Base class for handling plasma properties, specifically focusing on the electron energy distribution. More...

#include <PlasmaPhase.h>

Inheritance diagram for PlasmaPhase:

Detailed Description

Base class for handling plasma properties, specifically focusing on the electron energy distribution.

This class provides functionality to manage the the electron energy distribution using two primary methods for defining the electron distribution and electron temperature.

The first method utilizes setElectronTemperature(), which sets the electron temperature and calculates the electron energy distribution assuming an isotropic-velocity model. Note that all units in PlasmaPhase are in SI, except for electron energy, which is measured in volts.

The generalized electron energy distribution for an isotropic-velocity distribution (as described by Gudmundsson [13] and Khalilpour and Foroutan [22]) is given by:

\[ f(\epsilon) = c_1 \frac{\sqrt{\epsilon}}{\epsilon_m^{3/2}} \exp \left(-c_2 \left(\frac{\epsilon}{\epsilon_m}\right)^x \right), \]

where \( x = 1 \) corresponds to a Maxwellian distribution and \( x = 2 \) corresponds to a Druyvesteyn distribution. Here, \( \epsilon_m = \frac{3}{2} T_e \) [V] represents the mean electron energy.

The total probability distribution integrates to one:

\[ \int_0^{\infty} f(\epsilon) d\epsilon = 1. \]

According to Hagelaar and Pitchford [14], the electron energy probability function can be defined as \( F(\epsilon) = \frac{f(\epsilon)}{\sqrt{\epsilon}} \) with units of [V \(^{-3/2}\)]. The generalized form of the electron energy probability function for isotropic-velocity distributions is:

\[ F(\epsilon) = c_1 \frac{1}{\epsilon_m^{3/2}} \exp\left(-c_2 \left(\frac{\epsilon}{\epsilon_m}\right)^x\right), \]

and this form is used to model the isotropic electron energy distribution in PlasmaPhase.

The second method allows for manual definition of the electron energy distribution using setDiscretizedElectronEnergyDist(). In this approach, the electron temperature is derived from the mean electron energy, \( \epsilon_m \), which can be calculated as follows [14] :

\[ \epsilon_m = \int_0^{\infty} \epsilon^{3/2} F(\epsilon) d\epsilon. \]

This integral can be approximated using the trapezoidal rule,

\[ \epsilon_m = \sum_i \left(\epsilon_{i+1}^{5/2} - \epsilon_i^{5/2}\right) \frac{F(\epsilon_{i+1}) + F(\epsilon_i)}{2}, \]

where \( i \) is the index of discrete energy levels, or Simpson's rule.

Thermodynamic consistency of the two-temperature model

When the electron temperature \( T_\text{e} \) differs from the heavy-species temperature \( T \), this phase does not satisfy all of Cantera's standard-state consistency relations simultaneously: one of them is deliberately left unsatisfied. This is a consequence of two design commitments that this implementation makes, both of which are individually reasonable but which cannot be reconciled once \( T_\text{e} \neq T \):

Kinetics uses true concentrations. The generalized (activity) concentrations that drive the law of mass action are kept equal to the true molar concentrations, \( C^a_k = C_k \), so that reaction rates depend on actual number densities. Together with the standard concentration \( C^0_k = P/RT \) (the gas temperature, for all species; see standardConcentration()), this requires the reported activities to be
\[ a_k = \frac{C^a_k}{C^0_k} = X_k \frac{T}{\overline{T}}, \]
where \( \overline{T} \) is the mole-fraction-weighted mean temperature (see meanTemperature()). This is what getActivities() returns.
Chemical potentials keep the ideal-gas form. The chemical potentials retain the usual ideal-gas composition dependence, \( \mu_k = \mu^0_k(T_k) + R T_k \ln X_k \), with each species evaluated at its own temperature \( T_k \) ( \( T \) for heavy species, \( T_\text{e} \) for electrons; see getChemPotentials() and getStandardChemPotentials()). This is equivalent to an activity of \( X_k \).

When \( T_\text{e} \neq T \), these two demands imply different values for the activities – \( X_k\,T/\overline{T} \) versus \( X_k \) – which differ by the factor \( T/\overline{T} \). getActivities() reports the first; getChemPotentials() embodies the second; and the identity \( \mu_k = \mu^0_k + R T_k \ln a_k \) is therefore the relation left unsatisfied. This is why the consistency test chem_potentials_to_activities is a known failure for two-temperature states.

The practical consequence of this inconsistency is limited. It formally perturbs any chemical equilibrium computed for the phase, but the concept of chemical equilibrium in the absence of thermal equilibrium ( \( T_\text{e} \neq T \)) is itself ill-posed, so the perturbed quantity has little physical meaning in exactly the regime where the inconsistency appears. The trade-offs and potential approaches for a fully-consistent implementation are documented in https://github.com/Cantera/enhancements/issues/258#issuecomment-4857093158.

Warning: This class is an experimental part of Cantera and may be changed or removed without notice.

Todo:: Implement electron Boltzmann equation solver to solve EEDF. https://github.com/Cantera/enhancements/issues/127

Definition at line 125 of file PlasmaPhase.h.

Public Member Functions
	PlasmaPhase (const string &inputFile="", const string &id="")
	Construct and initialize a PlasmaPhase object directly from an input file.

string	type () const override
	String indicating the thermodynamic model implemented.

void	initThermo () override
	Initialize the ThermoPhase object after all species have been set up.

Overridden from IdealGasPhase or ThermoPhase
bool	addSpecies (shared_ptr< Species > spec) override
	Add a Species to this Phase.

virtual void	setSolution (std::weak_ptr< Solution > soln) override
	Set the link to the Solution object that owns this ThermoPhase.

void	getParameters (AnyMap &phaseNode) const override
	Store the parameters of a ThermoPhase object such that an identical one could be reconstructed using the newThermo(AnyMap&) function.

void	setParameters (const AnyMap &phaseNode, const AnyMap &rootNode=AnyMap()) override
	Set equation of state parameters from an AnyMap phase description.

Electron Species Information
size_t	electronSpeciesIndex () const
	Electron Species Index.

string	electronSpeciesName () const
	Electron species name.

Electron Energy Distribution Functions
void	setElectronEnergyLevels (span< const double > levels)
	Set electron energy levels.

void	getElectronEnergyLevels (span< double > levels) const
	Get electron energy levels.

void	setDiscretizedElectronEnergyDist (span< const double > levels, span< const double > distrb)
	Set discretized electron energy distribution.

void	getElectronEnergyDistribution (span< double > distrb) const
	Get electron energy distribution.

void	setIsotropicShapeFactor (double x)
	Set the shape factor of isotropic electron energy distribution.

double	isotropicShapeFactor () const
	The shape factor of isotropic electron energy distribution.

double	electronTemperature () const override
	Electron Temperature [K].

void	setElectronTemperature (double Te) override
	Set the internally stored electron temperature of the phase [K].

double	meanElectronEnergy () const
	Mean electron energy [eV].

void	setMeanElectronEnergy (double energy)
	Set mean electron energy [eV].

string	electronEnergyDistributionType () const
	Get electron energy distribution type.

void	setElectronEnergyDistributionType (const string &type)
	Set electron energy distribution type.

string	quadratureMethod () const
	Numerical quadrature method. Method: m_quadratureMethod.

void	setQuadratureMethod (const string &method)
	Set numerical quadrature method for integrating electron energy distribution function.

void	enableNormalizeElectronEnergyDist (bool enable)
	Set flag of automatically normalize electron energy distribution.

bool	normalizeElectronEnergyDistEnabled () const
	Flag of automatically normalize electron energy distribution.

size_t	nElectronEnergyLevels () const
	Number of electron levels.

size_t	nCollisions () const
	Number of electron collision cross sections.

const shared_ptr< Reaction >	collision (size_t i) const
	Get the Reaction object associated with electron collision i.

const shared_ptr< ElectronCollisionPlasmaRate >	collisionRate (size_t i) const
	Get the ElectronCollisionPlasmaRate object associated with electron collision i.

void	updateElectronEnergyDistribution ()
	Update the electron energy distribution.

int	distributionNumber () const
	Return the distribution number m_distNum.

int	levelNumber () const
	Return the electron energy level number m_levelNum.

const vector< size_t > &	kInelastic () const
	Get the indicies for inelastic electron collisions.

const vector< size_t > &	kElastic () const
	Get the indices for elastic electron collisions.

size_t	targetIndex (size_t i) const
	Return the target of a specific process.

double	electricFieldFrequency () const
	Get the frequency of the applied electric field [Hz].

double	electricField () const
	Get the applied electric field strength [V/m].

void	setElectricField (double E)
	Set the absolute electric field strength [V/m].

double	reducedElectricField () const
	Calculate the degree of ionization.

void	setReducedElectricField (double EN)
	Set reduced electric field given in [V·m²].

double	electronMobility () const
	The electron mobility (m²/V/s)

double	elasticPowerLoss ()
	The elastic power loss [J/s/m³].

double	jouleHeatingPower () const
	The joule heating power (W/m³)

void	beginEquilibrate () override
	Hook called at the beginning of an equilibrium calculation on this phase.

void	endEquilibrate () override
	Hook called at the end of an equilibrium calculation on this phase.

double	intrinsicHeating () override
	Intrinsic volumetric heating rate [W/m³].

Molar Thermodynamic Properties of the Solution
double	enthalpy_mole () const override
	Return the Molar enthalpy. Units: J/kmol.

double	entropy_mole () const override
	Return the molar entropy. Units: J/kmol/K.

double	gibbs_mole () const override
	Return the molar Gibbs free energy. Units: J/kmol.

double	intEnergy_mole () const override
	Return the molar internal energy. Units: J/kmol.

Mechanical Equation of State
double	meanTemperature () const
	Return the mean temperature of the plasma phase. Units: K.

double	pressure () const override
	Return the pressure of the plasma phase. Units: Pa.

void	setPressure (double p) override
	Set the pressure at constant temperature and composition. Units: Pa.

double	RTe () const
	Return the Gas Constant multiplied by the current electron temperature [J/kmol].

virtual double	electronPressure () const
	Return the electron pressure. Units: Pa.

double	thermalExpansionCoeff () const override
	Raise NotImplementedError, as there is an ambiguity on the temperature to use.

double	soundSpeed () const override
	Raise NotImplementedError, as there is an ambiguity on the temperature to use.

Chemical Potentials and Activities
double	standardConcentration (size_t k=0) const override
	Returns the standard concentration \( C^0_k \), which is used to normalize the generalized concentration.

void	getActivities (span< double > a) const override
	Get the array of non-dimensional activities at the current solution temperature, pressure, and solution concentration.

void	getActivityCoefficients (span< double > ac) const override
	Get the array of non-dimensional activity coefficients at the current solution temperature, pressure, and solution concentration.

Partial Molar Properties of the Solution
void	getChemPotentials (span< double > mu) const override
	Return the chemical potentials of the species in the solution. Units: J/kmol.

void	getPartialMolarEnthalpies (span< double > hbar) const override
	Return the partial molar enthalpies of the species in the solution. Units: J/kmol.

void	getPartialMolarEntropies (span< double > sbar) const override
	Return the partial molar entropies of the species in the solution. Units: J/kmol/K.

void	getPartialMolarIntEnergies (span< double > ubar) const override
	Return the partial molar internal energies of the species in the solution. Units: J/kmol.

void	getPartialMolarVolumes (span< double > vbar) const override
	Return the partial molar volumes of the species in the solution. Units: m³/kmol.

Properties of the Standard State of the Species in the Solution
void	getStandardChemPotentials (span< double > muStar) const override
	Return the standard chemical potentials of the species. Units: J/kmol.

void	getStandardVolumes (span< double > vol) const override
	Return the standard molar volumes of the species. Units: m³/kmol.

Thermodynamic Values for the Species Reference States
void	getGibbs_ref (span< double > g) const override
	Return the reference chemical potentials of the species. Units: J/kmol.

void	getStandardVolumes_ref (span< double > vol) const override
	Return the molar volumes of the species reference states. Units: m³/kmol.

Setting the State
For a plasma phase, setting the state requires specifying both the heavy-species (gas) temperature and the electron temperature.
void	setState (const AnyMap &state) override
	Set the state using an AnyMap containing any combination of properties supported by the thermodynamic model.

Public Member Functions inherited from IdealGasPhase
	IdealGasPhase (const string &inputFile="", const string &id="")
	Construct and initialize an IdealGasPhase ThermoPhase object directly from an input file.

string	type () const override
	String indicating the thermodynamic model implemented.

bool	isIdeal () const override
	Boolean indicating whether phase is ideal.

string	phaseOfMatter () const override
	String indicating the mechanical phase of the matter in this Phase.

bool	addSpecies (shared_ptr< Species > spec) override
	Add a Species to this Phase.

void	setToEquilState (span< const double > mu_RT) override
	This method is used by the ChemEquil equilibrium solver.

double	cp_mole () const override
	Molar heat capacity at constant pressure and composition [J/kmol/K].

double	cv_mole () const override
	Molar heat capacity at constant volume and composition [J/kmol/K].

void	setState_DP (double rho, double p) override
	Set the density and pressure at constant composition.

double	isothermalCompressibility () const override
	Returns the isothermal compressibility. Units: 1/Pa.

double	internalPressure () const override
	Return the internal pressure. Units: Pa.

void	getActivityConcentrations (span< double > c) const override
	This method returns the array of generalized concentrations.

void	getPartialMolarIntEnergies_TV (span< double > utilde) const override
	Return an array of partial molar internal energies at constant temperature and volume [J/kmol].

void	getPartialMolarCp (span< double > cpbar) const override
	Return an array of partial molar heat capacities for the species in the mixture.

void	getPartialMolarCv_TV (span< double > cvtilde) const override
	Return an array of species molar heat capacities associated with the constant-volume partial molar internal energies [J/kmol/K].

void	getEnthalpy_RT (span< double > hrt) const override
	Get the nondimensional Enthalpy functions for the species at their standard states at the current T and P of the solution.

void	getEntropy_R (span< double > sr) const override
	Get the array of nondimensional Entropy functions for the standard state species at the current T and P of the solution.

void	getGibbs_RT (span< double > grt) const override
	Get the nondimensional Gibbs functions for the species in their standard states at the current T and P of the solution.

void	getIntEnergy_RT (span< double > urt) const override
	Returns the vector of nondimensional Internal Energies of the standard state species at the current T and P of the solution.

void	getCp_R (span< double > cpr) const override
	Get the nondimensional Heat Capacities at constant pressure for the species standard states at the current T and P of the solution.

void	getEnthalpy_RT_ref (span< double > hrt) const override
	Returns the vector of nondimensional enthalpies of the reference state at the current temperature of the solution and the reference pressure for the species.

void	getGibbs_RT_ref (span< double > grt) const override
	Returns the vector of nondimensional Gibbs Free Energies of the reference state at the current temperature of the solution and the reference pressure for the species.

void	getEntropy_R_ref (span< double > er) const override
	Returns the vector of nondimensional entropies of the reference state at the current temperature of the solution and the reference pressure for each species.

void	getIntEnergy_RT_ref (span< double > urt) const override
	Returns the vector of nondimensional internal Energies of the reference state at the current temperature of the solution and the reference pressure for each species.

void	getCp_R_ref (span< double > cprt) const override
	Returns the vector of nondimensional constant pressure heat capacities of the reference state at the current temperature of the solution and reference pressure for each species.

Public Member Functions inherited from ThermoPhase
	ThermoPhase ()=default
	Constructor.

shared_ptr< ThermoPhase >	clone () const
	Create a new ThermoPhase object using the same species definitions, thermodynamic parameters, and state as this one.

double	RT () const
	Return the Gas Constant multiplied by the current temperature.

double	equivalenceRatio () const
	Compute the equivalence ratio for the current mixture from available oxygen and required oxygen.

virtual AnyMap	getAuxiliaryData ()
	Return intermediate or model-specific parameters used by particular derived classes.

virtual void	setSolution (std::weak_ptr< Solution > soln)
	Set the link to the Solution object that owns this ThermoPhase.

shared_ptr< Solution >	root () const
	Get the Solution object containing this ThermoPhase object and linked Kinetics and Transport objects.

string	type () const override
	String indicating the thermodynamic model implemented.

virtual double	refPressure () const
	Returns the reference pressure in Pa.

virtual double	minTemp (size_t k=npos) const
	Minimum temperature for which the thermodynamic data for the species or phase are valid.

double	Hf298SS (const size_t k) const
	Report the 298 K Heat of Formation of the standard state of one species (J kmol-1)

virtual void	modifyOneHf298SS (const size_t k, const double Hf298New)
	Modify the value of the 298 K Heat of Formation of one species in the phase (J kmol-1)

virtual void	resetHf298 (const size_t k=npos)
	Restore the original heat of formation of one or more species.

virtual double	maxTemp (size_t k=npos) const
	Maximum temperature for which the thermodynamic data for the species are valid.

bool	temperatureLimitsEnforced () const
	Returns `true` if temperature limits are enforced for this phase.

void	setTemperatureLimitsEnforced (bool enforce)
	Set whether temperature limits are enforced for this phase.

bool	chargeNeutralityNecessary () const
	Returns the chargeNeutralityNecessity boolean.

void	setElectricPotential (double v)
	Set the electric potential of this phase (V).

double	electricPotential () const
	Returns the electric potential of this phase (V).

virtual int	activityConvention () const
	This method returns the convention used in specification of the activities, of which there are currently two, molar- and molality-based conventions.

virtual int	standardStateConvention () const
	This method returns the convention used in specification of the standard state, of which there are currently two, temperature based, and variable pressure based.

virtual Units	standardConcentrationUnits () const
	Returns the units of the "standard concentration" for this phase.

virtual double	logStandardConc (size_t k=0) const
	Natural logarithm of the standard concentration of the kth species.

virtual void	getLnActivityCoefficients (span< double > lnac) const
	Get the array of non-dimensional molar-based ln activity coefficients at the current solution temperature, pressure, and solution concentration.

void	getElectrochemPotentials (span< double > mu) const
	Get the species electrochemical potentials.

double	enthalpy_mass () const
	Specific enthalpy. Units: J/kg.

double	intEnergy_mass () const
	Specific internal energy. Units: J/kg.

double	entropy_mass () const
	Specific entropy. Units: J/kg/K.

double	gibbs_mass () const
	Specific Gibbs function. Units: J/kg.

double	cp_mass () const
	Specific heat at constant pressure and composition [J/kg/K].

double	cv_mass () const
	Specific heat at constant volume and composition [J/kg/K].

virtual void	setState_TPX (double t, double p, span< const double > x)
	Set the temperature (K), pressure (Pa), and mole fractions.

virtual void	setState_TPX (double t, double p, const Composition &x)
	Set the temperature (K), pressure (Pa), and mole fractions.

virtual void	setState_TPX (double t, double p, const string &x)
	Set the temperature (K), pressure (Pa), and mole fractions.

virtual void	setState_TPY (double t, double p, span< const double > y)
	Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase.

virtual void	setState_TPY (double t, double p, const Composition &y)
	Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase.

virtual void	setState_TPY (double t, double p, const string &y)
	Set the internally stored temperature (K), pressure (Pa), and mass fractions of the phase.

virtual void	setState_TP (double t, double p)
	Set the temperature (K) and pressure (Pa)

virtual void	setState_HP (double h, double p, double tol=1e-9)
	Set the internally stored specific enthalpy (J/kg) and pressure (Pa) of the phase.

virtual void	setState_UV (double u, double v, double tol=1e-9)
	Set the specific internal energy (J/kg) and specific volume (m^3/kg).

virtual void	setState_SP (double s, double p, double tol=1e-9)
	Set the specific entropy (J/kg/K) and pressure (Pa).

virtual void	setState_SV (double s, double v, double tol=1e-9)
	Set the specific entropy (J/kg/K) and specific volume (m^3/kg).

virtual void	setState_ST (double s, double t, double tol=1e-9)
	Set the specific entropy (J/kg/K) and temperature (K).

virtual void	setState_TV (double t, double v, double tol=1e-9)
	Set the temperature (K) and specific volume (m^3/kg).

virtual void	setState_PV (double p, double v, double tol=1e-9)
	Set the pressure (Pa) and specific volume (m^3/kg).

virtual void	setState_UP (double u, double p, double tol=1e-9)
	Set the specific internal energy (J/kg) and pressure (Pa).

virtual void	setState_VH (double v, double h, double tol=1e-9)
	Set the specific volume (m^3/kg) and the specific enthalpy (J/kg)

virtual void	setState_TH (double t, double h, double tol=1e-9)
	Set the temperature (K) and the specific enthalpy (J/kg)

virtual void	setState_SH (double s, double h, double tol=1e-9)
	Set the specific entropy (J/kg/K) and the specific enthalpy (J/kg)

void	setMixtureFraction (double mixFrac, span< const double > fuelComp, span< const double > oxComp, ThermoBasis basis=ThermoBasis::molar)
	Set the mixture composition according to the mixture fraction = kg fuel / (kg oxidizer + kg fuel)

void	setMixtureFraction (double mixFrac, const string &fuelComp, const string &oxComp, ThermoBasis basis=ThermoBasis::molar)
	Set the mixture composition according to the mixture fraction = kg fuel / (kg oxidizer + kg fuel)

void	setMixtureFraction (double mixFrac, const Composition &fuelComp, const Composition &oxComp, ThermoBasis basis=ThermoBasis::molar)
	Set the mixture composition according to the mixture fraction = kg fuel / (kg oxidizer + kg fuel)

double	mixtureFraction (span< const double > fuelComp, span< const double > oxComp, ThermoBasis basis=ThermoBasis::molar, const string &element="Bilger") const
	Compute the mixture fraction = kg fuel / (kg oxidizer + kg fuel) for the current mixture given fuel and oxidizer compositions.

double	mixtureFraction (const string &fuelComp, const string &oxComp, ThermoBasis basis=ThermoBasis::molar, const string &element="Bilger") const
	Compute the mixture fraction = kg fuel / (kg oxidizer + kg fuel) for the current mixture given fuel and oxidizer compositions.

double	mixtureFraction (const Composition &fuelComp, const Composition &oxComp, ThermoBasis basis=ThermoBasis::molar, const string &element="Bilger") const
	Compute the mixture fraction = kg fuel / (kg oxidizer + kg fuel) for the current mixture given fuel and oxidizer compositions.

void	setEquivalenceRatio (double phi, span< const double > fuelComp, span< const double > oxComp, ThermoBasis basis=ThermoBasis::molar)
	Set the mixture composition according to the equivalence ratio.

void	setEquivalenceRatio (double phi, const string &fuelComp, const string &oxComp, ThermoBasis basis=ThermoBasis::molar)
	Set the mixture composition according to the equivalence ratio.

void	setEquivalenceRatio (double phi, const Composition &fuelComp, const Composition &oxComp, ThermoBasis basis=ThermoBasis::molar)
	Set the mixture composition according to the equivalence ratio.

double	equivalenceRatio (span< const double > fuelComp, span< const double > oxComp, ThermoBasis basis=ThermoBasis::molar) const
	Compute the equivalence ratio for the current mixture given the compositions of fuel and oxidizer.

double	equivalenceRatio (const string &fuelComp, const string &oxComp, ThermoBasis basis=ThermoBasis::molar) const
	Compute the equivalence ratio for the current mixture given the compositions of fuel and oxidizer.

double	equivalenceRatio (const Composition &fuelComp, const Composition &oxComp, ThermoBasis basis=ThermoBasis::molar) const
	Compute the equivalence ratio for the current mixture given the compositions of fuel and oxidizer.

double	stoichAirFuelRatio (span< const double > fuelComp, span< const double > oxComp, ThermoBasis basis=ThermoBasis::molar) const
	Compute the stoichiometric air to fuel ratio (kg oxidizer / kg fuel) given fuel and oxidizer compositions.

double	stoichAirFuelRatio (const string &fuelComp, const string &oxComp, ThermoBasis basis=ThermoBasis::molar) const
	Compute the stoichiometric air to fuel ratio (kg oxidizer / kg fuel) given fuel and oxidizer compositions.

double	stoichAirFuelRatio (const Composition &fuelComp, const Composition &oxComp, ThermoBasis basis=ThermoBasis::molar) const
	Compute the stoichiometric air to fuel ratio (kg oxidizer / kg fuel) given fuel and oxidizer compositions.

void	equilibrate (const string &XY, const string &solver="auto", double rtol=1e-9, int max_steps=50000, int max_iter=100, int estimate_equil=0, int log_level=0)
	Equilibrate a ThermoPhase object.

virtual bool	compatibleWithMultiPhase () const
	Indicates whether this phase type can be used with class MultiPhase for equilibrium calculations.

virtual double	critTemperature () const
	Critical temperature (K).

virtual double	critPressure () const
	Critical pressure (Pa).

virtual double	critVolume () const
	Critical volume (m3/kmol).

virtual double	critCompressibility () const
	Critical compressibility (unitless).

virtual double	critDensity () const
	Critical density (kg/m3).

virtual double	satTemperature (double p) const
	Return the saturation temperature given the pressure.

virtual double	satPressure (double t)
	Return the saturation pressure given the temperature.

virtual double	vaporFraction () const
	Return the fraction of vapor at the current conditions.

virtual void	setState_Tsat (double t, double x)
	Set the state to a saturated system at a particular temperature.

virtual void	setState_Psat (double p, double x)
	Set the state to a saturated system at a particular pressure.

void	setState_TPQ (double T, double P, double Q)
	Set the temperature, pressure, and vapor fraction (quality).

bool	addSpecies (shared_ptr< Species > spec) override
	Add a Species to this Phase.

void	modifySpecies (size_t k, shared_ptr< Species > spec) override
	Modify the thermodynamic data associated with a species.

virtual MultiSpeciesThermo &	speciesThermo (int k=-1)
	Return a changeable reference to the calculation manager for species reference-state thermodynamic properties.

virtual const MultiSpeciesThermo &	speciesThermo (int k=-1) const

void	initThermoFile (const string &inputFile, const string &id)
	Initialize a ThermoPhase object using an input file.

AnyMap	parameters (bool withInput=true) const
	Returns the parameters of a ThermoPhase object such that an identical one could be reconstructed using the newThermo(AnyMap&) function.

virtual void	getSpeciesParameters (const string &name, AnyMap &speciesNode) const
	Get phase-specific parameters of a Species object such that an identical one could be reconstructed and added to this phase.

const AnyMap &	input () const
	Access input data associated with the phase description.

AnyMap &	input ()

void	invalidateCache () override
	Invalidate any cached values which are normally updated only when a change in state is detected.

virtual void	getdlnActCoeffds (const double dTds, span< const double > dXds, span< double > dlnActCoeffds) const
	Get the change in activity coefficients wrt changes in state (temp, mole fraction, etc) along a line in parameter space or along a line in physical space.

virtual void	getdlnActCoeffdlnX_diag (span< double > dlnActCoeffdlnX_diag) const
	Get the array of ln mole fraction derivatives of the log activity coefficients - diagonal component only.

virtual void	getdlnActCoeffdlnN_diag (span< double > dlnActCoeffdlnN_diag) const
	Get the array of log species mole number derivatives of the log activity coefficients.

virtual void	getdlnActCoeffdlnN (const size_t ld, span< double > dlnActCoeffdlnN)
	Get the array of derivatives of the log activity coefficients with respect to the log of the species mole numbers.

virtual void	getdlnActCoeffdlnN_numderiv (const size_t ld, span< double > dlnActCoeffdlnN)

virtual string	report (bool show_thermo=true, double threshold=-1e-14) const
	returns a summary of the state of the phase as a string

Public Member Functions inherited from Phase
	Phase ()=default
	Default constructor.

	Phase (const Phase &)=delete

Phase &	operator= (const Phase &)=delete

virtual bool	isPure () const
	Return whether phase represents a pure (single species) substance.

virtual bool	hasPhaseTransition () const
	Return whether phase represents a substance with phase transitions.

virtual bool	isCompressible () const
	Return whether phase represents a compressible substance.

virtual map< string, size_t >	nativeState () const
	Return a map of properties defining the native state of a substance.

string	nativeMode () const
	Return string acronym representing the native state of a Phase.

virtual vector< string >	fullStates () const
	Return a vector containing full states defining a phase.

virtual vector< string >	partialStates () const
	Return a vector of settable partial property sets within a phase.

virtual size_t	partialStateSize () const
	Get the size of the partial state vector of the phase.

virtual void	savePartialState (span< double > state) const
	Save the current thermodynamic state of the phase, excluding composition.

virtual void	restorePartialState (span< const double > state)
	Set the internal thermodynamic state of the phase, excluding composition.

virtual size_t	stateSize () const
	Return size of vector defining internal state of the phase.

virtual void	saveState (span< double > state) const
	Write to array 'state' the current internal state.

virtual void	restoreState (span< const double > state)
	Restore the state of the phase from a previously saved state vector.

double	molecularWeight (size_t k) const
	Molecular weight of species `k`.

void	getMolecularWeights (span< double > weights) const
	Copy the vector of molecular weights into array weights.

span< const double >	molecularWeights () const
	Return a const reference to the internal vector of molecular weights.

span< const double >	inverseMolecularWeights () const
	Return a const reference to the internal vector of molecular weights.

void	getCharges (span< double > charges) const
	Copy the vector of species charges into array charges.

virtual void	setMolesNoTruncate (span< const double > N)
	Set the state of the object with moles in [kmol].

double	elementalMassFraction (const size_t m) const
	Elemental mass fraction of element m.

double	elementalMoleFraction (const size_t m) const
	Elemental mole fraction of element m.

double	charge (size_t k) const
	Dimensionless electrical charge of a single molecule of species k The charge is normalized by the the magnitude of the electron charge.

double	chargeDensity () const
	Charge density [C/m^3].

size_t	nDim () const
	Returns the number of spatial dimensions (1, 2, or 3)

void	setNDim (size_t ndim)
	Set the number of spatial dimensions (1, 2, or 3).

virtual bool	ready () const
	Returns a bool indicating whether the object is ready for use.

int	stateMFNumber () const
	Return the State Mole Fraction Number.

virtual void	invalidateCache ()
	Invalidate any cached values which are normally updated only when a change in state is detected.

bool	caseSensitiveSpecies () const
	Returns `true` if case sensitive species names are enforced.

void	setCaseSensitiveSpecies (bool cflag=true)
	Set flag that determines whether case sensitive species are enforced in look-up operations, for example speciesIndex.

vector< double >	getCompositionFromMap (const Composition &comp) const
	Converts a Composition to a vector with entries for each species Species that are not specified are set to zero in the vector.

void	massFractionsToMoleFractions (span< const double > Y, span< double > X) const
	Converts a mixture composition from mole fractions to mass fractions.

void	moleFractionsToMassFractions (span< const double > X, span< double > Y) const
	Converts a mixture composition from mass fractions to mole fractions.

string	name () const
	Return the name of the phase.

void	setName (const string &nm)
	Sets the string name for the phase.

string	elementName (size_t m) const
	Name of the element with index m.

size_t	elementIndex (const string &name, bool raise=true) const
	Return the index of element named 'name'.

const vector< string > &	elementNames () const
	Return a read-only reference to the vector of element names.

double	atomicWeight (size_t m) const
	Atomic weight of element m.

double	entropyElement298 (size_t m) const
	Entropy of the element in its standard state at 298 K and 1 bar.

int	atomicNumber (size_t m) const
	Atomic number of element m.

int	elementType (size_t m) const
	Return the element constraint type Possible types include:

int	changeElementType (int m, int elem_type)
	Change the element type of the mth constraint Reassigns an element type.

span< const double >	atomicWeights () const
	Return a read-only reference to the vector of atomic weights.

size_t	nElements () const
	Number of elements.

size_t	checkElementIndex (size_t m) const
	Check that the specified element index is in range.

double	nAtoms (size_t k, size_t m) const
	Number of atoms of element `m` in species `k`.

size_t	speciesIndex (const string &name, bool raise=true) const
	Returns the index of a species named 'name' within the Phase object.

string	speciesName (size_t k) const
	Name of the species with index k.

const vector< string > &	speciesNames () const
	Return a const reference to the vector of species names.

size_t	nSpecies () const
	Returns the number of species in the phase.

size_t	checkSpeciesIndex (size_t k) const
	Check that the specified species index is in range.

void	setMoleFractionsByName (const Composition &xMap)
	Set the species mole fractions by name.

void	setMoleFractionsByName (const string &x)
	Set the mole fractions of a group of species by name.

void	setMassFractionsByName (const Composition &yMap)
	Set the species mass fractions by name.

void	setMassFractionsByName (const string &x)
	Set the species mass fractions by name.

virtual void	setState_TD (double t, double rho)
	Set the internally stored temperature (K) and density (kg/m^3)

Composition	getMoleFractionsByName (double threshold=0.0) const
	Get the mole fractions by name.

double	moleFraction (size_t k) const
	Return the mole fraction of a single species.

double	moleFraction (const string &name) const
	Return the mole fraction of a single species.

Composition	getMassFractionsByName (double threshold=0.0) const
	Get the mass fractions by name.

double	massFraction (size_t k) const
	Return the mass fraction of a single species.

double	massFraction (const string &name) const
	Return the mass fraction of a single species.

void	getMoleFractions (span< double > x) const
	Get the species mole fraction vector.

virtual void	setMoleFractions (span< const double > x)
	Set the mole fractions to the specified values.

virtual void	setMoleFractions_NoNorm (span< const double > x)
	Set the mole fractions to the specified values without normalizing.

void	getMassFractions (span< double > y) const
	Get the species mass fractions.

span< const double >	massFractions () const
	Return a view of the mass fraction array.

virtual void	setMassFractions (span< const double > y)
	Set the mass fractions to the specified values and normalize them.

virtual void	setMassFractions_NoNorm (span< const double > y)
	Set the mass fractions to the specified values without normalizing.

virtual void	getConcentrations (span< double > c) const
	Get the species concentrations (kmol/m^3).

virtual double	concentration (const size_t k) const
	Concentration of species k.

virtual void	setConcentrations (span< const double > conc)
	Set the concentrations to the specified values within the phase.

virtual void	setConcentrationsNoNorm (span< const double > conc)
	Set the concentrations without ignoring negative concentrations.

double	temperature () const
	Temperature (K).

virtual double	density () const
	Density (kg/m^3).

virtual double	molarDensity () const
	Molar density (kmol/m^3).

virtual double	molarVolume () const
	Molar volume (m^3/kmol).

virtual void	setDensity (const double density_)
	Set the internally stored density (kg/m^3) of the phase.

virtual void	setTemperature (double temp)
	Set the internally stored temperature of the phase (K).

double	mean_X (span< const double > Q) const
	Evaluate the mole-fraction-weighted mean of an array Q.

double	meanMolecularWeight () const
	The mean molecular weight. Units: (kg/kmol)

double	sum_xlogx () const
	Evaluate \( \sum_k X_k \ln X_k \).

size_t	addElement (const string &symbol, double weight=-12345.0, int atomicNumber=0, double entropy298=ENTROPY298_UNKNOWN, int elem_type=CT_ELEM_TYPE_ABSPOS)
	Add an element.

vector< AnyMap >	elementDefinitions () const
	Return explicit element definitions needed to reconstruct this phase.

void	addSpeciesAlias (const string &name, const string &alias)
	Add a species alias (that is, a user-defined alternative species name).

void	addSpeciesLock ()
	Lock species list to prevent addition of new species.

void	removeSpeciesLock ()
	Decrement species lock counter.

virtual vector< string >	findIsomers (const Composition &compMap) const
	Return a vector with isomers names matching a given composition map.

virtual vector< string >	findIsomers (const string &comp) const
	Return a vector with isomers names matching a given composition string.

shared_ptr< Species >	species (const string &name) const
	Return the Species object for the named species.

shared_ptr< Species >	species (size_t k) const
	Return the Species object for species whose index is k.

void	ignoreUndefinedElements ()
	Set behavior when adding a species containing undefined elements to just skip the species.

void	addUndefinedElements ()
	Set behavior when adding a species containing undefined elements to add those elements to the phase.

void	throwUndefinedElements ()
	Set the behavior when adding a species containing undefined elements to throw an exception.

Protected Member Functions
void	updateThermo () const override
	Update the species reference state thermodynamic functions.

void	electronEnergyDistributionChanged ()
	When electron energy distribution changed, plasma properties such as electron-collision reaction rates need to be re-evaluated.

void	electronEnergyLevelChanged ()
	When electron energy level changed, plasma properties such as electron-collision reaction rates need to be re-evaluate.

void	checkElectronEnergyLevels () const
	Check the electron energy levels.

void	checkElectronEnergyDistribution () const
	Check the electron energy distribution.

void	setIsotropicElectronEnergyDistribution ()
	Set isotropic electron energy distribution.

void	updateElectronTemperatureFromEnergyDist ()
	Update electron temperature (K) From energy distribution.

void	normalizeElectronEnergyDistribution ()
	Electron energy distribution norm.

bool	updateInterpolatedCrossSection (size_t k)
	Update interpolated cross section of a collision.

void	updateElectronEnergyDistDifference ()
	Update electron energy distribution difference.

void	updateElasticElectronEnergyLossCoefficient (size_t i)
	Updates the elastic electron energy loss coefficient for collision index i.

void	updateElasticElectronEnergyLossCoefficients ()
	Update elastic electron energy loss coefficients.

Protected Member Functions inherited from IdealGasPhase
virtual void	updateThermo () const
	Update the species reference state thermodynamic functions.

span< const double >	enthalpy_RT_ref () const
	Returns a reference to the dimensionless reference state enthalpy vector.

span< const double >	gibbs_RT_ref () const
	Returns a reference to the dimensionless reference state Gibbs free energy vector.

span< const double >	entropy_R_ref () const
	Returns a reference to the dimensionless reference state Entropy vector.

span< const double >	cp_R_ref () const
	Returns a reference to the dimensionless reference state Heat Capacity vector.

virtual void	getParameters (AnyMap &phaseNode) const
	Store the parameters of a ThermoPhase object such that an identical one could be reconstructed using the newThermo(AnyMap&) function.

Protected Member Functions inherited from Phase
void	assertCompressible (const string &setter) const
	Ensure that phase is compressible.

void	assignDensity (const double density_)
	Set the internally stored constant density (kg/m^3) of the phase.

void	setMolecularWeight (const int k, const double mw)
	Set the molecular weight of a single species to a given value.

virtual void	compositionChanged ()
	Apply changes to the state which are needed after the composition changes.

Protected Attributes
double	m_isotropicShapeFactor = 1.0

size_t	m_nPoints = 1001
	Number of points of electron energy levels.

Eigen::ArrayXd	m_electronEnergyLevels
	electron energy levels [ev]. Length: m_nPoints

Eigen::ArrayXd	m_electronEnergyDist
	Normalized electron energy distribution vector [-] Length: m_nPoints.

size_t	m_electronSpeciesIndex = npos
	Index of electron species.

double	m_electronTemp
	Electron temperature [K].

string	m_distributionType = "isotropic"
	Electron energy distribution type. Can be "isotropic", "discretized" or "Boltzmann-two-term".

string	m_quadratureMethod = "simpson"
	Numerical quadrature method for electron energy distribution.

bool	m_do_normalizeElectronEnergyDist = true
	Flag of normalizing electron energy distribution.

vector< size_t >	m_kInelastic
	Indices of inelastic collisions in m_crossSections.

vector< size_t >	m_kElastic
	Indices of elastic collisions in m_crossSections.

double	m_electricField = 0.0
	electric field [V/m].

double	m_electricFieldFrequency = 0.0
	electric field freq [Hz].

vector< vector< double > >	m_crossSections
	Cross section data.

vector< vector< double > >	m_energyLevels
	Electron energy levels corresponding to the cross section data.

Eigen::ArrayXd	m_electronEnergyDistDiff
	ionization degree for the electron-electron collisions (tmp is the previous one)

vector< double >	m_elasticElectronEnergyLossCoefficients
	Elastic electron energy loss coefficients (eV m3/s)

Protected Attributes inherited from IdealGasPhase
double	m_p0 = -1.0
	Reference state pressure.

vector< double >	m_h0_RT
	Temporary storage for dimensionless reference state enthalpies.

vector< double >	m_cp0_R
	Temporary storage for dimensionless reference state heat capacities.

vector< double >	m_g0_RT
	Temporary storage for dimensionless reference state Gibbs energies.

vector< double >	m_s0_R
	Temporary storage for dimensionless reference state entropies.

vector< double >	m_expg0_RT

vector< double >	m_pp
	Temporary array containing internally calculated partial pressures.

Protected Attributes inherited from ThermoPhase
MultiSpeciesThermo	m_spthermo
	Pointer to the calculation manager for species reference-state thermodynamic properties.

AnyMap	m_input
	Data supplied via setParameters.

double	m_phi = 0.0
	Stored value of the electric potential for this phase. Units are Volts.

bool	m_chargeNeutralityNecessary = false
	Boolean indicating whether a charge neutrality condition is a necessity.

int	m_ssConvention = cSS_CONVENTION_TEMPERATURE
	Contains the standard state convention.

bool	m_enforceTemperatureLimits = false
	Whether to enforce temperature limits in iterative solvers.

double	m_tlast = 0.0
	last value of the temperature processed by reference state

std::weak_ptr< Solution >	m_soln
	reference to Solution

Protected Attributes inherited from Phase
ValueCache	m_cache
	Cached for saved calculations within each ThermoPhase.

size_t	m_kk = 0
	Number of species in the phase.

size_t	m_ndim = 3
	Dimensionality of the phase.

vector< double >	m_speciesComp
	Atomic composition of the species.

vector< double >	m_speciesCharge
	Vector of species charges.

map< string, shared_ptr< Species > >	m_species
	Map of Species objects.

size_t	m_nSpeciesLocks = 0
	Reference counter preventing species addition.

UndefElement::behavior	m_undefinedElementBehavior = UndefElement::add
	Flag determining behavior when adding species with an undefined element.

bool	m_caseSensitiveSpecies = false
	Flag determining whether case sensitive species names are enforced.

vector< double >	m_workS
	Vector of size m_kk, used as a temporary holding area.

Private Member Functions
void	setCollisions ()
	Set collisions.

void	addCollision (shared_ptr< Reaction > collision)
	Add a collision and record the target species.

Private Attributes
unique_ptr< EEDFTwoTermApproximation >	m_eedfSolver = nullptr
	Solver used to calculate the EEDF based on electron collision rates.

int	m_distNum = -1
	Electron energy distribution change variable.

int	m_levelNum = -1
	Electron energy level change variable.

vector< shared_ptr< Reaction > >	m_collisions
	The list of shared pointers of plasma collision reactions.

vector< shared_ptr< ElectronCollisionPlasmaRate > >	m_collisionRates
	The list of shared pointers of collision rates.

vector< size_t >	m_targetSpeciesIndices
	The collision-target species indices of m_collisions.

vector< bool >	m_interp_cs_ready
	The list of whether the interpolated cross sections is ready.

double	m_electronTempEquil = 0.0
	Saved electron temperature during an equilibrium solve.

bool	m_inEquilibrate = false
	Lock flag (default off)

std::vector< double >	m_work
	Work array.

Constructor & Destructor Documentation

◆ PlasmaPhase()

PlasmaPhase	(	const string &	inputFile = `""`,
		const string &	id = `""`
	)

explicit

Construct and initialize a PlasmaPhase object directly from an input file.

The constructor initializes the electron energy distribution to be a Maxwellian distribution (m_isotropicShapeFactor = 1.0). The initial electron energy grid is set to a linear space which starts at 0.01 eV and ends at 1 eV with 1000 points.

Parameters

inputFile	Name of the input file containing the phase definition to set up the object. If blank, an empty phase will be created.
id	ID of the phase in the input file. Defaults to the empty string.

Definition at line 24 of file PlasmaPhase.cpp.

◆ ~PlasmaPhase()

~PlasmaPhase ( )

Definition at line 43 of file PlasmaPhase.cpp.

Member Function Documentation

◆ type()

string type ( ) const

inlineoverridevirtual

String indicating the thermodynamic model implemented.

Usually corresponds to the name of the derived class, less any suffixes such as "Phase", TP", "VPSS", etc.

Since: Starting in Cantera 3.0, the name returned by this method corresponds to the canonical name used in the YAML input format.

Reimplemented from IdealGasPhase.

Definition at line 144 of file PlasmaPhase.h.

◆ initThermo()

void initThermo ( )

overridevirtual

Initialize the ThermoPhase object after all species have been set up.

This method is provided to allow subclasses to perform any initialization required after all species have been added. For example, it might be used to resize internal work arrays that must have an entry for each species. The base class implementation does nothing, and subclasses that do not require initialization do not need to overload this method. Derived classes which do override this function should call their parent class's implementation of this function as their last action.

When importing from an AnyMap phase description (or from a YAML file), setupPhase() adds all the species, stores the input data in m_input, and then calls this method to set model parameters from the data stored in m_input.

Reimplemented from ThermoPhase.

Definition at line 55 of file PlasmaPhase.cpp.

◆ addSpecies()

bool addSpecies ( shared_ptr< Species > spec )

overridevirtual

Add a Species to this Phase.

Returns true if the species was successfully added, or false if the species was ignored.

Derived classes which need to size arrays according to the number of species should overload this method. The derived class implementation should call the base class method, and, if this returns true (indicating that the species has been added), adjust their array sizes accordingly.

See also: ignoreUndefinedElements addUndefinedElements throwUndefinedElements

Reimplemented from IdealGasPhase.

Definition at line 95 of file PlasmaPhase.cpp.

◆ setSolution()

void setSolution ( std::weak_ptr< Solution > soln )

overridevirtual

Set the link to the Solution object that owns this ThermoPhase.

Parameters

soln	Weak pointer to the parent Solution object

Reimplemented from ThermoPhase.

Definition at line 115 of file PlasmaPhase.cpp.

◆ getParameters()

void getParameters ( AnyMap & phaseNode ) const

overridevirtual

Store the parameters of a ThermoPhase object such that an identical one could be reconstructed using the newThermo(AnyMap&) function.

This does not include user-defined fields available in input().

Reimplemented from ThermoPhase.

Definition at line 126 of file PlasmaPhase.cpp.

◆ setParameters()

void setParameters	(	const AnyMap &	phaseNode,
		const AnyMap &	rootNode = `AnyMap()`
	)

overridevirtual

Set equation of state parameters from an AnyMap phase description.

Phases that need additional parameters from the root node should override this method.

Reimplemented from ThermoPhase.

Definition at line 146 of file PlasmaPhase.cpp.

◆ electronSpeciesIndex()

size_t electronSpeciesIndex ( ) const

inline

Electron Species Index.

Definition at line 162 of file PlasmaPhase.h.

◆ electronSpeciesName()

string electronSpeciesName ( ) const

inline

Electron species name.

Definition at line 167 of file PlasmaPhase.h.

◆ setElectronEnergyLevels()

void setElectronEnergyLevels ( span< const double > levels )

Set electron energy levels.

Parameters

levels The vector of electron energy levels [eV]. Length: m_nPoints.

Definition at line 327 of file PlasmaPhase.cpp.

◆ getElectronEnergyLevels()

void getElectronEnergyLevels ( span< double > levels ) const

inline

Get electron energy levels.

Parameters

levels The vector of electron energy levels [eV]. Length: m_nPoints

Definition at line 182 of file PlasmaPhase.h.

◆ setDiscretizedElectronEnergyDist()

void setDiscretizedElectronEnergyDist	(	span< const double >	levels,
		span< const double >	distrb
	)

Set discretized electron energy distribution.

Parameters

levels	The vector of electron energy levels [eV]. Length: m_nPoints.
distrb	The vector of electron energy distribution. Length: m_nPoints.

Definition at line 382 of file PlasmaPhase.cpp.

◆ getElectronEnergyDistribution()

void getElectronEnergyDistribution ( span< double > distrb ) const

inline

Get electron energy distribution.

Parameters

distrb The vector of electron energy distribution. Length: m_nPoints.

Definition at line 197 of file PlasmaPhase.h.

◆ setIsotropicShapeFactor()

void setIsotropicShapeFactor ( double x )

Set the shape factor of isotropic electron energy distribution.

Note that \( x = 1 \) and \( x = 2 \) correspond to the Maxwellian and Druyvesteyn distribution, respectively.

Parameters

x	The shape factor

Definition at line 420 of file PlasmaPhase.cpp.

◆ isotropicShapeFactor()

double isotropicShapeFactor ( ) const

inline

The shape factor of isotropic electron energy distribution.

Definition at line 208 of file PlasmaPhase.h.

◆ electronTemperature()

double electronTemperature ( ) const

inlineoverridevirtual

Electron Temperature [K].

Returns: The electron temperature of the phase.

Reimplemented from Phase.

Definition at line 214 of file PlasmaPhase.h.

◆ setElectronTemperature()

void setElectronTemperature ( double Te )

overridevirtual

Set the internally stored electron temperature of the phase [K].

Parameters

Te	Electron temperature in Kelvin.

Reimplemented from Phase.

Definition at line 291 of file PlasmaPhase.cpp.

◆ meanElectronEnergy()

double meanElectronEnergy ( ) const

inline

Mean electron energy [eV].

Definition at line 222 of file PlasmaPhase.h.

◆ setMeanElectronEnergy()

void setMeanElectronEnergy ( double energy )

Set mean electron energy [eV].

This method also sets electron temperature accordingly.

Definition at line 323 of file PlasmaPhase.cpp.

◆ electronEnergyDistributionType()

string electronEnergyDistributionType ( ) const

inline

Get electron energy distribution type.

Definition at line 231 of file PlasmaPhase.h.

◆ setElectronEnergyDistributionType()

void setElectronEnergyDistributionType ( const string & type )

Set electron energy distribution type.

Definition at line 264 of file PlasmaPhase.cpp.

◆ quadratureMethod()

string quadratureMethod ( ) const

inline

Numerical quadrature method. Method: m_quadratureMethod.

Definition at line 239 of file PlasmaPhase.h.

◆ setQuadratureMethod()

void setQuadratureMethod ( const string & method )

inline

Set numerical quadrature method for integrating electron energy distribution function.

Method: m_quadratureMethod

Definition at line 245 of file PlasmaPhase.h.

◆ enableNormalizeElectronEnergyDist()

void enableNormalizeElectronEnergyDist ( bool enable )

inline

Set flag of automatically normalize electron energy distribution.

Flag: m_do_normalizeElectronEnergyDist

Definition at line 251 of file PlasmaPhase.h.

◆ normalizeElectronEnergyDistEnabled()

bool normalizeElectronEnergyDistEnabled ( ) const

inline

Flag of automatically normalize electron energy distribution.

Flag: m_do_normalizeElectronEnergyDist

Definition at line 257 of file PlasmaPhase.h.

◆ nElectronEnergyLevels()

size_t nElectronEnergyLevels ( ) const

inline

Number of electron levels.

Definition at line 262 of file PlasmaPhase.h.

◆ nCollisions()

size_t nCollisions ( ) const

inline

Number of electron collision cross sections.

Definition at line 267 of file PlasmaPhase.h.

◆ collision()

const shared_ptr< Reaction > collision ( size_t i ) const

inline

Get the Reaction object associated with electron collision i.

Since: New in Cantera 3.2.

Definition at line 273 of file PlasmaPhase.h.

◆ collisionRate()

const shared_ptr< ElectronCollisionPlasmaRate > collisionRate ( size_t i ) const

inline

Get the ElectronCollisionPlasmaRate object associated with electron collision i.

Since: New in Cantera 3.2.

Definition at line 280 of file PlasmaPhase.h.

◆ updateElectronEnergyDistribution()

void updateElectronEnergyDistribution ( )

Update the electron energy distribution.

Definition at line 216 of file PlasmaPhase.cpp.

◆ distributionNumber()

int distributionNumber ( ) const

inline

Return the distribution number m_distNum.

Definition at line 288 of file PlasmaPhase.h.

◆ levelNumber()

int levelNumber ( ) const

inline

Return the electron energy level number m_levelNum.

Definition at line 293 of file PlasmaPhase.h.

◆ kInelastic()

const vector< size_t > & kInelastic ( ) const

inline

Get the indicies for inelastic electron collisions.

Since: New in Cantera 3.2.

Definition at line 299 of file PlasmaPhase.h.

◆ kElastic()

const vector< size_t > & kElastic ( ) const

inline

Get the indices for elastic electron collisions.

Since: New in Cantera 3.2.

Definition at line 305 of file PlasmaPhase.h.

◆ targetIndex()

size_t targetIndex ( size_t i ) const

inline

Return the target of a specific process.

Since: New in Cantera 3.2.

Definition at line 311 of file PlasmaPhase.h.

◆ electricFieldFrequency()

double electricFieldFrequency ( ) const

inline

Get the frequency of the applied electric field [Hz].

Since: New in Cantera 3.2.

Definition at line 317 of file PlasmaPhase.h.

◆ electricField()

double electricField ( ) const

inline

Get the applied electric field strength [V/m].

Definition at line 322 of file PlasmaPhase.h.

◆ setElectricField()

void setElectricField ( double E )

inline

Set the absolute electric field strength [V/m].

Definition at line 327 of file PlasmaPhase.h.

◆ reducedElectricField()

double reducedElectricField ( ) const

inline

Calculate the degree of ionization.

Get the reduced electric field strength [V·m²].

Definition at line 339 of file PlasmaPhase.h.

◆ setReducedElectricField()

void setReducedElectricField ( double EN )

inline

Set reduced electric field given in [V·m²].

Definition at line 344 of file PlasmaPhase.h.

◆ electronMobility()

double electronMobility ( ) const

The electron mobility (m²/V/s)

\[ \mu = \nu_d / E, \]

where \( \nu_d \) is the drift velocity (m²/s), and \( E \) is the electric field strength (V/m).

Definition at line 640 of file PlasmaPhase.cpp.

◆ elasticPowerLoss()

double elasticPowerLoss ( )

The elastic power loss [J/s/m³].

\[ P_k = N_A N_A C_e e \sum_k C_k K_k, \]

where \( C_k \) and \( C_e \) are the concentration (kmol/m³) of the target species and electrons, respectively. \( K_k \) is the elastic electron energy loss coefficient (eV-m³/s).

Definition at line 613 of file PlasmaPhase.cpp.

◆ jouleHeatingPower()

double jouleHeatingPower ( ) const

The joule heating power (W/m³)

\[ q_J = \sigma * E^2, \]

where \( \sigma \) is the conductivity (S/m), defined by:

\[ \sigma = e * n_e * \mu_e \]

and \( E \) is the electric field strength (V/m).

Definition at line 881 of file PlasmaPhase.cpp.

◆ beginEquilibrate()

void beginEquilibrate ( )

overridevirtual

Hook called at the beginning of an equilibrium calculation on this phase.

Non-equilibrium phase models can override this to adjust internal state while an equilibrium solver is active (e.g., locking the electron temperature to the gas temperature).

Since: New in Cantera 4.0.

Reimplemented from ThermoPhase.

Definition at line 300 of file PlasmaPhase.cpp.

◆ endEquilibrate()

void endEquilibrate ( )

overridevirtual

Hook called at the end of an equilibrium calculation on this phase.

Any changes made in beginEquilibrate() are undone here.

Since: New in Cantera 4.0.

Reimplemented from ThermoPhase.

Definition at line 312 of file PlasmaPhase.cpp.

◆ intrinsicHeating()

double intrinsicHeating ( )

overridevirtual

Intrinsic volumetric heating rate [W/m³].

Returns the power density generated by internal processes within this phase (e.g., Joule heating in a plasma). The default implementation returns zero, and phases that don't have intrinsic heating don't override this method.

Since: New in Cantera 4.0.

Reimplemented from ThermoPhase.

Definition at line 900 of file PlasmaPhase.cpp.

◆ enthalpy_mole()

double enthalpy_mole ( ) const

overridevirtual

Return the Molar enthalpy. Units: J/kmol.

For an ideal gas mixture with electrons at a different temperature than the heavy species, the molar enthalpy is calculated as:

\[ \begin{align} \hat h(T, T_\text{e}) &= \sum_{k} X_k h^0_k(T_k) \\ &= \sum_{k \neq e} X_k h^0_k(T) + X_\text{e} h_\text{e}^0(T_\text{e}) \end{align} \]

where heavy-species properties are evaluated at \( T \), electron properties at \( T_\text{e} \), and \( P \) is the total pressure of the mixture. For an ideal gas, enthalpy is independent of pressure. The standard-state pure-species enthalpies \( h^0_k(T_k) \) are computed by the species thermodynamic property manager.

Reimplemented from IdealGasPhase.

Definition at line 656 of file PlasmaPhase.cpp.

◆ entropy_mole()

double entropy_mole ( ) const

overridevirtual

Return the molar entropy. Units: J/kmol/K.

For an ideal gas mixture with electrons at a different temperature than the heavy species, the molar entropy is calculated as:

\[ \hat s(T,T_\text{e},P) = \sum_k X_k \hat s^0_k(T_k) - \hat R \ln \frac{P}{P^0} \]

where heavy-species properties are evaluated at \( T \), electron properties at \( T_\text{e} \), and \( P \) is the total pressure of the mixture.

Reimplemented from IdealGasPhase.

Definition at line 678 of file PlasmaPhase.cpp.

◆ gibbs_mole()

double gibbs_mole ( ) const

overridevirtual

Return the molar Gibbs free energy. Units: J/kmol.

For an ideal gas mixture with electrons at a different temperature than the heavy species, the molar Gibbs free energy is calculated as:

\[ \begin{align} \hat g(T,T_\text{e},P) &= \sum_{k} X_k \tilde{g}_k(T_k, P) = \sum_{k} X_k \mu_k(T_k, P) \\ &= \sum_{k} X_k \left[\mu^0_k(T_k) + R T_k \ln \left( \frac{X_k P}{P^0} \right) \right] \\ \end{align} \]

where heavy-species properties are evaluated at \( T \), electron properties at \( T_\text{e} \), and \( P \) is the total pressure of the mixture.

Reimplemented from ThermoPhase.

Definition at line 689 of file PlasmaPhase.cpp.

◆ intEnergy_mole()

double intEnergy_mole ( ) const

overridevirtual

Return the molar internal energy. Units: J/kmol.

For an ideal gas mixture with electrons at a different temperature than the heavy species, the molar internal energy is calculated as:

\[ \hat u(T,T_\text{e},P) = \sum_{k} X_k \tilde{u}_k(T_k) = \sum_{k} X_k (\tilde{h}_k(T_k) - R T_k) \]

where heavy-species properties are evaluated at \( T \), electron properties at \( T_\text{e} \), and \( P \) is the total pressure of the mixture. For an ideal gas, internal energy is independent of pressure.

Reimplemented from ThermoPhase.

Definition at line 667 of file PlasmaPhase.cpp.

◆ meanTemperature()

double meanTemperature ( ) const

Return the mean temperature of the plasma phase. Units: K.

In a plasma phase, the electron temperature can differ from the heavy-species (gas) temperature. Therefore, the mean temperature is defined as a mole-fraction-weighted average of the electron and heavy-species temperatures:

\[ \begin{align} \overline{T} &= \sum_{k \neq e} X_k T + X_\text{e} T_\text{e} \\ &= (1 - X_\text{e}) T + X_\text{e} T_\text{e} \\ &= T + X_\text{e} (T_\text{e} - T) \end{align} \]

See the pressure() method for usage of the mean temperature in calculating the pressure of the plasma phase.

Definition at line 704 of file PlasmaPhase.cpp.

◆ pressure()

double pressure ( ) const

overridevirtual

Return the pressure of the plasma phase. Units: Pa.

The pressure of the plasma phase is calculated using the mean temperature, which is a mole-fraction-weighted average of the electron and heavy-species temperatures.

\[ \begin{align} P &= \sum_k n_k k_\text{B} T_k \\ &= \sum_{k \neq e} n_k k_\text{B} T + n_\text{e} k_\text{B} T_\text{e} \\ &= (n_\text{total} - n_\text{e}) k_\text{B} T + n_\text{e} k_\text{B} T_\text{e} \\ &= n_\text{total} (1 - X_\text{e}) k_\text{B} T + n_\text{total} X_\text{e} k_\text{B} T_\text{e} \\ &= n_\text{total} k_\text{B} \overline{T} \\ \end{align} \]

where \( \overline{T} \) is the mean temperature of the plasma phase, defined in the meanTemperature() method. Here, \( n_k \) is the number density of species k [in 1/m³], \( n_\text{total} \) is the total number density of the phase [in 1/m³], \( X_\text{e} \) is the mole fraction of electrons, \( T \) is the heavy-species (gas) temperature [K], \( T_\text{e} \) is the electron temperature [K], and \( k_\text{B} \) is the Boltzmann constant [J/K].

The number density times Boltzmann constant can be expressed as \( n_\text{total} k_\text{B} = C_\text{total} R \), where \( C_\text{total} \) is the total molar concentration of the phase [kmol/m³] and \( R \) is the gas constant [J/kmol/K], so that:

\[ P = C_\text{total} R \overline{T}. \]

Here, the pressure is set via the density, via:

\[ P = R \overline{T} \frac{\rho}{\overline{W}} \]

where \( \overline{W} \) is the mean molecular weight.

Reimplemented from IdealGasPhase.

Definition at line 712 of file PlasmaPhase.cpp.

◆ setPressure()

void setPressure ( double p )

inlineoverridevirtual

Set the pressure at constant temperature and composition. Units: Pa.

This method is implemented by setting the mass density to

\[ \rho = \frac{P \overline{W}}{\hat R \overline{T} }. \]

where \( \overline{W} \) is the mean molecular weight, and \( \overline{T} \) is the mean temperature (see meanTemperature()).

Parameters

p	Pressure [Pa].

Reimplemented from IdealGasPhase.

Definition at line 532 of file PlasmaPhase.h.

◆ RTe()

double RTe ( ) const

inline

Return the Gas Constant multiplied by the current electron temperature [J/kmol].

Definition at line 537 of file PlasmaPhase.h.

◆ electronPressure()

virtual double electronPressure ( ) const

inlinevirtual

Return the electron pressure. Units: Pa.

The partial pressure of electrons is calculated using the electron temperature:

\[ P_\text{e} = n_\text{e} k_\text{B} T_\text{e} = C_\text{e} R T_\text{e}, \]

where \( n_\text{e} \) is the particular density of electrons [in 1/m³], \( k_\text{B} \) is the Boltzmann constant [J/K], \( C_\text{e} \) is the molar concentration of electrons [in kmol/m³], \( R \) is the gas constant [J/kmol/K], and \( T_\text{e} \) is the electron temperature [K].

Definition at line 553 of file PlasmaPhase.h.

◆ thermalExpansionCoeff()

double thermalExpansionCoeff ( ) const

inlineoverridevirtual

Raise NotImplementedError, as there is an ambiguity on the temperature to use.

Reimplemented from IdealGasPhase.

Definition at line 559 of file PlasmaPhase.h.

◆ soundSpeed()

double soundSpeed ( ) const

inlineoverridevirtual

Raise NotImplementedError, as there is an ambiguity on the temperature to use.

Reimplemented from IdealGasPhase.

Definition at line 564 of file PlasmaPhase.h.

◆ standardConcentration()

double standardConcentration ( size_t k = 0 ) const

overridevirtual

Returns the standard concentration \( C^0_k \), which is used to normalize the generalized concentration.

Units: m³/kmol.

The standard concentration is chosen to be equal to

\[ C^0_k = \frac{P}{R T} \]

where \( P \) is the total pressure of the mixture, \( R \) is the gas constant, and \( T \) is the gas temperature.

Note: The gas temperature \( T \) (not the electron temperature or the mean temperature) is used for all species, including electrons. Consequently \( C^0_\text{e} = P/RT \neq 1/V^0_\text{e} = P/R T_\text{e} \) when \( T_\text{e} \neq T \). This is intentional: the reciprocal relation \( C^0_k = 1/V^0_k \) is a coincidence of the single-temperature ideal gas and is not a thermodynamic requirement. See the class documentation.

Parameters

k	Parameter indicating the species. The default is to assume this refers to species 0.

Reimplemented from IdealGasPhase.

Definition at line 721 of file PlasmaPhase.cpp.

◆ getActivities()

void getActivities ( span< double > a ) const

overridevirtual

Get the array of non-dimensional activities at the current solution temperature, pressure, and solution concentration.

Since \( a_k = C^a_k / C^0_k \), where \( C^a_k = C_k \) is the true molar concentration, and \( C^0_k \) is the standard concentration defined above, the activities are equal to \( a_k = X_k T / \overline{T} \).

Note: These activities are defined for consistency with the kinetics (law-of-mass-action) concentrations and, when \( T_\text{e} \neq T \), differ by a factor of \( T/\overline{T} \) from the activities implied by the chemical-potential model ( \( a_k = X_k \)). See the class documentation for a discussion of this intentional inconsistency.

Parameters

a	Output vector of activities. Length: m_kk.

Reimplemented from ThermoPhase.

Definition at line 726 of file PlasmaPhase.cpp.

◆ getActivityCoefficients()

void getActivityCoefficients ( span< double > ac ) const

overridevirtual

Get the array of non-dimensional activity coefficients at the current solution temperature, pressure, and solution concentration.

The activity coefficients are defined by \( \gamma_k = a_k / X_k \). With the current definition of the activities, the activity coefficients are equal to \( \gamma_k = T / \overline{T} \).

Parameters

ac	Output vector of activity coefficients. Length: m_kk.

Reimplemented from IdealGasPhase.

Definition at line 734 of file PlasmaPhase.cpp.

◆ getChemPotentials()

void getChemPotentials ( span< double > mu ) const

overridevirtual

Return the chemical potentials of the species in the solution. Units: J/kmol.

The chemical potential of species k is calculated as:

\[ \begin{align} \mu_k(T_k, X_k, P) &= \mu_k^o(T_k, P) + R T_k \ln(X_k) \\ &= \mu^0_k(T_k)(T_k) + R T_k \ln\left(\frac{P}{P^0}\right) + R T_k \ln(X_k) \\ &= h^0_k(T_k) - T_k s^0_k(T_k) + R T_k \ln\left(\frac{P X_k}{P^0}\right) \\ \end{align} \]

Note that it is also equal to the partial molar Gibbs free energy.

Reimplemented from IdealGasPhase.

Definition at line 748 of file PlasmaPhase.cpp.

◆ getPartialMolarEnthalpies()

void getPartialMolarEnthalpies ( span< double > hbar ) const

overridevirtual

Return the partial molar enthalpies of the species in the solution. Units: J/kmol.

The partial molar enthalpy of species k is \( \tilde{h}_k(T_k,P) = h^o_k(T,P) = h^{ref}_k(T_k) \), where heavy-species properties are evaluated at the gas temperature \( T \), and electron properties are evaluated at the electron temperature \( T_e \).

Reimplemented from IdealGasPhase.

Definition at line 756 of file PlasmaPhase.cpp.

◆ getPartialMolarEntropies()

void getPartialMolarEntropies ( span< double > sbar ) const

overridevirtual

Return the partial molar entropies of the species in the solution. Units: J/kmol/K.

The partial molar enthalpy of species k is:

\[ \tilde{s}_k(T_k, P) = s^0_k(T_k) - R \ln \frac{X_k P}{P^0} \]

where heavy-species properties are evaluated at the gas temperature, and electron properties are evaluated at the electron temperature. Here, \( P \) is the total pressure of the mixture, as defined in pressure().

Reimplemented from IdealGasPhase.

Definition at line 768 of file PlasmaPhase.cpp.

◆ getPartialMolarIntEnergies()

void getPartialMolarIntEnergies ( span< double > ubar ) const

overridevirtual

Return the partial molar internal energies of the species in the solution. Units: J/kmol.

The partial molar internal energy of species k is calculated as:

\[ \tilde{u}_k(T_k,P) = \tilde{h}_k(T_k,P) - R T_k = h^{ref}_k(T_k) - R T_k \]

where \( \tilde{h}_k \) is the partial molar enthalpy of species k, and \( T_k \) is the temperature at which the partial molar enthalpy is evaluated. For heavy species, the partial molar enthalpy is evaluated at the gas temperature, while for electrons, it is evaluated at the electron temperature.

Reimplemented from IdealGasPhase.

Definition at line 778 of file PlasmaPhase.cpp.

◆ getPartialMolarVolumes()

void getPartialMolarVolumes ( span< double > vbar ) const

overridevirtual

Return the partial molar volumes of the species in the solution. Units: m³/kmol.

For a multitemperature system,

\[ v_k = \frac{R T_k}{P} \]

where \( T_k \) is the temperature at which the partial molar enthalpy is evaluated.

Reimplemented from IdealGasPhase.

Definition at line 790 of file PlasmaPhase.cpp.

◆ getStandardChemPotentials()

void getStandardChemPotentials ( span< double > muStar ) const

overridevirtual

Return the standard chemical potentials of the species. Units: J/kmol.

The standard chemical potentials (or standard state Gibbs free energy) of species k is calculated as:

\[ \begin{align} \mu^0_k(T_k, X_k, P) &= mu^0_k(T_k)(T_k) + R T_k \ln\left(\frac{P}{P^0}\right) \\ &= h^0_k(T_k) - T_k s^0_k(T_k) + R T_k \ln\left(\frac{P X_k}{P^0}\right) \\ \end{align} \]

Here, \( P \) is the total pressure of the mixture, as defined in pressure().

Reimplemented from IdealGasPhase.

Definition at line 803 of file PlasmaPhase.cpp.

◆ getStandardVolumes()

void getStandardVolumes ( span< double > vol ) const

overridevirtual

Return the standard molar volumes of the species. Units: m³/kmol.

For a multitemperature system,

\[ v_k = \frac{R T_k}{P}, \]

where \( T_k \) is the temperature at which the standard molar volume is evaluated.

Reimplemented from IdealGasPhase.

Definition at line 821 of file PlasmaPhase.cpp.

◆ getGibbs_ref()

void getGibbs_ref ( span< double > g ) const

overridevirtual

Return the reference chemical potentials of the species. Units: J/kmol.

The reference chemical potentials (or reference state Gibbs free energy) of species k is calculated as:

\[ \mu^0_k(T_k) = h^0_k(T_k) - T_k s^0_k(T_k) \]

Reimplemented from IdealGasPhase.

Definition at line 834 of file PlasmaPhase.cpp.

◆ getStandardVolumes_ref()

void getStandardVolumes_ref ( span< double > vol ) const

overridevirtual

Return the molar volumes of the species reference states. Units: m³/kmol.

The molar volumes of the species reference states of species k is calculated as:

\[ v^o_k(T_k) = \frac{R T_k}{P^0} \]

Parameters

vol	Output vector containing the standard state volumes. Length: m_kk.

Reimplemented from IdealGasPhase.

Definition at line 846 of file PlasmaPhase.cpp.

◆ setState()

void setState ( const AnyMap & state )

overridevirtual

Set the state using an AnyMap containing any combination of properties supported by the thermodynamic model.

Accepted keys are:

X (mole fractions)
Y (mass fractions)
T or Tg or gas-temperature [K]
Te or electron-temperature [K]
P or pressure [Pa]
H or enthalpy [J/kg]
U or internal-energy [J/kg]
S or entropy [J/kg/K]
V or specific-volume [m^3/kg]
D or density [kg/m^3]

Composition can be specified as either an AnyMap of species names to values or as a composition string. All other values can be given as floating point values in Cantera's default units, or as strings with the units specified, which will be converted using the Units class.

If no thermodynamic property pair is given, or only one of temperature or pressure is given, then 298.15 K and 101325 Pa will be used as necessary to fully set the state.

Set the electron temperature first, and call ThermoPhase::setState.

Reimplemented from ThermoPhase.

Definition at line 856 of file PlasmaPhase.cpp.

◆ updateThermo()

void updateThermo ( ) const

overrideprotectedvirtual

Update the species reference state thermodynamic functions.

This method is called each time a thermodynamic property is requested, to check whether the internal species properties within the object need to be updated (like getPartialMolarCp, getEnthalpy_RT, getEntropy_R, getGibbs_RT, getIntEnergy_RT, getCp_R, and getEnthalpy_RT_ref and alike). Currently, this updates the species thermo polynomial values for the current value of the gas temperature for heavy species, and of the electron temperature for the electron species. A check is made to see if gas or electron temperatures have changed since the last evaluation. This object does not contain any persistent data that depends on the concentration, that needs to be updated. The state object modifies its concentration dependent information at the time the setMoleFractions() (or equivalent) call is made.

Reimplemented from IdealGasPhase.

Definition at line 66 of file PlasmaPhase.cpp.

◆ electronEnergyDistributionChanged()

void electronEnergyDistributionChanged ( )

protected

When electron energy distribution changed, plasma properties such as electron-collision reaction rates need to be re-evaluated.

Definition at line 336 of file PlasmaPhase.cpp.

◆ electronEnergyLevelChanged()

void electronEnergyLevelChanged ( )

protected

When electron energy level changed, plasma properties such as electron-collision reaction rates need to be re-evaluate.

In addition, the cross-sections need to be interpolated at the new level.

Definition at line 341 of file PlasmaPhase.cpp.

◆ checkElectronEnergyLevels()

void checkElectronEnergyLevels ( ) const

protected

Check the electron energy levels.

The values of electron energy levels need to be positive and monotonically increasing.

Definition at line 354 of file PlasmaPhase.cpp.

◆ checkElectronEnergyDistribution()

void checkElectronEnergyDistribution ( ) const

protected

Check the electron energy distribution.

This method check the electron energy distribution for the criteria below.

The values of electron energy distribution cannot be negative.
If the last value of electron energy distribution is larger than 0.01, it will raise a warning to suggest using a higher electron energy levels.

Definition at line 365 of file PlasmaPhase.cpp.

◆ setIsotropicElectronEnergyDistribution()

void setIsotropicElectronEnergyDistribution ( )

protected

Set isotropic electron energy distribution.

Definition at line 276 of file PlasmaPhase.cpp.

◆ updateElectronTemperatureFromEnergyDist()

void updateElectronTemperatureFromEnergyDist ( )

protected

Update electron temperature (K) From energy distribution.

m_electronTemp

Definition at line 400 of file PlasmaPhase.cpp.

◆ normalizeElectronEnergyDistribution()

void normalizeElectronEnergyDistribution ( )

protected

Electron energy distribution norm.

Definition at line 252 of file PlasmaPhase.cpp.

◆ updateInterpolatedCrossSection()

bool updateInterpolatedCrossSection ( size_t k )

protected

Update interpolated cross section of a collision.

Definition at line 521 of file PlasmaPhase.cpp.

◆ updateElectronEnergyDistDifference()

void updateElectronEnergyDistDifference ( )

protected

Update electron energy distribution difference.

Definition at line 533 of file PlasmaPhase.cpp.

◆ updateElasticElectronEnergyLossCoefficient()

void updateElasticElectronEnergyLossCoefficient ( size_t i )

protected

Updates the elastic electron energy loss coefficient for collision index i.

Calculates the elastic energy loss coefficient using the current electron energy distribution and cross sections.

Definition at line 590 of file PlasmaPhase.cpp.

◆ updateElasticElectronEnergyLossCoefficients()

void updateElasticElectronEnergyLossCoefficients ( )

protected

Update elastic electron energy loss coefficients.

Used by elasticPowerLoss() and other plasma property calculations that depends on m_elasticElectronEnergyLossCoefficients. This function calls updateInterpolatedCrossSection() before calling updateElasticElectronEnergyLossCoefficient()

Definition at line 559 of file PlasmaPhase.cpp.

◆ setCollisions()

void setCollisions ( )

private

Set collisions.

This function sets the list of collisions and the list of target species using addCollision.

Definition at line 425 of file PlasmaPhase.cpp.

◆ addCollision()

void addCollision ( shared_ptr< Reaction > collision )

private

Add a collision and record the target species.

Definition at line 459 of file PlasmaPhase.cpp.

Member Data Documentation

◆ m_isotropicShapeFactor

double m_isotropicShapeFactor = 1.0

protected

Definition at line 852 of file PlasmaPhase.h.

◆ m_nPoints

size_t m_nPoints = 1001

protected

Number of points of electron energy levels.

Definition at line 855 of file PlasmaPhase.h.

◆ m_electronEnergyLevels

Eigen::ArrayXd m_electronEnergyLevels

protected

electron energy levels [ev]. Length: m_nPoints

Definition at line 858 of file PlasmaPhase.h.

◆ m_electronEnergyDist

Eigen::ArrayXd m_electronEnergyDist

protected

Normalized electron energy distribution vector [-] Length: m_nPoints.

Definition at line 862 of file PlasmaPhase.h.

◆ m_electronSpeciesIndex

size_t m_electronSpeciesIndex = npos

protected

Index of electron species.

Definition at line 865 of file PlasmaPhase.h.

◆ m_electronTemp

double m_electronTemp

protected

Electron temperature [K].

Definition at line 868 of file PlasmaPhase.h.

◆ m_distributionType

string m_distributionType = "isotropic"

protected

Electron energy distribution type. Can be "isotropic", "discretized" or "Boltzmann-two-term".

Definition at line 871 of file PlasmaPhase.h.

◆ m_quadratureMethod

string m_quadratureMethod = "simpson"

protected

Numerical quadrature method for electron energy distribution.

Definition at line 874 of file PlasmaPhase.h.

◆ m_do_normalizeElectronEnergyDist

bool m_do_normalizeElectronEnergyDist = true

protected

Flag of normalizing electron energy distribution.

Definition at line 877 of file PlasmaPhase.h.

◆ m_kInelastic

vector<size_t> m_kInelastic

protected

Indices of inelastic collisions in m_crossSections.

Definition at line 880 of file PlasmaPhase.h.

◆ m_kElastic

vector<size_t> m_kElastic

protected

Indices of elastic collisions in m_crossSections.

Definition at line 883 of file PlasmaPhase.h.

◆ m_electricField

double m_electricField = 0.0

protected

electric field [V/m].

Definition at line 886 of file PlasmaPhase.h.

◆ m_electricFieldFrequency

double m_electricFieldFrequency = 0.0

protected

electric field freq [Hz].

Definition at line 889 of file PlasmaPhase.h.

◆ m_crossSections

vector<vector<double> > m_crossSections

protected

Cross section data.

m_crossSections[i][j], where i is the specific process, j is the index of vector. Unit: [m^2]

Definition at line 893 of file PlasmaPhase.h.

◆ m_energyLevels

vector<vector<double> > m_energyLevels

protected

Electron energy levels corresponding to the cross section data.

m_energyLevels[i][j], where i is the specific process, j is the index of vector. Unit: [eV]

Definition at line 897 of file PlasmaPhase.h.

◆ m_electronEnergyDistDiff

Eigen::ArrayXd m_electronEnergyDistDiff

protected

ionization degree for the electron-electron collisions (tmp is the previous one)

Electron energy distribution Difference dF/dε (V^-5/2)

Definition at line 903 of file PlasmaPhase.h.

◆ m_elasticElectronEnergyLossCoefficients

vector<double> m_elasticElectronEnergyLossCoefficients

protected

Elastic electron energy loss coefficients (eV m3/s)

The elastic electron energy loss coefficient for species k is,

\[ K_k = \frac{2 m_e}{m_k} \sqrt{\frac{2 e}{m_e}} \int_0^{\infty} \sigma_k \epsilon^2 \left( F_0 + \frac{k_\text{B} T}{e} \frac{\partial F_0}{\partial \epsilon} \right) d \epsilon, \]

where \( m_e \) [kg] is the electron mass, \( \epsilon \) [V] is the electron energy, \( \sigma_k \) [m2] is the reaction collision cross section, \( F_0 \) [V^(-3/2)] is the normalized electron energy distribution function.

Definition at line 916 of file PlasmaPhase.h.

◆ m_eedfSolver

unique_ptr<EEDFTwoTermApproximation> m_eedfSolver = nullptr

private

Solver used to calculate the EEDF based on electron collision rates.

Definition at line 935 of file PlasmaPhase.h.

◆ m_distNum

int m_distNum = -1

private

Electron energy distribution change variable.

Whenever m_electronEnergyDist changes, this int is incremented.

Definition at line 939 of file PlasmaPhase.h.

◆ m_levelNum

int m_levelNum = -1

private

Electron energy level change variable.

Whenever m_electronEnergyLevels changes, this int is incremented.

Definition at line 943 of file PlasmaPhase.h.

◆ m_collisions

vector<shared_ptr<Reaction> > m_collisions

private

The list of shared pointers of plasma collision reactions.

Definition at line 946 of file PlasmaPhase.h.

◆ m_collisionRates

vector<shared_ptr<ElectronCollisionPlasmaRate> > m_collisionRates

private

The list of shared pointers of collision rates.

Definition at line 949 of file PlasmaPhase.h.

◆ m_targetSpeciesIndices

vector<size_t> m_targetSpeciesIndices

private

The collision-target species indices of m_collisions.

Definition at line 952 of file PlasmaPhase.h.

◆ m_interp_cs_ready

vector<bool> m_interp_cs_ready

private

The list of whether the interpolated cross sections is ready.

Definition at line 955 of file PlasmaPhase.h.

◆ m_electronTempEquil

double m_electronTempEquil = 0.0

private

Saved electron temperature during an equilibrium solve.

Definition at line 965 of file PlasmaPhase.h.

◆ m_inEquilibrate

bool m_inEquilibrate = false

private

Lock flag (default off)

Definition at line 968 of file PlasmaPhase.h.

◆ m_work

std::vector<double> m_work

mutableprivate

Work array.

Definition at line 971 of file PlasmaPhase.h.

The documentation for this class was generated from the following files:

Detailed Description

Thermodynamic consistency of the two-temperature model

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Constructor & Destructor Documentation

◆ PlasmaPhase()

◆ ~PlasmaPhase()

Member Function Documentation

◆ type()

◆ initThermo()

◆ addSpecies()

◆ setSolution()

◆ getParameters()

◆ setParameters()

◆ electronSpeciesIndex()

◆ electronSpeciesName()

◆ setElectronEnergyLevels()

◆ getElectronEnergyLevels()

◆ setDiscretizedElectronEnergyDist()

◆ getElectronEnergyDistribution()

◆ setIsotropicShapeFactor()

◆ isotropicShapeFactor()

◆ electronTemperature()

◆ setElectronTemperature()

◆ meanElectronEnergy()

◆ setMeanElectronEnergy()

◆ electronEnergyDistributionType()

◆ setElectronEnergyDistributionType()

◆ quadratureMethod()

◆ setQuadratureMethod()

◆ enableNormalizeElectronEnergyDist()

◆ normalizeElectronEnergyDistEnabled()

◆ nElectronEnergyLevels()

◆ nCollisions()

◆ collision()

◆ collisionRate()

◆ updateElectronEnergyDistribution()

◆ distributionNumber()

◆ levelNumber()

◆ kInelastic()

◆ kElastic()

◆ targetIndex()

◆ electricFieldFrequency()

◆ electricField()

◆ setElectricField()

◆ reducedElectricField()

◆ setReducedElectricField()

◆ electronMobility()

◆ elasticPowerLoss()

◆ jouleHeatingPower()

◆ beginEquilibrate()

◆ endEquilibrate()

◆ intrinsicHeating()

◆ enthalpy_mole()

◆ entropy_mole()

◆ gibbs_mole()

◆ intEnergy_mole()

◆ meanTemperature()

◆ pressure()

◆ setPressure()

◆ RTe()

◆ electronPressure()

◆ thermalExpansionCoeff()

◆ soundSpeed()

◆ standardConcentration()

◆ getActivities()

◆ getActivityCoefficients()

◆ getChemPotentials()

◆ getPartialMolarEnthalpies()

◆ getPartialMolarEntropies()

◆ getPartialMolarIntEnergies()

◆ getPartialMolarVolumes()

◆ getStandardChemPotentials()

◆ getStandardVolumes()

◆ getGibbs_ref()

◆ getStandardVolumes_ref()

◆ setState()