NeumannCircuitVoltageMoles_KV

A Neumann boundary condition based on Kirchhoff's law of voltage

Overview

NeumannCircuitVoltageMoles_KV is a Neumann boundary condition that equates the plasma and drive potential to the plasma current using Kirchoff’s voltage law for a circuit.

The Kirchoff’s voltage law at the cathode is defined as

Where is the driven potential, is the potential at cathode, is the elemental charge , and are the ion and and electron particle fluxes, respectively, is the cross-sectional area of the plasma, and is the ballast resistance. Within NeumannCircuitVoltageMoles_KV, the charged species' flux at the boundary is assumed to be given by:

Where the subscripts , and represents properties of electrons, ions and electron energy respectively, is the normal vector of the boundary, is the mobility coefficient, is the species density, is the thermal velocity of the species, is the mean energy density of electrons, is the Boltzmann constant, is the gas temperature, and is electron density emitted by the surface. is defined such that the outflow is non-zero when the drift velocity is directed towards the wall and zero otherwise. is defined as the fraction of particles reflected by the surface.

To convert Kirchoff’s voltage law into a Neumann type BC, the set of equations are rearranged, so that this boundary condition solves for the potential flux normal for the boundary, such that:

When converting the density to logarithmic-molar form and applying a scaling factor of the mesh and voltage, the strong form for NeumannCircuitVoltageMoles_KV is defined as

Where , and is the molar density of the electrons, ions and electron energy in logarithmic form, is Avogadro's number, is the scaling factor of the potential, and is the scaling factor of the mesh.

Example Input File Syntax

[BCs]
  [potential_left]
    type = NeumannCircuitVoltageMoles_KV
    variable = potential
    boundary = left
    function = potential_bc_func
    ions = Arp
    data_provider = data_provider
    electrons = em
    electron_energy = mean_en
    r = 0
    position_units = ${dom0Scale}
    emission_coeffs = 0.05
  []
[]
(test/tests/1d_dc/mean_en.i)

Input Parameters

  • boundaryThe list of boundary IDs from the mesh where this object applies

    C++ Type:std::vector<BoundaryName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The list of boundary IDs from the mesh where this object applies

  • data_providerThe name of the UserObject that can provide some data to materials, bcs, etc.

    C++ Type:UserObjectName

    Unit:(no unit assumed)

    Controllable:No

    Description:The name of the UserObject that can provide some data to materials, bcs, etc.

  • electron_energyThe mean electron energy density in log form

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The mean electron energy density in log form

  • electronsThe electron density in log form

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The electron density in log form

  • emission_coeffsThe secondary electron emission coefficient for each ion provided in `ions`

    C++ Type:std::vector<std::string>

    Unit:(no unit assumed)

    Controllable:No

    Description:The secondary electron emission coefficient for each ion provided in `ions`

  • functionThe function.

    C++ Type:FunctionName

    Unit:(no unit assumed)

    Controllable:No

    Description:The function.

  • ionsA list of ion densities in log-molar form

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:A list of ion densities in log-molar form

  • position_unitsUnits of position.

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Units of position.

  • potential_unitsThe potential units.

    C++ Type:std::string

    Unit:(no unit assumed)

    Controllable:No

    Description:The potential units.

  • rThe reflection coefficient applied to both electrons and ions

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:The reflection coefficient applied to both electrons and ions

  • variableThe name of the variable that this residual object operates on

    C++ Type:NonlinearVariableName

    Unit:(no unit assumed)

    Controllable:No

    Description:The name of the variable that this residual object operates on

Required Parameters

  • displacementsThe displacements

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The displacements

  • prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

  • use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Optional Parameters

  • absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution

    C++ Type:std::vector<TagName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution

  • extra_matrix_tagsThe extra tags for the matrices this Kernel should fill

    C++ Type:std::vector<TagName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The extra tags for the matrices this Kernel should fill

  • extra_vector_tagsThe extra tags for the vectors this Kernel should fill

    C++ Type:std::vector<TagName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The extra tags for the vectors this Kernel should fill

  • matrix_tagssystemThe tag for the matrices this Kernel should fill

    Default:system

    C++ Type:MultiMooseEnum

    Unit:(no unit assumed)

    Options:nontime, system

    Controllable:No

    Description:The tag for the matrices this Kernel should fill

  • vector_tagsnontimeThe tag for the vectors this Kernel should fill

    Default:nontime

    C++ Type:MultiMooseEnum

    Unit:(no unit assumed)

    Options:nontime, time

    Controllable:No

    Description:The tag for the vectors this Kernel should fill

Tagging Parameters

  • control_tagsAdds user-defined labels for accessing object parameters via control logic.

    C++ Type:std::vector<std::string>

    Unit:(no unit assumed)

    Controllable:No

    Description:Adds user-defined labels for accessing object parameters via control logic.

  • diag_save_inThe name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

    C++ Type:std::vector<AuxVariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The name of auxiliary variables to save this BC's diagonal jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

  • enableTrueSet the enabled status of the MooseObject.

    Default:True

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:Yes

    Description:Set the enabled status of the MooseObject.

  • implicitTrueDetermines whether this object is calculated using an implicit or explicit form

    Default:True

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Determines whether this object is calculated using an implicit or explicit form

  • save_inThe name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

    C++ Type:std::vector<AuxVariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The name of auxiliary variables to save this BC's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

  • seed0The seed for the master random number generator

    Default:0

    C++ Type:unsigned int

    Unit:(no unit assumed)

    Controllable:No

    Description:The seed for the master random number generator

  • use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

Input Files