Updating BCs Documentation

doc/content/bib/documentation.bib

@@ -54,3 +54,86 @@ @article{greenberg1993electron
   year={1993},
   publisher={American Institute of Physics}
 }
+
+
+@article{hagelaar2000boundary,
+  title={Boundary conditions in fluid models of gas discharges},
+  author={Hagelaar, GJM and De Hoog, FJ and Kroesen, GMW},
+  journal={Physical Review E},
+  volume={62},
+  number={1},
+  pages={1452},
+  year={2000},
+  publisher={APS},
+  doi = {10.1103/PhysRevE.62.1452}
+}
+
+@article{lymberopoulos1994modeling,
+  title={Modeling and simulation of glow discharge plasma reactors},
+  author={Lymberopoulos, Dimitris P and Economou, Demetre J},
+  journal={Journal of Vacuum Science \& Technology A: Vacuum, Surfaces, and Films},
+  volume={12},
+  number={4},
+  pages={1229--1236},
+  year={1994},
+  publisher={American Vacuum Society},
+  doi = {10.1116/1.579300}
+}
+
+@article{forbes2006simple,
+  title={Simple good approximations for the special elliptic functions in standard Fowler-Nordheim tunneling theory for a Schottky-Nordheim barrier},
+  author={Forbes, Richard G},
+  journal={Applied physics letters},
+  volume={89},
+  number={11},
+  year={2006},
+  publisher={AIP Publishing},
+  doi = {10.1063/1.2354582}
+}
+
+@article{forbes2008physics,
+  title={Physics of generalized Fowler-Nordheim-type equations},
+  author={Forbes, Richard G},
+  journal={Journal of Vacuum Science \& Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena},
+  volume={26},
+  number={2},
+  pages={788--793},
+  year={2008},
+  publisher={AIP Publishing},
+  doi = {10.1116/1.2827505}
+}
+
+@article{sakiyama2006corona,
+  title={Corona-glow transition in the atmospheric pressure RF-excited plasma needle},
+  author={Sakiyama, Y and Graves, David B},
+  journal={Journal of Physics D: Applied Physics},
+  volume={39},
+  number={16},
+  pages={3644},
+  year={2006},
+  publisher={IOP Publishing},
+  doi = {10.1088/0022-3727/39/16/018}
+}
+
+@article{sakiyama2007nonthermal,
+  title={Nonthermal atmospheric rf plasma in one-dimensional spherical coordinates: asymmetric sheath structure and the discharge mechanism},
+  author={Sakiyama, Yukinori and Graves, David B},
+  journal={Journal of applied physics},
+  volume={101},
+  number={7},
+  year={2007},
+  publisher={AIP Publishing},
+  doi = {https://doi.org/10.1063/1.2715745}
+}
+
+@article{go2012theoretical,
+  title={Theoretical analysis of ion-enhanced thermionic emission for low-temperature, non-equilibrium gas discharges},
+  author={Go, David B},
+  journal={Journal of Physics D: Applied Physics},
+  volume={46},
+  number={3},
+  pages={035202},
+  year={2012},
+  publisher={IOP Publishing},
+  doi ={10.1088/0022-3727/46/3/035202}
+}

doc/content/source/bcs/CircuitDirichletPotential.md

@@ -1,21 +1,59 @@
 # CircuitDirichletPotential
 
-!alert construction title=Undocumented Class
-The CircuitDirichletPotential has not been documented. The content listed below should be used as a starting point for
-documenting the class, which includes the typical automatic documentation associated with a
-MooseObject; however, what is contained is ultimately determined by what is necessary to make the
-documentation clear for users.
-
 !syntax description /BCs/CircuitDirichletPotential
 
 ## Overview
 
-!! Replace these lines with information regarding the CircuitDirichletPotential object.
+`CircuitDirichletPotential` is a Dirichlet boundary condition for a potential based on Kirchoff's voltage law.
+
+The formulation of the potential at the wall is:
+
+\begin{equation}
+V_\text{source} + V_\text{cathode} = e \Gamma A R
+\end{equation}
+
+Where $V_\text{source}$ is driven the potential, $V_\text{cathode}$ is the potential at cathode,
+$\Gamma$ is the charged particle flux at the boundary, $e$ is the elemental charge, $A$ is the cross-sectional area of the plasma, and
+$R$ is the ballast resistance. When converting the density to log-molar form and applying a scaling factor for both the mesh and voltage,
+`CircuitDirichletPotential` is defined as
+
+\begin{equation}
+V_\text{source} + V_\text{cathode} = e N_{A} \Gamma \frac{A}{l_{c}^2} \frac{R}{V_{c}}
+\end{equation}
+
+Where $N_{A}$ is Avogadro's number, $l_{c}$ is the scaling factor of the mesh, and $V_{c}$ is the scaling factor of the potential.
+
+
+The charged particle flux is supplied as a [Postprocessor](syntax/Postprocessors/index.md) (usually the [`SideCurrent`](/postprocessors/SideCurrent.md) Postprocessor).
+
+!alert warning title=Untested Class
+The CircuitDirichletPotential does not have a formalized test, yet. For this reason,
+users should be aware of unforeseen bugs when using CircuitDirichletPotential. To
+report a bug or discuss future contributions to Zapdos, please refer to the
+[Zapdos GitHub Discussions page](https://github.com/shannon-lab/zapdos/discussions).
+For standards of how to contribute to Zapdos and the MOOSE framework,
+please refer to the [MOOSE Contributing page](framework/contributing.md).
 
 ## Example Input File Syntax
 
 !! Describe and include an example of how to use the CircuitDirichletPotential object.
 
+```text
+[BCs]
+  [circuit_potential]
+    type = CircuitDirichletPotential
+    variable = potential
+    current = SideCurrent
+    position_units = 1.0
+    potential_units = V
+    resist = 100 #in Ohms
+    surface = anode
+    surface_potential = 100 #in V
+    boundary = 'electrode'
+  []
+[]
+```
+
 !syntax parameters /BCs/CircuitDirichletPotential
 
 !syntax inputs /BCs/CircuitDirichletPotential

doc/content/source/bcs/DCIonBC.md

@@ -1,20 +1,42 @@
 # DCIonBC
 
-!alert construction title=Undocumented Class
-The DCIonBC has not been documented. The content listed below should be used as a starting point for
-documenting the class, which includes the typical automatic documentation associated with a
-MooseObject; however, what is contained is ultimately determined by what is necessary to make the
-documentation clear for users.
-
 !syntax description /BCs/DCIonBC
 
 ## Overview
 
-!! Replace these lines with information regarding the DCIonBC object.
+`DCIonBC` is an electric field driven outflow boundary condition. `DCIonBC` assumes the electrostatic approximation for the electric field.
+
+The electrostatic electric field driven outflow is defined as
+
+\begin{equation}
+a =
+\begin{cases}
+1, & \text{sign}_{j} \mu_{j} \ \text{-} \nabla (V) \cdot \textbf{n} > 0\\
+0, & \text{sign}_{j} \mu_{j} \ \text{-} \nabla (V) \cdot \textbf{n} \leq 0\\
+\end{cases} \\[10pt]
+\Gamma_{j} \cdot \textbf{n} = a \ \text{sign}_{j} \mu_{j} \ \text{-} \nabla (V) \cdot \textbf{n} \ n_{j}
+\end{equation}
+
+Where $\Gamma$ is the outflow normal to the boundary, $\textbf{n}$ is the normal vector of the boundary, $\text{sign}_{j}$ indicates the advection behavior ($\text{+}1$ for positively charged species and $\text{-}1$ for negatively charged species), $\mu_{j}$ is the mobility coefficient, $n_{j}$ is the density, and $V$ is
+the electrostatic potential. $a$ is defined such that the outflow is only defined when the drift velocity is direct towards the wall and zero otherwise. When converting the density to logarithmic form and applying a scaling
+factor of the mesh, the strong form for `DCIonBC` is defined as
+
+\begin{equation}
+a =
+\begin{cases}
+1, & \text{sign}_{j} \mu_{j} \ \text{-} \nabla (V) \cdot \textbf{n} > 0\\
+0, & \text{sign}_{j} \mu_{j} \ \text{-} \nabla (V) \cdot \textbf{n} \leq 0\\
+\end{cases} \\[10pt]
+\Gamma_{j} \cdot \textbf{n} = a \ \text{sign}_{j} \mu_{j} \ \text{-} \nabla (V / l_{c}) \cdot \textbf{n} \ \exp(N_{j})
+\end{equation}
+
+Where $N_{j}$ is the molar density of the species in logarithmic form and
+$l_{c}$ is the scaling factor of the mesh.
+
 
 ## Example Input File Syntax
 
-!! Describe and include an example of how to use the DCIonBC object.
+!listing test/tests/1d_dc/mean_en.i block=BCs/OHm_physical
 
 !syntax parameters /BCs/DCIonBC
 

doc/content/source/bcs/DriftDiffusionDoNothingBC.md

@@ -1,21 +1,52 @@
 # DriftDiffusionDoNothingBC
 
-!alert construction title=Undocumented Class
-The DriftDiffusionDoNothingBC has not been documented. The content listed below should be used as a starting point for
-documenting the class, which includes the typical automatic documentation associated with a
-MooseObject; however, what is contained is ultimately determined by what is necessary to make the
-documentation clear for users.
-
 !syntax description /BCs/DriftDiffusionDoNothingBC
 
 ## Overview
 
-!! Replace these lines with information regarding the DriftDiffusionDoNothingBC object.
+`DriftDiffusionDoNothingBC` is an outflow boundary condition where the outflow at the
+boundary is equal to the bulk dift-diffusion equations.
+`DriftDiffusionDoNothingBC` assumes the electrostatic approximation for the electric field.
+
+The outflow is defined as
+
+\begin{equation}
+\Gamma_{j} \cdot \textbf{n} = \text{sign}_{j} \mu_{j} n_{j} \left( - \nabla (V) \right) \cdot \textbf{n} - D_{j} \nabla (n_{j}) \cdot \textbf{n}
+\end{equation}
+
+Where $\Gamma$ is the outflow normal to the boundary, $\textbf{n}$ is the normal vector of the boundary, $\text{sign}_{j}$ indicates the advection behavior ($\text{+}1$ for positively charged species, $\text{-}1$ for negatively charged species and $\text{0}$ for neutral species), $\mu_{j}$ is the mobility coefficient, $D_{j}$ is the diffusion coefficient, $n_{j}$ is the density, and $V$ is
+the potential. When converting the density to logarithmic form and applying a scaling factor of the mesh, the strong form for `DriftDiffusionDoNothingBC` is defined as
+
+\begin{equation}
+\Gamma_{j} \cdot \textbf{n} = \text{sign}_{j} \mu_{j} \exp(N_{j}) \left( - \nabla (V / l_{c})\right) \cdot \textbf{n} - D_{j} \exp(N_{j}) \nabla (N_{j} / l_{c}) \cdot \textbf{n}
+\end{equation}
+
+Where $N_{j}$ is the molar density of the species in logarithmic form and
+$l_{c}$ is the scaling factor of the mesh.
+
+!alert warning title=Untested Class
+The DriftDiffusionDoNothingBC does not have a formalized test, yet. For this reason,
+users should be aware of unforeseen bugs when using DriftDiffusionDoNothingBC. To
+report a bug or discuss future contributions to Zapdos, please refer to the
+[Zapdos GitHub Discussions page](https://github.com/shannon-lab/zapdos/discussions).
+For standards of how to contribute to Zapdos and the MOOSE framework,
+please refer to the [MOOSE Contributing page](framework/contributing.md).
 
 ## Example Input File Syntax
 
 !! Describe and include an example of how to use the DriftDiffusionDoNothingBC object.
 
+```text
+[BCs]
+  [electron_gap_drift_diffusion]
+    type = DriftDiffusionDoNothingBC
+    variable = electrons
+    position_units = 1.0
+    boundary = 'gap'
+  []
+[]
+```
+
 !syntax parameters /BCs/DriftDiffusionDoNothingBC
 
 !syntax inputs /BCs/DriftDiffusionDoNothingBC

doc/content/source/bcs/EconomouDielectricBC.md

@@ -1,20 +1,31 @@
 # EconomouDielectricBC
 
-!alert construction title=Undocumented Class
-The EconomouDielectricBC has not been documented. The content listed below should be used as a starting point for
-documenting the class, which includes the typical automatic documentation associated with a
-MooseObject; however, what is contained is ultimately determined by what is necessary to make the
-documentation clear for users.
-
 !syntax description /BCs/EconomouDielectricBC
 
 ## Overview
 
-!! Replace these lines with information regarding the EconomouDielectricBC object.
+`EconomouDielectricBC` is a type of [`PenaltyDirichletBC`](/bcs/ADPenaltyDirichletBC.md) for the potential on the boundary of a grounded ideal dielectric.
+
+The potential at the boundary of a grounded ideal dielectric is defined as
+
+\begin{equation}
+\frac{\epsilon_{i}}{d_{i}}\frac{\partial V_{i}}{\partial t} = e(\Gamma_{+} \cdot \textbf{n} -\Gamma_{e} \cdot \textbf{n})+\epsilon_{0}\frac{\partial (E \cdot \textbf{n}) }{\partial t} \\[10pt]
+E = \text{-} \nabla (V)\\[10pt]
+\Gamma_{e} \cdot \textbf{n}  = \frac{1}{4}\sqrt{\frac{8 k T_{e}}{\pi m_{e}}} \ n_e - \gamma \Gamma_{+} \cdot \textbf{n} \\[10pt]
+\Gamma_{+} \cdot \textbf{n}  = a \ \mu_{+} \ \text{-} \nabla (V) \cdot \textbf{n} \ n_{+} \\[10pt]
+a =
+\begin{cases}
+1, & \mu_{j} \ \text{-} \nabla (V) \cdot \textbf{n} > 0\\
+0, & \mu_{j} \ \text{-} \nabla (V) \cdot \textbf{n} \leq 0\\
+\end{cases}
+\end{equation}
+
+Where $\epsilon_{i}$ is the permittivity of the dielectric, $d_{i}$ is the thickness of the dielectric, $V_{i}$ is the voltage on the dielectric, $\textbf{n}$ is the normal to the boundary, $e$ is the elemental charge, $\epsilon_{0}$ is the permittivity of free space, and $E$ is the E-field normal to the dielectric. $\Gamma_{e}$ and $\Gamma_{+}$ are the electron and ion outflow flux and are defined with the [`SakiyamaElectronDiffusionBC`](/bcs/SakiyamaElectronDiffusionBC.md), [`SakiyamaSecondaryElectronBC`](/bcs/SakiyamaSecondaryElectronBC.md) and [`SakiyamaIonAdvectionBC`](/bcs/SakiyamaIonAdvectionBC.md) (please refer to those BC's for more information on the fluxes).
 
 ## Example Input File Syntax
 
-!! Describe and include an example of how to use the EconomouDielectricBC object.
+
+!listing test/tests/DriftDiffusionAction/2D_RF_Plasma_actions.i block=BCs/potential_Dielectric
 
 !syntax parameters /BCs/EconomouDielectricBC
 

doc/content/source/bcs/ElectronAdvectionDoNothingBC.md

@@ -1,21 +1,53 @@
 # ElectronAdvectionDoNothingBC
 
-!alert construction title=Undocumented Class
-The ElectronAdvectionDoNothingBC has not been documented. The content listed below should be used as a starting point for
-documenting the class, which includes the typical automatic documentation associated with a
-MooseObject; however, what is contained is ultimately determined by what is necessary to make the
-documentation clear for users.
-
 !syntax description /BCs/ElectronAdvectionDoNothingBC
 
 ## Overview
 
-!! Replace these lines with information regarding the ElectronAdvectionDoNothingBC object.
+`ElectronAdvectionDoNothingBC` is an outflow boundary condition where the outflow at the
+boundary is equal to the bulk electron advection equation.
+`ElectronAdvectionDoNothingBC` assumes the electrostatic approximation for the electric field.
+
+The outflow is defined as
+
+\begin{equation}
+\Gamma_{e} \cdot \textbf{n} = \text{-} \mu_{e} n_{e} \left( \text{-} \nabla (V)\right) \cdot \textbf{n} 
+\end{equation}
+
+Where $\Gamma$ is the outflow normal to the boundary, $\textbf{n}$ is the normal of the boundary, $\mu_{e}$ is the mobility coefficient, $n_{e}$ is the electron density, and $V$ is the electric potential. When converting the density to logarithmic form and applying a scaling
+factor of the mesh, the strong form for `ElectronAdvectionDoNothingBC` is defined as
+
+\begin{equation}
+\Gamma_{e} \cdot \textbf{n} = \text{-} \mu_{e} \exp(N_{e}) \left(  \text{-} \nabla (V / l_{c}) \right) \cdot \textbf{n}
+\end{equation}
+
+Where $N_{j}$ is the molar density of the species in logarithmic form and
+$l_{c}$ is the scaling factor of the mesh.
+
+!alert warning title=Untested Class
+The ElectronAdvectionDoNothingBC does not have a formalized test, yet. For this reason,
+users should be aware of unforeseen bugs when using ElectronAdvectionDoNothingBC. To
+report a bug or discuss future contributions to Zapdos, please refer to the
+[Zapdos GitHub Discussions page](https://github.com/shannon-lab/zapdos/discussions).
+For standards of how to contribute to Zapdos and the MOOSE framework,
+please refer to the [MOOSE Contributing page](framework/contributing.md).
 
 ## Example Input File Syntax
 
 !! Describe and include an example of how to use the ElectronAdvectionDoNothingBC object.
 
+```text
+[BCs]
+  [electron_gap_advection]
+    type = ElectronAdvectionDoNothingBC
+    variable = electrons
+    potential = potential
+    position_units = 1.0
+    boundary = 'gap'
+  []
+[]
+```
+
 !syntax parameters /BCs/ElectronAdvectionDoNothingBC
 
 !syntax inputs /BCs/ElectronAdvectionDoNothingBC