate thrice and poloidal once |
|
|
|
\(\partial_{\rho \rho \rho \zeta} \omega\) |
radians |
Toroidal stream function, fourth derivative wrt radial coordinate thrice and toroidal once |
|
|
|
\(\partial_{\rho \rho \theta} \omega\) |
radians |
Toroidal stream function, third derivative, wrt radius twice and poloidal angle |
|
|
|
\(\partial_{\rho \rho \theta \theta} \omega\) |
radians |
Toroidal stream function, fourth derivative, wrt radius twice and poloidal angle twice |
|
|
|
\(\partial_{\rho \theta \zeta} \omega\) |
radians |
Toroidal stream function, fourth derivative wrt radius twice, poloidal angle, and toroidal angle |
|
|
|
\(\partial_{\rho \rho \zeta} \omega\) |
radians |
Toroidal stream function, third derivative, wrt radius twice and toroidal angle |
|
|
|
\(\partial_{\rho \rho \zeta \zeta} \omega\) |
radians |
Toroidal stream function, fourth derivative, wrt radius twice and toroidal angle twice |
|
|
|
\(\partial_{\rho \theta} \omega\) |
radians |
Toroidal stream function, second derivative wrt radius and poloidal angle |
|
|
|
\(\partial_{\rho \theta \theta} \omega\) |
radians |
Toroidal stream function, third derivative wrt radius and poloidal angle twice |
|
|
|
\(\partial_{\rho \theta \theta \theta} \omega\) |
radians |
Toroidal stream function, third derivative wrt radius and poloidal angle thrice |
|
|
|
\(\partial_{\rho \theta \theta \zeta} \omega\) |
radians |
Toroidal stream function, fourth derivative wrt radius once, poloidal angle twice, and toroidal angle once |
|
|
|
\(\partial_{\rho \theta \zeta} \omega\) |
radians |
Toroidal stream function, third derivative wrt radius, poloidal angle, and toroidal angle |
|
|
|
\(\partial_{\rho \theta \zeta \zeta} \omega\) |
radians |
Toroidal stream function, fourth derivative wrt radius, poloidal angle, and toroidal angle twice |
|
|
|
\(\partial_{\rho \zeta} \omega\) |
radians |
Toroidal stream function, second derivative wrt radius and toroidal angle |
|
|
|
\(\partial_{\rho \zeta \zeta} \omega\) |
radians |
Toroidal stream function, third derivative wrt radius and toroidal angle twice |
|
|
|
\(\partial_{\rho \zeta \zeta \zeta} \omega\) |
radians |
Toroidal stream function, third derivative wrt radius and toroidal angle thrice |
|
|
|
\(\partial_{\theta} \omega\) |
radians |
Toroidal stream function, first poloidal derivative |
|
|
|
\(\partial_{\theta \theta} \omega\) |
radians |
Toroidal stream function, second poloidal derivative |
|
|
|
\(\partial_{\theta \theta \theta} \omega\) |
radians |
Toroidal stream function, third poloidal derivative |
|
|
|
\(\partial_{\theta \theta \zeta} \omega\) |
radians |
Toroidal stream function, third derivative wrt poloidal angle twice and toroidal angle |
|
|
|
\(\partial_{\theta \zeta} \omega\) |
radians |
Toroidal stream function, second derivative wrt poloidal and toroidal angles |
|
|
|
\(\partial_{\theta \zeta \zeta} \omega\) |
radians |
Toroidal stream function, third derivative wrt poloidal angle and toroidal angle twice |
|
|
|
\(\partial_{\zeta} \omega\) |
radians |
Toroidal stream function, first toroidal derivative |
|
|
|
\(\partial_{\zeta \zeta} \omega\) |
radians |
Toroidal stream function, second toroidal derivative |
|
|
|
\(\partial_{\zeta \zeta \zeta} \omega\) |
radians |
Toroidal stream function, third toroidal derivative |
|
|
|
\(\phi\) |
radians |
Toroidal angle in lab frame |
|
|
|
\(\partial_{\rho} \phi\) |
radians |
Toroidal angle in lab frame, derivative wrt radial 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 |
|
|
|
\(\partial_{\theta} \phi\) |
radians |
Toroidal angle in lab frame, derivative wrt poloidal 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 |
|
|
|
\(\partial_{\zeta} \phi\) |
radians |
Toroidal angle in lab frame, derivative wrt toroidal coordinate |
|
|
|
\(\partial_{\zeta \zeta} \phi\) |
radians |
Toroidal angle in lab frame, second derivative wrt toroidal coordinate |
|
|
|
\(\rho\) |
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) |
|
|
|
\(\vartheta\) |
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 |
|
|
|
\(\partial_{\rho} \theta\) |
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 |
|
|
|
\(J^{\rho}\) |
Amperes / cubic meter |
Contravariant radial component of plasma current density |
|
|
|
\(J^{\theta} \sqrt{g}\) |
Amperes |
Contravariant poloidal component of plasma current density, weighted by 3-D volume Jacobian |
|
|
|
\(J^{\theta}\) |
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 |
|
|
|
\(\mathbf{J} \sqrt{g}\) |
Ampere meters |
Plasma current density weighted by 3-D volume Jacobian |
|
|
|
\(\partial_{\rho} (\mathbf{J} \sqrt{g})\) |
Ampere meters |
Plasma current density weighted by 3-D volume Jacobian, radial derivative |
|
|
|
\(J_{R}\) |
Amperes / square meter |
Radial component of plasma current density in lab frame |
|
|
|
\(J_{\phi}\) |
Amperes / square meter |
Toroidal component of plasma current density in lab frame |
|
|
|
\(J_{Z}\) |
Amperes / square meter |
Vertical component of plasma current density in lab frame |
|
|
|
\(|\mathbf{J}|\) |
Amperes / square meter |
Magnitude 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 (note units are not Amperes) |
|
|
|
\(\mathbf{J} \cdot \hat{\mathbf{b}}\) |
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 |
|
|
|
\(F_{\mathrm{helical}}\) |
Amperes |
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 |
|
|
|
:math:` sqrt{g}(B^{theta} nabla zeta - B^{zeta} nabla theta)` |
Tesla * square meter |
Helical basis vector weighted by 3-D volume Jacobian |
|
|
|
\(|B^{\theta} \nabla \zeta - B^{\zeta} \nabla \theta|\) |
Tesla / square meter |
Magnitude of helical basis vector |
|
|
|
\(|\sqrt{g}(B^{\theta} \nabla \zeta - B^{\zeta} \nabla \theta)|\) |
Tesla * square meter |
Magnitude of helical basis vector weighted by 3-D volume Jacobian |
|
|
|
\(F_{anisotropic}\) |
Newtons / cubic meter |
Anisotropic force balance error |
|
|
|
\(W_B\) |
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 |
|
|
|
\(\psi' / \sqrt{g}\) |
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 |
|
|
|
\(\partial_{\rho} (\psi' / \sqrt{g})\) |
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 |
|
|
|
\(\partial_{\theta} (\psi' / \sqrt{g})\) |
Tesla / meter |
|
||
|
\(\partial_{\theta} B^{\theta}\) |
Tesla / meter |
Contravariant poloidal component of magnetic field, derivative wrt poloidal coordinate |
|
|
|
\(\partial_{\theta} B^{\zeta}\) |
Tesla / meter |
Contravariant toroidal component of magnetic field, derivative wrt poloidal coordinate |
|
|
|
\(\partial_{\theta} \mathbf{B}\) |
Tesla |
Magnetic field, derivative wrt poloidal angle |
|
|
|
\(\partial_{\zeta} (\psi' / \sqrt{g})\) |
Tesla / meter |
|
||
|
\(\partial_{\zeta} B^{\theta}\) |
Tesla / meter |
Contravariant poloidal component of magnetic field, derivative wrt toroidal coordinate |
|
|
|
\(\partial_{\zeta} B^{\zeta}\) |
Tesla / meter |
Contravariant toroidal component of magnetic field, derivative wrt toroidal coordinate |
|
|
|
\(\partial_{\zeta} \mathbf{B}\) |
Tesla |
Magnetic field, derivative wrt toroidal angle |
|
|
|
\(\partial_{\rho \rho} (\psi' / \sqrt{g})\) |
Tesla / meters |
|
||
|
\(\partial_{\rho\rho} B^{\theta}\) |
Tesla / meter |
Contravariant poloidal component of magnetic field, second derivative wrt radial and radial coordinates |
|
|
|
\(\partial_{\rho\rho} B^{\zeta}\) |
Tesla / meter |
Contravariant toroidal component of magnetic field, second derivative wrt radial and radial coordinates |
|
|
|
\(\partial_{\rho\rho} \mathbf{B}\) |
Tesla |
Magnetic field, second derivative wrt radial coordinate |
|
|
|
\(\partial_{\theta \theta} (\psi' / \sqrt{g})\) |
Tesla / meter |
|
||
|
\(\partial_{\theta\theta} B^{\theta}\) |
Tesla / meter |
Contravariant poloidal component of magnetic field, second derivative wrt poloidal and poloidal coordinates |
|
|
|
\(\partial_{\theta\theta} B^{\zeta}\) |
Tesla / meter |
Contravariant toroidal component of magnetic field, second derivative wrt poloidal and poloidal coordinates |
|
|
|
\(\partial_{\theta\theta} \mathbf{B}\) |
Tesla |
Magnetic field, second derivative wrt poloidal angle |
|
|
|
\(\partial_{\zeta \zeta} (\psi' / \sqrt{g})\) |
Tesla / meter |
|
||
|
\(\partial_{\zeta\zeta} B^{\theta}\) |
Tesla / meter |
Contravariant poloidal component of magnetic field, second derivative wrt toroidal and toroidal coordinates |
|
|
|
\(\partial_{\zeta\zeta} B^{\zeta}\) |
Tesla / meter |
Contravariant toroidal component of magnetic field, second derivative wrt toroidal and toroidal coordinates |
|
|
|
\(\partial_{\zeta\zeta} \mathbf{B}\) |
Tesla |
Magnetic field, second derivative wrt toroidal angle |
|
|
|
\(\partial_{\rho\theta} (\psi' / \sqrt{g})\) |
Tesla / meters |
|
||
|
\(\partial_{\rho\theta} B^{\theta}\) |
Tesla / meter |
Contravariant poloidal component of magnetic field, second derivative wrt radial and poloidal coordinates |
|
|
|
\(\partial_{\rho\theta} B^{\zeta}\) |
Tesla / meter |
Contravariant toroidal component of magnetic field, second derivative wrt radial and poloidal coordinates |
|
|
|
\(\partial_{\rho\theta} \mathbf{B}\) |
Tesla |
Magnetic field, second derivative wrt radial coordinate and poloidal angle |
|
|
|
\(\partial_{\theta\zeta} (\psi' / \sqrt{g})\) |
Tesla / meter |
|
||
|
\(\partial_{\theta\zeta} B^{\theta}\) |
Tesla / meter |
Contravariant poloidal component of magnetic field, second derivative wrt poloidal and toroidal coordinates |
|
|
|
\(\partial_{\theta\zeta} B^{\zeta}\) |
Tesla / meter |
Contravariant toroidal component of magnetic field, second derivative wrt poloidal and toroidal coordinates |
|
|
|
\(\partial_{\theta\zeta} \mathbf{B}\) |
Tesla |
Magnetic field, second derivative wrt poloidal and toroidal angles |
|
|
|
\(\partial_{\rho\zeta} (\psi' / \sqrt{g})\) |
Tesla / meters |
|
||
|
\(\partial_{\rho\zeta} B^{\theta}\) |
Tesla / meter |
Contravariant poloidal component of magnetic field, second derivative wrt radial and toroidal coordinates |
|
|
|
\(\partial_{\rho\zeta} B^{\zeta}\) |
Tesla / meter |
Contravariant toroidal component of magnetic field, second derivative wrt radial and toroidal coordinates |
|
|
|
\(\partial_{\rho\zeta} \mathbf{B}\) |
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 |
|
||
|
\(\partial_{\theta} (\mathbf{B} \cdot \nabla B)\) |
Tesla squared / meters |
|
||
|
\(\partial_{\zeta} (\mathbf{B} \cdot \nabla B)\) |
Tesla squared / meters |
|
||
|
\(\min_{\theta \zeta} |\mathbf{B}|\) |
Tesla |
Minimum field strength on each flux surface |
|
|
|
\(\max_{\theta \zeta} |\mathbf{B}|\) |
Tesla |
Maximum field strength on each flux surface |
|
|
|
\((B_{max} - B_{min}) / (B_{min} + B_{max})\) |
None |
Mirror ratio on each flux surface |
|
|
|
\((r / R_0)_{\mathrm{effective}}\) |
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 |
|
|
|
\(\mathbf{K}_{VC} = \mathbf{n} \times \mathbf{B}\) |
Amps / meter |
Virtual casing sheet current |
|
|
|
\(V\) |
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 |
|
|
|
\(\partial_{\rho\rho\rho} V(\rho)\) |
cubic meters |
Volume enclosed by flux surfaces, third derivative wrt radial coordinate |
|
|
|
\(A(\zeta)\) |
square meters |
Cross-sectional area as function of zeta |
|
|
|
\(A\) |
square meters |
Average cross-sectional area |
|
|
|
\(A(\rho)\) |
square meters |
Average cross-sectional area enclosed by flux surfaces |
|
|
|
\(S\) |
square meters |
Surface area of outermost flux surface |
|
|
|
\(S(\rho)\) |
square meters |
Surface area of flux surfaces |
|
|
|
\(\partial_{\rho} S(\rho)\) |
square meters |
Surface area of flux surfaces, derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho\rho} S(\rho)\) |
square meters |
Surface area of flux surfaces, second derivative wrt radial coordinate |
|
|
|
\(R_{0}\) |
meters |
Average major radius |
|
|
|
\(a\) |
meters |
Average minor radius |
|
|
|
\(R_{0} / a\) |
None |
Aspect ratio |
|
|
|
\(P(\zeta)\) |
meters |
Perimeter of cross section as function of zeta |
|
|
|
\(a_{\mathrm{major}} / a_{\mathrm{minor}}\) |
None |
Elongation at a toroidal cross-section |
|
|
|
\(L_{\mathrm{SFF},\rho}\) |
meters |
L coefficient of second fundamental form of constant rho surface |
|
|
|
\(M_{\mathrm{SFF},\rho}\) |
meters |
M coefficient of second fundamental form of constant rho surface |
|
|
|
\(N_{\mathrm{SFF},\rho}\) |
meters |
N coefficient of second fundamental form of constant rho surface |
|
|
|
\(k_{1,\rho}\) |
Inverse meters |
First principle curvature of constant rho surfaces |
|
|
|
\(k_{2,\rho}\) |
Inverse meters |
Second principle curvature of constant rho surfaces |
|
|
|
\(K_{\rho}\) |
meters squared |
Gaussian curvature of constant rho surfaces |
|
|
|
\(H_{\rho}\) |
meters |
Mean curvature of constant rho surfaces |
|
|
|
\(L_{\mathrm{SFF},\theta}\) |
meters |
L coefficient of second fundamental form of constant theta surface |
|
|
|
\(M_{\mathrm{SFF},\theta}\) |
meters |
M coefficient of second fundamental form of constant theta surface |
|
|
|
\(N_{\mathrm{SFF},\theta}\) |
meters |
N coefficient of second fundamental form of constant theta surface |
|
|
|
\(k_{1,\theta}\) |
Inverse meters |
First principle curvature of constant theta surfaces |
|
|
|
\(k_{2,\theta}\) |
Inverse meters |
Second principle curvature of constant theta surfaces |
|
|
|
\(K_{\theta}\) |
meters squared |
Gaussian curvature of constant theta surfaces |
|
|
|
\(H_{\theta}\) |
meters |
Mean curvature of constant theta surfaces |
|
|
|
\(L_{\mathrm{SFF},\zeta}\) |
meters |
L coefficient of second fundamental form of constant zeta surface |
|
|
|
\(M_{\mathrm{SFF},\zeta}\) |
meters |
M coefficient of second fundamental form of constant zeta surface |
|
|
|
\(N_{\mathrm{SFF},\zeta}\) |
meters |
N coefficient of second fundamental form of constant zeta surface |
|
|
|
\(k_{1,\zeta}\) |
Inverse meters |
First principle curvature of constant zeta surfaces |
|
|
|
\(k_{2,\zeta}\) |
Inverse meters |
Second principle curvature of constant zeta surfaces |
|
|
|
\(K_{\zeta}\) |
meters squared |
Gaussian curvature of constant zeta surfaces |
|
|
|
\(H_{\zeta}\) |
meters |
Mean curvature of constant zeta surfaces |
|
|
|
\(\sqrt{g}\) |
cubic meters |
Jacobian determinant of flux coordinate system |
|
|
|
\(\sqrt{g}_{PEST}\) |
cubic meters |
Jacobian determinant of PEST flux coordinate system |
|
|
|
\(|\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface |
|
|
|
\(\partial_{\rho} |\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho\rho} |\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface second derivative wrt radial coordinate |
|
|
|
\(\partial_{\zeta}|e_{\theta} \times e_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface,derivative wrt toroidal angle |
|
|
|
\(|\mathbf{e}_{\zeta} \times \mathbf{e}_{\rho}|\) |
square meters |
2D Jacobian determinant for constant theta surface |
|
|
|
\(|\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\) |
square meters |
2D Jacobian determinant for constant zeta surface |
|
|
|
\(\partial_{\rho} |\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\) |
square meters |
2D Jacobian determinant for constant zeta surface derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho \rho} |\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\) |
square meters |
2D Jacobian determinant for constant zeta surface second derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho} \sqrt{g}\) |
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 |
|
|
|
\(\partial_{\rho\rho\rho} \sqrt{g}\) |
cubic meters |
Jacobian determinant of flux coordinate system, third derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho\rho\theta} \sqrt{g}\) |
cubic meters |
Jacobian determinant of flux coordinate system, third derivative wrt radial coordinate twice and poloidal angle once |
|
|
|
\(\partial_{\theta\theta} \sqrt{g}\) |
cubic meters |
Jacobian determinant of flux coordinate system, second derivative wrt poloidal angle |
|
|
|
\(\partial_{\rho\theta\theta} \sqrt{g}\) |
cubic meters |
Jacobian determinant of flux coordinate system, third derivative wrt radial coordinate once and poloidal angle twice. |
|
|
|
\(\partial_{\zeta\zeta} \sqrt{g}\) |
cubic meters |
Jacobian determinant of flux coordinate system, second derivative wrt toroidal angle |
|
|
|
\(\partial_{\rho\zeta\zeta} \sqrt{g}\) |
cubic meters |
Jacobian determinant of flux coordinate system, third derivative wrt radial coordinate once and toroidal angle twice |
|
|
|
\(\partial_{\rho\theta} \sqrt{g}\) |
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 |
|
|
|
\(\partial_{\rho\theta\zeta} \sqrt{g}\) |
cubic meters |
Jacobian determinant of flux coordinate system, third derivative wrt radial, poloidal, and toroidal coordinate |
|
|
|
\(\partial_{\rho\zeta} \sqrt{g}\) |
cubic meters |
Jacobian determinant of flux coordinate system, second derivative wrt radial coordinate and toroidal angle |
|
|
|
\(\partial_{\rho\rho\zeta} \sqrt{g}\) |
cubic meters |
Jacobian determinant of flux coordinate system, third derivative wrt radial coordinate twice and toroidal angle once |
|
|
|
\(g_{\rho\rho}\) |
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 |
|
|
|
\(\partial_{\rho\rho\rho} g_{\theta\theta}\) |
square meters |
Poloidal/Poloidal element of covariant metric tensor, third derivative wrt rho |
|
|
|
\(\partial_{\rho\rho} g_{\theta\zeta}\) |
square meters |
Poloidal/Toroidal element of covariant metric tensor, second derivative wrt rho |
|
|
|
\(\partial_{\rho\rho\rho} g_{\theta\zeta}\) |
square meters |
Poloidal/Toroidal element of covariant metric tensor, third 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 |
|
|
|
\(\partial_{\rho} g^{\rho \rho}\) |
inverse square meters |
Radial/Radial element of contravariant metric tensor, first radial derivative |
|
|
|
\(\partial_{\rho} g^{\rho \theta}\) |
inverse square meters |
Radial/Poloidal element of contravariant metric tensor, first radial derivative |
|
|
|
\(\partial_{\rho} g^{\rho \zeta}\) |
inverse square meters |
Radial/Toroidal element of contravariant metric tensor, first radial derivative |
|
|
|
\(\partial_{\rho} g^{\theta \theta}\) |
inverse square meters |
Poloidal/Poloidal element of contravariant metric tensor, first radial derivative |
|
|
|
\(\partial_{\rho} g^{\theta \zeta}\) |
inverse square meters |
Poloidal/Toroidal element of contravariant metric tensor, first radial derivative |
|
|
|
\(\partial_{\rho} g^{\zeta \zeta}\) |
inverse square meters |
Toroidal/Toroidal element of contravariant metric tensor, first radial derivative |
|
|
|
\(\partial_{\theta} g^{\rho \rho}\) |
inverse square meters |
Radial/Radial element of contravariant metric tensor, first poloidal derivative |
|
|
|
\(\partial_{\theta} g^{\rho \theta}\) |
inverse square meters |
Radial/Poloidal element of contravariant metric tensor, first poloidal derivative |
|
|
|
\(\partial_{\theta} g^{\rho \zeta}\) |
inverse square meters |
Radial/Toroidal element of contravariant metric tensor, first poloidal derivative |
|
|
|
\(\partial_{\theta} g^{\theta \theta}\) |
inverse square meters |
Poloidal/Poloidal element of contravariant metric tensor, first poloidal derivative |
|
|
|
\(\partial_{\theta} g^{\theta \zeta}\) |
inverse square meters |
Poloidal/Toroidal element of contravariant metric tensor, first poloidal derivative |
|
|
|
\(\partial_{\theta} g^{\zeta \zeta}\) |
inverse square meters |
Toroidal/Toroidal element of contravariant metric tensor, first poloidal derivative |
|
|
|
\(\partial_{\zeta} g^{\rho \rho}\) |
inverse square meters |
Radial/Radial element of contravariant metric tensor, first toroidal derivative |
|
|
|
\(\partial_{\zeta} g^{\rho \theta}\) |
inverse square meters |
Radial/Poloidal element of contravariant metric tensor, first toroidal derivative |
|
|
|
\(\partial_{\zeta} g^{\rho \zeta}\) |
inverse square meters |
Radial/Toroidal element of contravariant metric tensor, first toroidal derivative |
|
|
|
\(\partial_{\zeta} g^{\theta \theta}\) |
inverse square meters |
Poloidal/Poloidal element of contravariant metric tensor, first toroidal derivative |
|
|
|
\(\partial_{\zeta} g^{\theta \zeta}\) |
inverse square meters |
Poloidal/Toroidal element of contravariant metric tensor, first toroidal derivative |
|
|
|
\(\partial_{\zeta} g^{\zeta \zeta}\) |
inverse square meters |
Toroidal/Toroidal element of contravariant metric tensor, first toroidal derivative |
|
|
|
\(|\nabla \rho|\) |
inverse meters |
Magnitude of contravariant radial basis vector |
|
|
|
\(|\nabla\psi|\) |
Webers per meter |
Toroidal flux gradient (normalized by 2pi) magnitude |
|
|
|
\(|\nabla\psi|^{2}\) |
Webers squared per square meter |
Toroidal flux gradient (normalized by 2pi) magnitude squared |
|
|
|
\(|\nabla \theta|\) |
inverse meters |
Magnitude of contravariant poloidal basis vector |
|
|
|
\(|\nabla \zeta|\) |
inverse meters |
Magnitude of contravariant toroidal basis vector |
|
|
|
\(B_{\theta, m, n}\) |
Tesla * meters |
Fourier coefficients for covariant poloidal component of magnetic field |
|
|
|
\(B_{\zeta, m, n}\) |
Tesla * meters |
Fourier coefficients for covariant toroidal component of magnetic field |
|
|
|
\(w_{\mathrm{Boozer},m,n}\) |
Tesla * meters |
RHS of eq 10 in Hirshman 1995 ‘Transformation from VMEC to Boozer Coordinates’ |
|
|
|
\(w_{\mathrm{Boozer}}\) |
Tesla * meters |
Inverse Fourier transform of RHS of eq 10 in Hirshman 1995 ‘Transformation from VMEC to Boozer Coordinates’ |
|
|
|
\(\partial_{\theta} w_{\mathrm{Boozer}}\) |
Tesla * meters |
Inverse Fourier transform of RHS of eq 10 in Hirshman 1995 ‘Transformation from VMEC to Boozer Coordinates’, poloidal derivative |
|
|
|
\(\partial_{\zeta} w_{\mathrm{Boozer}}\) |
Tesla * meters |
Inverse Fourier transform of RHS of eq 10 in Hirshman 1995 ‘Transformation from VMEC to Boozer Coordinates’, toroidal derivative |
|
|
|
\(\nu = \zeta_{B} - \zeta\) |
radians |
Boozer toroidal stream function |
|
|
|
\(\partial_{\theta} \nu\) |
radians |
Boozer toroidal stream function, derivative wrt poloidal angle |
|
|
|
\(\partial_{\zeta} \nu\) |
radians |
Boozer toroidal stream function, derivative wrt toroidal angle |
|
|
|
\(\theta_{B}\) |
radians |
Boozer poloidal angular coordinate |
|
|
|
\(\zeta_{B}\) |
radians |
Boozer toroidal angular coordinate |
|
|
|
\(\sqrt{g}_{B}\) |
None |
Jacobian determinant of Boozer coordinates |
|
|
|
\(B_{mn}^{\mathrm{Boozer}}\) |
Tesla |
Boozer harmonics of magnetic field |
|
|
|
\(\mathrm{Boozer~modes}\) |
None |
Boozer harmonics |
|
|
|
\((M \iota - N) (\mathbf{B} \times \nabla \psi) \cdot \nabla B - (M G + N I) \mathbf{B} \cdot \nabla B\) |
Tesla cubed |
Two-term quasisymmetry metric |
|
|
|
\(\nabla \psi \times \nabla B \cdot \nabla (\mathbf{B} \cdot \nabla B)\) |
Tesla quarted / square meters |
Triple product quasisymmetry metric |
|
|
|
\(1/|B|^2 (\mathbf{b} \times \nabla B) \cdot \nabla \psi\) |
None |
Measure of cross field drift at each point, unweighted by particle energy |
|
|
|
\(\Psi\) |
Webers |
Toroidal flux |
|
|
|
\(\psi = \Psi / (2 \pi)\) |
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 |
|
|
|
\(\partial_{\rho} \chi\) |
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 |
|
|
|
\(\partial_{\rho \rho} T_e\) |
electron-Volts |
Electron temperature, second radial derivative |
|
|
|
\(n_e\) |
1 / cubic meters |
Electron density |
|
|
|
\(\partial_{\rho} n_e\) |
1 / cubic meters |
Electron density, first radial derivative |
|
|
|
\(\partial_{\rho \rho} n_e\) |
1 / cubic meters |
Electron density, second radial derivative |
|
|
|
\(T_i\) |
electron-Volts |
Ion temperature |
|
|
|
\(\partial_{\rho} T_i\) |
electron-Volts |
Ion temperature, first radial derivative |
|
|
|
\(\partial_{\rho \rho} T_i\) |
electron-Volts |
Ion temperature, second 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 |
|
|
|
\(\partial_{\theta} p\) |
Pascals |
Pressure, first poloidal derivative |
|
|
|
\(\partial_{\zeta} p\) |
Pascals |
Pressure, first toroidal 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 |
|
|
|
\(\beta_a = \mu_0 (p_{||} - p_{\perp})/B^2\) |
None |
Pressure anisotropy |
|
|
|
\(\partial_{\rho} \beta_a = \mu_0 (p_{||} - p_{\perp})/B^2\) |
None |
Pressure anisotropy, first radial derivative |
|
|
|
\(\partial_{\theta} \beta_a = \mu_0 (p_{||} - p_{\perp})/B^2\) |
None |
Pressure anisotropy, first poloidal derivative |
|
|
|
\(\partial_{\zeta} \beta_a = \mu_0 (p_{||} - p_{\perp})/B^2\) |
None |
Pressure anisotropy, first toroidal derivative |
|
|
|
\(\nabla \beta_a = \nabla \mu_0 (p_{||} - p_{\perp})/B^2\) |
Inverse meters |
Pressure anisotropy 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 |
|
|
|
\(\iota~\mathrm{from~current}\) |
None |
Rotational transform (normalized by 2pi), current contribution |
|
|
|
\(\iota~\mathrm{in~vacuum}\) |
None |
Rotational transform (normalized by 2pi), vacuum contribution |
|
|
|
\(\iota_{\mathrm{numerator}}~\mathrm{from~current}\) |
inverse meters |
Numerator of rotational transform formula, current contribution |
|
|
|
\(\iota_{\mathrm{numerator}}~\mathrm{in~vacuum}\) |
inverse meters |
Numerator of rotational transform formula, vacuum contribution |
|
|
|
\(\partial_{\rho} \iota_{\mathrm{numerator}}~\mathrm{from~current}\) |
inverse meters |
Numerator of rotational transform formula, current contribution, first radial derivative |
|
|
|
\(\partial_{\rho} \iota_{\mathrm{numerator}}~\mathrm{in~vacuum}\) |
inverse meters |
Numerator of rotational transform formula, vacuum contribution, first radial derivative |
|
|
|
\(\iota_{\mathrm{numerator}}\) |
inverse meters |
Numerator of rotational transform formula |
|
|
|
\(\partial_{\rho} \iota_{\mathrm{numerator}}\) |
inverse meters |
Numerator of rotational transform formula, first radial derivative |
|
|
|
\(\partial_{\rho\rho} \iota_{\mathrm{numerator}}\) |
inverse meters |
Numerator of rotational transform formula, second radial derivative |
|
|
|
\(\partial_{\rho\rho\rho} \iota_{\mathrm{numerator}}\) |
inverse meters |
Numerator of rotational transform formula, third radial derivative |
|
|
|
\(\iota_{\mathrm{denominator}}\) |
inverse meters |
Denominator of rotational transform formula |
|
|
|
\(\partial_{\rho} \iota_{\mathrm{denominator}}\) |
inverse meters |
Denominator of rotational transform formula, first radial derivative |
|
|
|
\(\partial_{\rho\rho} \iota_{\mathrm{denominator}}\) |
inverse meters |
Denominator of rotational transform formula, second radial derivative |
|
|
|
\(\partial_{\rho\rho\rho} \iota_{\mathrm{denominator}}\) |
inverse meters |
Denominator of rotational transform formula, third radial derivative |
|
|
|
\(\partial_{\psi} \iota\) |
Inverse Webers |
Rotational transform, radial derivative wrt toroidal flux |
|
|
|
\(q = 1/\iota\) |
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 |
|
|
|
\(\partial_{\rho\rho} G\) |
Tesla * meters |
Boozer poloidal current enclosed by flux surfaces, second derivative wrt radial coordinate |
|
|
|
\(\frac{2\pi}{\mu_0} I\) |
Amperes |
Net toroidal current enclosed by flux surfaces |
|
|
|
\(\frac{2\pi}{\mu_0} \partial_{\rho} I\) |
Amperes |
Net toroidal current enclosed by flux surfaces, derivative wrt radial coordinate |
|
|
|
\(\frac{2\pi}{\mu_0} \partial_{\rho\rho} I\) |
Amperes |
Net toroidal current enclosed by flux surfaces, second derivative wrt radial coordinate |
|
|
|
\(-\rho \frac{\partial_{\rho}\iota}{\iota}\) |
None |
Global magnetic shear |
|
|
|
\(D_{\mathrm{shear}}\) |
Inverse Webers squared |
Mercier stability criterion magnetic shear term |
|
|
|
\(D_{\mathrm{current}}\) |
Inverse Webers squared |
Mercier stability criterion toroidal current term |
|
|
|
\(D_{\mathrm{well}}\) |
Inverse Webers squared |
Mercier stability criterion magnetic well term |
|
|
|
\(D_{\mathrm{geodesic}}\) |
Inverse Webers squared |
Mercier stability criterion geodesic curvature term |
|
|
|
\(D_{\mathrm{Mercier}}\) |
Inverse Webers squared |
Mercier stability criterion (positive/negative value denotes stability/instability) |
|
|
|
\(\mathrm{Magnetic~Well}\) |
None |
Magnetic well proxy for MHD stability (positive/negative value denotes stability/instability) |
|
desc.geometry.curve.FourierRZCurve
Name |
Label |
Units |
Description |
Module |
Aliases |
|---|---|---|---|---|---|
|
\(0\) |
None |
Zeros |
|
|
|
\(s\) |
None |
Curve parameter, on [0, 2pi) |
|
|
|
\(ds\) |
None |
Spacing of curve parameter |
|
|
|
\(X\) |
meters |
Cartesian X coordinate. |
|
|
|
\(Y\) |
meters |
Cartesian Y coordinate. |
|
|
|
\(R\) |
meters |
Cylindrical radial position along curve |
|
|
|
\(\phi\) |
radians |
Toroidal phi position along curve |
|
|
|
\(Z\) |
meters |
Cylindrical vertical position along curve |
|
|
|
\(\mathbf{x}\) |
meters |
Position vector along curve |
|
|
|
\(\partial_{s} \mathbf{x}\) |
meters |
Position vector along curve, first derivative |
|
|
|
\(\partial_{ss} \mathbf{x}\) |
meters |
Position vector along curve, second derivative |
|
|
|
\(\partial_{sss} \mathbf{x}\) |
meters |
Position vector along curve, third derivative |
|
|
|
\(\mathbf{T}_{\mathrm{Frenet-Serret}}\) |
None |
Tangent unit vector to curve in Frenet-Serret frame |
|
|
|
\(\mathbf{N}_{\mathrm{Frenet-Serret}}\) |
None |
Normal unit vector to curve in Frenet-Serret frame |
|
|
|
\(\mathbf{B}_{\mathrm{Frenet-Serret}}\) |
None |
Binormal unit vector to curve in Frenet-Serret frame |
|
|
|
\(\kappa\) |
Inverse meters |
Scalar curvature of the curve |
|
|
|
\(\tau\) |
Inverse meters |
Scalar torsion of the curve |
|
|
|
\(L\) |
meters |
Length of the curve |
|
desc.geometry.curve.FourierXYZCurve
Name |
Label |
Units |
Description |
Module |
Aliases |
|---|---|---|---|---|---|
|
\(0\) |
None |
Zeros |
|
|
|
\(s\) |
None |
Curve parameter, on [0, 2pi) |
|
|
|
\(ds\) |
None |
Spacing of curve parameter |
|
|
|
\(X\) |
meters |
Cartesian X coordinate. |
|
|
|
\(Y\) |
meters |
Cartesian Y coordinate. |
|
|
|
\(R\) |
meters |
Cylindrical radial position along curve |
|
|
|
\(\phi\) |
radians |
Toroidal phi position along curve |
|
|
|
\(Z\) |
meters |
Cylindrical vertical position along curve |
|
|
|
\(\mathbf{x}\) |
meters |
Position vector along curve |
|
|
|
\(\partial_{s} \mathbf{x}\) |
meters |
Position vector along curve, first derivative |
|
|
|
\(\partial_{ss} \mathbf{x}\) |
meters |
Position vector along curve, second derivative |
|
|
|
\(\partial_{sss} \mathbf{x}\) |
meters |
Position vector along curve, third derivative |
|
|
|
\(\mathbf{T}_{\mathrm{Frenet-Serret}}\) |
None |
Tangent unit vector to curve in Frenet-Serret frame |
|
|
|
\(\mathbf{N}_{\mathrm{Frenet-Serret}}\) |
None |
Normal unit vector to curve in Frenet-Serret frame |
|
|
|
\(\mathbf{B}_{\mathrm{Frenet-Serret}}\) |
None |
Binormal unit vector to curve in Frenet-Serret frame |
|
|
|
\(\kappa\) |
Inverse meters |
Scalar curvature of the curve |
|
|
|
\(\tau\) |
Inverse meters |
Scalar torsion of the curve |
|
|
|
\(L\) |
meters |
Length of the curve |
|
desc.geometry.curve.FourierPlanarCurve
Name |
Label |
Units |
Description |
Module |
Aliases |
|---|---|---|---|---|---|
|
\(0\) |
None |
Zeros |
|
|
|
\(s\) |
None |
Curve parameter, on [0, 2pi) |
|
|
|
\(ds\) |
None |
Spacing of curve parameter |
|
|
|
\(X\) |
meters |
Cartesian X coordinate. |
|
|
|
\(Y\) |
meters |
Cartesian Y coordinate. |
|
|
|
\(R\) |
meters |
Cylindrical radial position along curve |
|
|
|
\(\phi\) |
radians |
Toroidal phi position along curve |
|
|
|
\(Z\) |
meters |
Cylindrical vertical position along curve |
|
|
|
\(\mathbf{x}\) |
meters |
Position vector along curve |
|
|
|
\(\partial_{s} \mathbf{x}\) |
meters |
Position vector along curve, first derivative |
|
|
|
\(\partial_{ss} \mathbf{x}\) |
meters |
Position vector along curve, second derivative |
|
|
|
\(\partial_{sss} \mathbf{x}\) |
meters |
Position vector along curve, third derivative |
|
|
|
\(\mathbf{T}_{\mathrm{Frenet-Serret}}\) |
None |
Tangent unit vector to curve in Frenet-Serret frame |
|
|
|
\(\mathbf{N}_{\mathrm{Frenet-Serret}}\) |
None |
Normal unit vector to curve in Frenet-Serret frame |
|
|
|
\(\mathbf{B}_{\mathrm{Frenet-Serret}}\) |
None |
Binormal unit vector to curve in Frenet-Serret frame |
|
|
|
\(\kappa\) |
Inverse meters |
Scalar curvature of the curve |
|
|
|
\(\tau\) |
Inverse meters |
Scalar torsion of the curve |
|
|
|
\(L\) |
meters |
Length of the curve |
|
desc.geometry.curve.SplineXYZCurve
Name |
Label |
Units |
Description |
Module |
Aliases |
|---|---|---|---|---|---|
|
\(0\) |
None |
Zeros |
|
|
|
\(s\) |
None |
Curve parameter, on [0, 2pi) |
|
|
|
\(ds\) |
None |
Spacing of curve parameter |
|
|
|
\(X\) |
meters |
Cartesian X coordinate. |
|
|
|
\(Y\) |
meters |
Cartesian Y coordinate. |
|
|
|
\(R\) |
meters |
Cylindrical radial position along curve |
|
|
|
\(\phi\) |
radians |
Toroidal phi position along curve |
|
|
|
\(Z\) |
meters |
Cylindrical vertical position along curve |
|
|
|
\(\mathbf{x}\) |
meters |
Position vector along curve |
|
|
|
\(\partial_{s} \mathbf{x}\) |
meters |
Position vector along curve, first derivative |
|
|
|
\(\partial_{ss} \mathbf{x}\) |
meters |
Position vector along curve, second derivative |
|
|
|
\(\partial_{sss} \mathbf{x}\) |
meters |
Position vector along curve, third derivative |
|
|
|
\(\mathbf{T}_{\mathrm{Frenet-Serret}}\) |
None |
Tangent unit vector to curve in Frenet-Serret frame |
|
|
|
\(\mathbf{N}_{\mathrm{Frenet-Serret}}\) |
None |
Normal unit vector to curve in Frenet-Serret frame |
|
|
|
\(\mathbf{B}_{\mathrm{Frenet-Serret}}\) |
None |
Binormal unit vector to curve in Frenet-Serret frame |
|
|
|
\(\kappa\) |
Inverse meters |
Scalar curvature of the curve |
|
|
|
\(\tau\) |
Inverse meters |
Scalar torsion of the curve |
|
|
|
\(L\) |
meters |
Length of the curve |
|
desc.geometry.surface.FourierRZToroidalSurface
Name |
Label |
Units |
Description |
Module |
Aliases |
|---|---|---|---|---|---|
|
\(\mathbf{e}^{\theta} \sqrt{g}\) |
square meters |
Contravariant poloidal basis vector weighted by 3-D volume Jacobian |
|
|
|
\(\hat{\mathbf{n}}_{\rho}\) |
None |
Unit vector normal to constant rho surface (direction of e^rho) |
|
|
|
\(\partial_{\zeta}\hat{\mathbf{n}}_{\rho}\) |
None |
Unit vector normal to constant rho surface (direction of e^rho), derivative wrt toroidal angle |
|
|
|
\(\hat{\mathbf{n}}_{\theta}\) |
None |
Unit vector normal to constant theta surface (direction of e^theta) |
|
|
|
\(\hat{\mathbf{n}}_{\zeta}\) |
None |
Unit vector normal to constant zeta surface (direction of e^zeta) |
|
|
|
\(0\) |
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 |
|
|
|
\(V\) |
cubic meters |
Volume |
|
|
|
\(A(\zeta)\) |
square meters |
Cross-sectional area as function of zeta |
|
|
|
\(A\) |
square meters |
Average cross-sectional area |
|
|
|
\(S\) |
square meters |
Surface area of outermost flux surface |
|
|
|
\(R_{0}\) |
meters |
Average major radius |
|
|
|
\(a\) |
meters |
Average minor radius |
|
|
|
\(R_{0} / a\) |
None |
Aspect ratio |
|
|
|
\(P(\zeta)\) |
meters |
Perimeter of cross section as function of zeta |
|
|
|
\(a_{\mathrm{major}} / a_{\mathrm{minor}}\) |
None |
Elongation at a toroidal cross-section |
|
|
|
\(L_{\mathrm{SFF},\rho}\) |
meters |
L coefficient of second fundamental form of constant rho surface |
|
|
|
\(M_{\mathrm{SFF},\rho}\) |
meters |
M coefficient of second fundamental form of constant rho surface |
|
|
|
\(N_{\mathrm{SFF},\rho}\) |
meters |
N coefficient of second fundamental form of constant rho surface |
|
|
|
\(k_{1,\rho}\) |
Inverse meters |
First principle curvature of constant rho surfaces |
|
|
|
\(k_{2,\rho}\) |
Inverse meters |
Second principle curvature of constant rho surfaces |
|
|
|
\(K_{\rho}\) |
meters squared |
Gaussian curvature of constant rho surfaces |
|
|
|
\(H_{\rho}\) |
meters |
Mean curvature of constant rho surfaces |
|
|
|
\(|\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface |
|
|
|
\(\partial_{\rho} |\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho\rho} |\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface second derivative wrt radial coordinate |
|
|
|
\(\partial_{\zeta}|e_{\theta} \times e_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface,derivative wrt toroidal angle |
|
|
|
\(|\mathbf{e}_{\zeta} \times \mathbf{e}_{\rho}|\) |
square meters |
2D Jacobian determinant for constant theta surface |
|
|
|
\(|\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\) |
square meters |
2D Jacobian determinant for constant zeta surface |
|
|
|
\(\partial_{\rho} |\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\) |
square meters |
2D Jacobian determinant for constant zeta surface derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho \rho} |\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\) |
square meters |
2D Jacobian determinant for constant zeta surface second derivative wrt radial coordinate |
|
|
|
\(g_{\rho\rho}\) |
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 |
|
|
|
\(\mathbf{r}\) |
meters |
Position vector along surface |
|
|
|
\(X\) |
meters |
Cartesian X coordinate. |
|
|
|
\(Y\) |
meters |
Cartesian Y coordinate. |
|
|
|
\(R\) |
meters |
Cylindrical radial position along surface |
|
|
|
\(\phi\) |
radians |
Toroidal phi position along surface |
|
|
|
\(\partial_{\rho} \phi\) |
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 |
|
|
|
\(Z\) |
meters |
Cylindrical vertical position along surface |
|
|
|
\(\mathbf{e}_{\rho}\) |
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 |
|
|
|
\(\partial_{\rho \rho} \mathbf{e}_{\rho}\) |
meters |
Covariant radial basis vector, second 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 |
|
|
|
\(\partial_{\rho \rho} \mathbf{e}_{\theta}\) |
meters |
Covariant poloidal basis vector, second 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 |
|
|
|
\(\partial_{\rho \rho} \mathbf{e}_{\zeta}\) |
meters |
Covariant toroidal basis vector, second 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 |
|
desc.geometry.surface.ZernikeRZToroidalSection
Name |
Label |
Units |
Description |
Module |
Aliases |
|---|---|---|---|---|---|
|
\(\mathbf{e}^{\theta} \sqrt{g}\) |
square meters |
Contravariant poloidal basis vector weighted by 3-D volume Jacobian |
|
|
|
\(\hat{\mathbf{n}}_{\rho}\) |
None |
Unit vector normal to constant rho surface (direction of e^rho) |
|
|
|
\(\partial_{\zeta}\hat{\mathbf{n}}_{\rho}\) |
None |
Unit vector normal to constant rho surface (direction of e^rho), derivative wrt toroidal angle |
|
|
|
\(\hat{\mathbf{n}}_{\theta}\) |
None |
Unit vector normal to constant theta surface (direction of e^theta) |
|
|
|
\(\hat{\mathbf{n}}_{\zeta}\) |
None |
Unit vector normal to constant zeta surface (direction of e^zeta) |
|
|
|
\(0\) |
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 |
|
|
|
\(A(\zeta)\) |
square meters |
Cross-sectional area as function of zeta |
|
|
|
\(A\) |
square meters |
Average cross-sectional area |
|
|
|
\(P(\zeta)\) |
meters |
Perimeter of cross section as function of zeta |
|
|
|
\(a_{\mathrm{major}} / a_{\mathrm{minor}}\) |
None |
Elongation at a toroidal cross-section |
|
|
|
\(L_{\mathrm{SFF},\zeta}\) |
meters |
L coefficient of second fundamental form of constant zeta surface |
|
|
|
\(M_{\mathrm{SFF},\zeta}\) |
meters |
M coefficient of second fundamental form of constant zeta surface |
|
|
|
\(N_{\mathrm{SFF},\zeta}\) |
meters |
N coefficient of second fundamental form of constant zeta surface |
|
|
|
\(k_{1,\zeta}\) |
Inverse meters |
First principle curvature of constant zeta surfaces |
|
|
|
\(k_{2,\zeta}\) |
Inverse meters |
Second principle curvature of constant zeta surfaces |
|
|
|
\(K_{\zeta}\) |
meters squared |
Gaussian curvature of constant zeta surfaces |
|
|
|
\(H_{\zeta}\) |
meters |
Mean curvature of constant zeta surfaces |
|
|
|
\(|\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface |
|
|
|
\(\partial_{\rho} |\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho\rho} |\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface second derivative wrt radial coordinate |
|
|
|
\(\partial_{\zeta}|e_{\theta} \times e_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface,derivative wrt toroidal angle |
|
|
|
\(|\mathbf{e}_{\zeta} \times \mathbf{e}_{\rho}|\) |
square meters |
2D Jacobian determinant for constant theta surface |
|
|
|
\(|\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\) |
square meters |
2D Jacobian determinant for constant zeta surface |
|
|
|
\(\partial_{\rho} |\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\) |
square meters |
2D Jacobian determinant for constant zeta surface derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho \rho} |\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\) |
square meters |
2D Jacobian determinant for constant zeta surface second derivative wrt radial coordinate |
|
|
|
\(g_{\rho\rho}\) |
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 |
|
|
|
\(X\) |
meters |
Cartesian X coordinate. |
|
|
|
\(Y\) |
meters |
Cartesian Y coordinate. |
|
|
|
\(R\) |
meters |
Cylindrical radial position along surface |
|
|
|
\(\phi\) |
radians |
Toroidal phi position along surface |
|
|
|
\(\partial_{\rho} \phi\) |
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 |
|
|
|
\(Z\) |
meters |
Cylindrical vertical position along surface |
|
|
|
\(\mathbf{r}\) |
meters |
Position vector along surface |
|
|
|
\(\mathbf{e}_{\rho}\) |
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 |
|
|
|
\(\partial_{\rho \rho} \mathbf{e}_{\rho}\) |
meters |
Covariant radial basis vector, second 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 |
|
|
|
\(\partial_{\rho \rho} \mathbf{e}_{\theta}\) |
meters |
Covariant poloidal basis vector, second 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 |
|
|
|
\(\partial_{\rho \rho} \mathbf{e}_{\zeta}\) |
meters |
Covariant toroidal basis vector, second 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 |
|
desc.coils.FourierRZCoil
Name |
Label |
Units |
Description |
Module |
Aliases |
|---|---|---|---|---|---|
|
\(0\) |
None |
Zeros |
|
|
|
\(s\) |
None |
Curve parameter, on [0, 2pi) |
|
|
|
\(ds\) |
None |
Spacing of curve parameter |
|
|
|
\(X\) |
meters |
Cartesian X coordinate. |
|
|
|
\(Y\) |
meters |
Cartesian Y coordinate. |
|
|
|
\(R\) |
meters |
Cylindrical radial position along curve |
|
|
|
\(\phi\) |
radians |
Toroidal phi position along curve |
|
|
|
\(Z\) |
meters |
Cylindrical vertical position along curve |
|
|
|
\(\mathbf{x}\) |
meters |
Position vector along curve |
|
|
|
\(\partial_{s} \mathbf{x}\) |
meters |
Position vector along curve, first derivative |
|
|
|
\(\partial_{ss} \mathbf{x}\) |
meters |
Position vector along curve, second derivative |
|
|
|
\(\partial_{sss} \mathbf{x}\) |
meters |
Position vector along curve, third derivative |
|
|
|
\(\mathbf{T}_{\mathrm{Frenet-Serret}}\) |
None |
Tangent unit vector to curve in Frenet-Serret frame |
|
|
|
\(\mathbf{N}_{\mathrm{Frenet-Serret}}\) |
None |
Normal unit vector to curve in Frenet-Serret frame |
|
|
|
\(\mathbf{B}_{\mathrm{Frenet-Serret}}\) |
None |
Binormal unit vector to curve in Frenet-Serret frame |
|
|
|
\(\kappa\) |
Inverse meters |
Scalar curvature of the curve |
|
|
|
\(\tau\) |
Inverse meters |
Scalar torsion of the curve |
|
|
|
\(L\) |
meters |
Length of the curve |
|
desc.coils.FourierXYZCoil
Name |
Label |
Units |
Description |
Module |
Aliases |
|---|---|---|---|---|---|
|
\(0\) |
None |
Zeros |
|
|
|
\(s\) |
None |
Curve parameter, on [0, 2pi) |
|
|
|
\(ds\) |
None |
Spacing of curve parameter |
|
|
|
\(X\) |
meters |
Cartesian X coordinate. |
|
|
|
\(Y\) |
meters |
Cartesian Y coordinate. |
|
|
|
\(R\) |
meters |
Cylindrical radial position along curve |
|
|
|
\(\phi\) |
radians |
Toroidal phi position along curve |
|
|
|
\(Z\) |
meters |
Cylindrical vertical position along curve |
|
|
|
\(\mathbf{x}\) |
meters |
Position vector along curve |
|
|
|
\(\partial_{s} \mathbf{x}\) |
meters |
Position vector along curve, first derivative |
|
|
|
\(\partial_{ss} \mathbf{x}\) |
meters |
Position vector along curve, second derivative |
|
|
|
\(\partial_{sss} \mathbf{x}\) |
meters |
Position vector along curve, third derivative |
|
|
|
\(\mathbf{T}_{\mathrm{Frenet-Serret}}\) |
None |
Tangent unit vector to curve in Frenet-Serret frame |
|
|
|
\(\mathbf{N}_{\mathrm{Frenet-Serret}}\) |
None |
Normal unit vector to curve in Frenet-Serret frame |
|
|
|
\(\mathbf{B}_{\mathrm{Frenet-Serret}}\) |
None |
Binormal unit vector to curve in Frenet-Serret frame |
|
|
|
\(\kappa\) |
Inverse meters |
Scalar curvature of the curve |
|
|
|
\(\tau\) |
Inverse meters |
Scalar torsion of the curve |
|
|
|
\(L\) |
meters |
Length of the curve |
|
desc.coils.FourierPlanarCoil
Name |
Label |
Units |
Description |
Module |
Aliases |
|---|---|---|---|---|---|
|
\(0\) |
None |
Zeros |
|
|
|
\(s\) |
None |
Curve parameter, on [0, 2pi) |
|
|
|
\(ds\) |
None |
Spacing of curve parameter |
|
|
|
\(X\) |
meters |
Cartesian X coordinate. |
|
|
|
\(Y\) |
meters |
Cartesian Y coordinate. |
|
|
|
\(R\) |
meters |
Cylindrical radial position along curve |
|
|
|
\(\phi\) |
radians |
Toroidal phi position along curve |
|
|
|
\(Z\) |
meters |
Cylindrical vertical position along curve |
|
|
|
\(\mathbf{x}\) |
meters |
Position vector along curve |
|
|
|
\(\partial_{s} \mathbf{x}\) |
meters |
Position vector along curve, first derivative |
|
|
|
\(\partial_{ss} \mathbf{x}\) |
meters |
Position vector along curve, second derivative |
|
|
|
\(\partial_{sss} \mathbf{x}\) |
meters |
Position vector along curve, third derivative |
|
|
|
\(\mathbf{T}_{\mathrm{Frenet-Serret}}\) |
None |
Tangent unit vector to curve in Frenet-Serret frame |
|
|
|
\(\mathbf{N}_{\mathrm{Frenet-Serret}}\) |
None |
Normal unit vector to curve in Frenet-Serret frame |
|
|
|
\(\mathbf{B}_{\mathrm{Frenet-Serret}}\) |
None |
Binormal unit vector to curve in Frenet-Serret frame |
|
|
|
\(\kappa\) |
Inverse meters |
Scalar curvature of the curve |
|
|
|
\(\tau\) |
Inverse meters |
Scalar torsion of the curve |
|
|
|
\(L\) |
meters |
Length of the curve |
|
desc.magnetic_fields._current_potential.CurrentPotentialField
Name |
Label |
Units |
Description |
Module |
Aliases |
|---|---|---|---|---|---|
|
\(\mathbf{e}^{\theta} \sqrt{g}\) |
square meters |
Contravariant poloidal basis vector weighted by 3-D volume Jacobian |
|
|
|
\(\hat{\mathbf{n}}_{\rho}\) |
None |
Unit vector normal to constant rho surface (direction of e^rho) |
|
|
|
\(\partial_{\zeta}\hat{\mathbf{n}}_{\rho}\) |
None |
Unit vector normal to constant rho surface (direction of e^rho), derivative wrt toroidal angle |
|
|
|
\(\hat{\mathbf{n}}_{\theta}\) |
None |
Unit vector normal to constant theta surface (direction of e^theta) |
|
|
|
\(\hat{\mathbf{n}}_{\zeta}\) |
None |
Unit vector normal to constant zeta surface (direction of e^zeta) |
|
|
|
\(0\) |
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 |
|
|
|
\(V\) |
cubic meters |
Volume |
|
|
|
\(A(\zeta)\) |
square meters |
Cross-sectional area as function of zeta |
|
|
|
\(A\) |
square meters |
Average cross-sectional area |
|
|
|
\(S\) |
square meters |
Surface area of outermost flux surface |
|
|
|
\(R_{0}\) |
meters |
Average major radius |
|
|
|
\(a\) |
meters |
Average minor radius |
|
|
|
\(R_{0} / a\) |
None |
Aspect ratio |
|
|
|
\(P(\zeta)\) |
meters |
Perimeter of cross section as function of zeta |
|
|
|
\(a_{\mathrm{major}} / a_{\mathrm{minor}}\) |
None |
Elongation at a toroidal cross-section |
|
|
|
\(L_{\mathrm{SFF},\rho}\) |
meters |
L coefficient of second fundamental form of constant rho surface |
|
|
|
\(M_{\mathrm{SFF},\rho}\) |
meters |
M coefficient of second fundamental form of constant rho surface |
|
|
|
\(N_{\mathrm{SFF},\rho}\) |
meters |
N coefficient of second fundamental form of constant rho surface |
|
|
|
\(k_{1,\rho}\) |
Inverse meters |
First principle curvature of constant rho surfaces |
|
|
|
\(k_{2,\rho}\) |
Inverse meters |
Second principle curvature of constant rho surfaces |
|
|
|
\(K_{\rho}\) |
meters squared |
Gaussian curvature of constant rho surfaces |
|
|
|
\(H_{\rho}\) |
meters |
Mean curvature of constant rho surfaces |
|
|
|
\(|\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface |
|
|
|
\(\partial_{\rho} |\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho\rho} |\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface second derivative wrt radial coordinate |
|
|
|
\(\partial_{\zeta}|e_{\theta} \times e_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface,derivative wrt toroidal angle |
|
|
|
\(|\mathbf{e}_{\zeta} \times \mathbf{e}_{\rho}|\) |
square meters |
2D Jacobian determinant for constant theta surface |
|
|
|
\(|\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\) |
square meters |
2D Jacobian determinant for constant zeta surface |
|
|
|
\(\partial_{\rho} |\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\) |
square meters |
2D Jacobian determinant for constant zeta surface derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho \rho} |\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\) |
square meters |
2D Jacobian determinant for constant zeta surface second derivative wrt radial coordinate |
|
|
|
\(g_{\rho\rho}\) |
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 |
|
|
|
\(\mathbf{r}\) |
meters |
Position vector along surface |
|
|
|
\(X\) |
meters |
Cartesian X coordinate. |
|
|
|
\(Y\) |
meters |
Cartesian Y coordinate. |
|
|
|
\(R\) |
meters |
Cylindrical radial position along surface |
|
|
|
\(\phi\) |
radians |
Toroidal phi position along surface |
|
|
|
\(\partial_{\rho} \phi\) |
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 |
|
|
|
\(Z\) |
meters |
Cylindrical vertical position along surface |
|
|
|
\(\mathbf{e}_{\rho}\) |
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 |
|
|
|
\(\partial_{\rho \rho} \mathbf{e}_{\rho}\) |
meters |
Covariant radial basis vector, second 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 |
|
|
|
\(\partial_{\rho \rho} \mathbf{e}_{\theta}\) |
meters |
Covariant poloidal basis vector, second 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 |
|
|
|
\(\partial_{\rho \rho} \mathbf{e}_{\zeta}\) |
meters |
Covariant toroidal basis vector, second 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 |
|
|
|
\(\Phi\) |
Amperes |
Surface current potential |
|
|
|
\(\partial_{\theta}\Phi\) |
Amperes |
Surface current potential, poloidal derivative |
|
|
|
\(\partial_{\zeta}\Phi\) |
Amperes |
Surface current potential, toroidal derivative |
|
|
|
\(\mathbf{K}\) |
Amperes per meter |
Surface current density, defined as thesurface normal vector cross the gradient of the current potential. |
|
desc.magnetic_fields._current_potential.FourierCurrentPotentialField
Name |
Label |
Units |
Description |
Module |
Aliases |
|---|---|---|---|---|---|
|
\(\mathbf{e}^{\theta} \sqrt{g}\) |
square meters |
Contravariant poloidal basis vector weighted by 3-D volume Jacobian |
|
|
|
\(\hat{\mathbf{n}}_{\rho}\) |
None |
Unit vector normal to constant rho surface (direction of e^rho) |
|
|
|
\(\partial_{\zeta}\hat{\mathbf{n}}_{\rho}\) |
None |
Unit vector normal to constant rho surface (direction of e^rho), derivative wrt toroidal angle |
|
|
|
\(\hat{\mathbf{n}}_{\theta}\) |
None |
Unit vector normal to constant theta surface (direction of e^theta) |
|
|
|
\(\hat{\mathbf{n}}_{\zeta}\) |
None |
Unit vector normal to constant zeta surface (direction of e^zeta) |
|
|
|
\(0\) |
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 |
|
|
|
\(V\) |
cubic meters |
Volume |
|
|
|
\(A(\zeta)\) |
square meters |
Cross-sectional area as function of zeta |
|
|
|
\(A\) |
square meters |
Average cross-sectional area |
|
|
|
\(S\) |
square meters |
Surface area of outermost flux surface |
|
|
|
\(R_{0}\) |
meters |
Average major radius |
|
|
|
\(a\) |
meters |
Average minor radius |
|
|
|
\(R_{0} / a\) |
None |
Aspect ratio |
|
|
|
\(P(\zeta)\) |
meters |
Perimeter of cross section as function of zeta |
|
|
|
\(a_{\mathrm{major}} / a_{\mathrm{minor}}\) |
None |
Elongation at a toroidal cross-section |
|
|
|
\(L_{\mathrm{SFF},\rho}\) |
meters |
L coefficient of second fundamental form of constant rho surface |
|
|
|
\(M_{\mathrm{SFF},\rho}\) |
meters |
M coefficient of second fundamental form of constant rho surface |
|
|
|
\(N_{\mathrm{SFF},\rho}\) |
meters |
N coefficient of second fundamental form of constant rho surface |
|
|
|
\(k_{1,\rho}\) |
Inverse meters |
First principle curvature of constant rho surfaces |
|
|
|
\(k_{2,\rho}\) |
Inverse meters |
Second principle curvature of constant rho surfaces |
|
|
|
\(K_{\rho}\) |
meters squared |
Gaussian curvature of constant rho surfaces |
|
|
|
\(H_{\rho}\) |
meters |
Mean curvature of constant rho surfaces |
|
|
|
\(|\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface |
|
|
|
\(\partial_{\rho} |\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho\rho} |\mathbf{e}_{\theta} \times \mathbf{e}_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface second derivative wrt radial coordinate |
|
|
|
\(\partial_{\zeta}|e_{\theta} \times e_{\zeta}|\) |
square meters |
2D Jacobian determinant for constant rho surface,derivative wrt toroidal angle |
|
|
|
\(|\mathbf{e}_{\zeta} \times \mathbf{e}_{\rho}|\) |
square meters |
2D Jacobian determinant for constant theta surface |
|
|
|
\(|\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\) |
square meters |
2D Jacobian determinant for constant zeta surface |
|
|
|
\(\partial_{\rho} |\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\) |
square meters |
2D Jacobian determinant for constant zeta surface derivative wrt radial coordinate |
|
|
|
\(\partial_{\rho \rho} |\mathbf{e}_{\rho} \times \mathbf{e}_{\theta}|\) |
square meters |
2D Jacobian determinant for constant zeta surface second derivative wrt radial coordinate |
|
|
|
\(g_{\rho\rho}\) |
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 |
|
|
|
\(\mathbf{r}\) |
meters |
Position vector along surface |
|
|
|
\(X\) |
meters |
Cartesian X coordinate. |
|
|
|
\(Y\) |
meters |
Cartesian Y coordinate. |
|
|
|
\(R\) |
meters |
Cylindrical radial position along surface |
|
|
|
\(\phi\) |
radians |
Toroidal phi position along surface |
|
|
|
\(\partial_{\rho} \phi\) |
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 |
|
|
|
\(Z\) |
meters |
Cylindrical vertical position along surface |
|
|
|
\(\mathbf{e}_{\rho}\) |
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 |
|
|
|
\(\partial_{\rho \rho} \mathbf{e}_{\rho}\) |
meters |
Covariant radial basis vector, second 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 |
|
|
|
\(\partial_{\rho \rho} \mathbf{e}_{\theta}\) |
meters |
Covariant poloidal basis vector, second 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 |
|
|
|
\(\partial_{\rho \rho} \mathbf{e}_{\zeta}\) |
meters |
Covariant toroidal basis vector, second 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 |
|
|
|
\(\Phi\) |
Amperes |
Surface current potential |
|
|
|
\(\partial_{\theta}\Phi\) |
Amperes |
Surface current potential, poloidal derivative |
|
|
|
\(\partial_{\zeta}\Phi\) |
Amperes |
Surface current potential, toroidal derivative |
|
|
|
\(\mathbf{K}\) |
Amperes per meter |
Surface current density, defined as thesurface normal vector cross the gradient of the current potential. |
|
desc.coils.SplineXYZCoil
Name |
Label |
Units |
Description |
Module |
Aliases |
|---|---|---|---|---|---|
|
\(0\) |
None |
Zeros |
|
|
|
\(s\) |
None |
Curve parameter, on [0, 2pi) |
|
|
|
\(ds\) |
None |
Spacing of curve parameter |
|
|
|
\(X\) |
meters |
Cartesian X coordinate. |
|
|
|
\(Y\) |
meters |
Cartesian Y coordinate. |
|
|
|
\(R\) |
meters |
Cylindrical radial position along curve |
|
|
|
\(\phi\) |
radians |
Toroidal phi position along curve |
|
|
|
\(Z\) |
meters |
Cylindrical vertical position along curve |
|
|
|
\(\mathbf{x}\) |
meters |
Position vector along curve |
|
|
|
\(\partial_{s} \mathbf{x}\) |
meters |
Position vector along curve, first derivative |
|
|
|
\(\partial_{ss} \mathbf{x}\) |
meters |
Position vector along curve, second derivative |
|
|
|
\(\partial_{sss} \mathbf{x}\) |
meters |
Position vector along curve, third derivative |
|
|
|
\(\mathbf{T}_{\mathrm{Frenet-Serret}}\) |
None |
Tangent unit vector to curve in Frenet-Serret frame |
|
|
|
\(\mathbf{N}_{\mathrm{Frenet-Serret}}\) |
None |
Normal unit vector to curve in Frenet-Serret frame |
|
|
|
\(\mathbf{B}_{\mathrm{Frenet-Serret}}\) |
None |
Binormal unit vector to curve in Frenet-Serret frame |
|
|
|
\(\kappa\) |
Inverse meters |
Scalar curvature of the curve |
|
|
|
\(\tau\) |
Inverse meters |
Scalar torsion of the curve |
|
|
|
\(L\) |
meters |
Length of the curve |
|
desc.magnetic_fields._core.OmnigenousField
Name |
Label |
Units |
Description |
Module |
Aliases |
|---|---|---|---|---|---|
|
\(\rho\) |
None |
Radial coordinate, proportional to the square root of the toroidal flux |
|
|
|
\(\eta\) |
radians |
Intermediate omnigenity coordinate along field lines |
|
|
|
\(\alpha\) |
radians |
Field line label, defined on [0, 2pi) |
|
|
|
\(h = \theta + (N / M) \zeta\) |
radians |
Omnigenity symmetry angle |
|
|
|
\((\theta_{B},\zeta_{B})\) |
radians |
Boozer angular coordinates |
|
|
|
\(|\mathbf{B}|\) |
Tesla |
Magnitude of omnigenous magnetic field |
|