Composition-resolved electron-heavy momentum-transfer collision model. More...

#include <CollisionModel.h>

Classes
struct	SpeciesSpec
	Per-species spec, in species-index order. More...

Public Member Functions
	CollisionModel ()=default
	CollisionModel (const std::vector< SpeciesSpec > &specs, double Te_min, double Te_max, std::size_t Te_n, bool spitzer_correction=true)
	Build per-species Qbar(Te) tables on a log-spaced Te grid [Te_min, Te_max].
bool	empty () const
void	evaluate (double Te, double n_e, const double *n_k, std::size_t nsp, double &sigma, double &nu_E, double &cond_maxwell_2) const
	Composition-resolved electron transport.
double	conductivity (double Te, double n_e, const double *n_k, std::size_t nsp) const
	Conductivity only [S/m].

Static Public Member Functions
static double	electronElectronCollisionFrequency (double n_e, double Te)
	Electron-electron collision frequency \(\nu_{ee}\) [1/s] (Mitchner II-8.11e with Z=1), the closed-form ingredient of the first Maxwellian-distribution condition term \(C_1 = \nu_{ee}/m_e\) (Mitchner VIII-3.8).
static double	meanCrossSection (const std::vector< double > &energy_J, const std::vector< double > &sigma_m2, double Te, double x_max=20.0, int N=1000)
	The Maxwellian momentum-transfer kernel Qbar(Te) [m^2] (single source of truth; also exposed to Python for validation).
static std::vector< double >	meanCrossSectionTable (const std::vector< double > &energy_J, const std::vector< double > &sigma_m2, const std::vector< double > &Te, double x_max=20.0, int N=1000)
	Tabulated variant of meanCrossSection, evaluated at each Te in the input vector.

Detailed Description

Composition-resolved electron-heavy momentum-transfer collision model.

Ports rizer's Python collision physics (Mitchner & Kruger 1973, as implemented in rizer/plasma/momentum_transfer_cross_sections.py, rizer/plasma/collision_frequency.py, and rizer/plasma/equations.py, and assembled in PlasmaExtension.electrical_conductivity / plasma_power_elastic) to C++, so a 0D/1D plasma reactor can evaluate the electrical conductivity and the elastic energy-exchange frequency natively from the live composition every RHS, rather than from a frozen \(\nu_m(T_e)\) table.

Per-species kinds (mirrors get_momentum_transfer_cross_section_model):

Tabulated neutral: Maxwellian-averaged cross section, precomputed on a Te grid at build and linearly interpolated live (Mitchner II-6.30):
\[ \overline{Q}_k(T_e) = \frac{2}{3} \int_0^{x_\text{max}} x^2 e^{-x} Q(k_B T_e x)\, dx. \]
Hard-sphere neutral: \(\overline{Q} = \frac{4}{3} \pi r^2\) (Te-independent).
Ion (Z>0): Coulomb closed form (Mitchner II-8.10), \(\nu_{ei} = n_i \, c_\text{st} \, T_e^{-1.5} \, \ln\Lambda\).
Electron: skipped in the heavy sums.

Conductivity (Mitchner II-13.7b):

\[ \sigma = \frac{n_e e^2}{m_e \nu_{eH}}, \]

\[ \nu_{eH} = \sum_\text{neutrals} n_k \overline{Q}_k(T_e) v_\text{th}(T_e) + \sum_\text{ions} \nu_{ei}, \]

with the Spitzer e-e correction (II-13.18) bridged smoothly from a factor of 1 to 1.98 via the ion collision fraction \(f_\text{ion} = \nu_\text{ions} / \nu_{eH}\). Elastic exchange (II-7.6 / VI-5.1):

\[ \nu_E = \sum_\text{heavy} \left(\frac{2 m_e}{m_h}\right) \nu_{eh}, \]

such that

\[ P_\text{el} = \nu_E \, n_e \, \frac{3}{2} k_B (T_e - T_g). \]

Definition at line 56 of file CollisionModel.h.

Constructor & Destructor Documentation

◆ CollisionModel() [1/2]

rizer::CollisionModel::CollisionModel ( )

default

◆ CollisionModel() [2/2]

rizer::CollisionModel::CollisionModel	(	const std::vector< SpeciesSpec > &	specs,
		double	Te_min,
		double	Te_max,
		std::size_t	Te_n,
		bool	spitzer_correction = true )

Build per-species Qbar(Te) tables on a log-spaced Te grid [Te_min, Te_max].

Parameters

specs	Per-species collision specs, in species-index order
Te_min	Lower bound of the precomputed Qbar(Te) grid [K]
Te_max	Upper bound of the precomputed Qbar(Te) grid [K]
Te_n	Number of log-spaced points in the Qbar(Te) grid
spitzer_correction	true: apply the Spitzer e-e correction (II-13.18); false: Lorentz gas only

Definition at line 120 of file CollisionModel.cpp.

Member Function Documentation

◆ conductivity()

double rizer::CollisionModel::conductivity	(	double	Te,
		double	n_e,
		const double *	n_k,
		std::size_t	nsp ) const

Conductivity only [S/m].

Parameters

Te	Electron temperature [K]
n_e	Electron number density [m^-3]
n_k	Per-species number density array, length nsp [m^-3]
nsp	Number of species / length of n_k

Definition at line 242 of file CollisionModel.cpp.

◆ electronElectronCollisionFrequency()

double rizer::CollisionModel::electronElectronCollisionFrequency	(	double	n_e,
		double	Te )

static

Electron-electron collision frequency \(\nu_{ee}\) [1/s] (Mitchner II-8.11e with Z=1), the closed-form ingredient of the first Maxwellian-distribution condition term \(C_1 = \nu_{ee}/m_e\) (Mitchner VIII-3.8).

Depends only on n_e, Te (no per-species composition), so this is a static function rather than an instance method.

Parameters

n_e	Electron number density [m^-3]
Te	Electron temperature [K]

Definition at line 250 of file CollisionModel.cpp.

◆ empty()

bool rizer::CollisionModel::empty ( ) const

inline

Definition at line 80 of file CollisionModel.h.

◆ evaluate()

void rizer::CollisionModel::evaluate	(	double	Te,
		double	n_e,
		const double *	n_k,
		std::size_t	nsp,
		double &	sigma,
		double &	nu_E,
		double &	cond_maxwell_2 ) const

Composition-resolved electron transport.

Parameters

	Te	Electron temperature [K]
	n_e	Electron number density [m^-3]
	n_k	Per-species number density [m^-3] (length nsp)
	nsp	Number of species (length of n_k)
[out]	sigma	Electrical conductivity [S/m]
[out]	nu_E	Elastic energy-exchange frequency [1/s]
[out]	cond_maxwell_2	\(\sum_h \bar\nu_{eh}/m_h\) [1/kg/s], the second Maxwellian-distribution condition term (Mitchner VIII-3.8); see PlasmaExtension.conditions_for_maxwellian_distribution.

Definition at line 172 of file CollisionModel.cpp.

◆ meanCrossSection()

double rizer::CollisionModel::meanCrossSection	(	const std::vector< double > &	energy_J,
		const std::vector< double > &	sigma_m2,
		double	Te,
		double	x_max = 20.0,
		int	N = 1000 )

static

The Maxwellian momentum-transfer kernel Qbar(Te) [m^2] (single source of truth; also exposed to Python for validation).

Q interpolated from (energy_J, sigma_m2), zero outside the tabulated range.

Parameters

energy_J	Tabulated cross-section energy abscissa [J]
sigma_m2	Tabulated momentum-transfer cross section [m^2]
Te	Electron temperature at which to evaluate Qbar [K]
x_max	Upper limit of the reduced-energy integration variable \(x = E / (k_B T_e)\)
N	Number of trapezoid points spanning [0, x_max]

Definition at line 74 of file CollisionModel.cpp.

◆ meanCrossSectionTable()

std::vector< double > rizer::CollisionModel::meanCrossSectionTable	(	const std::vector< double > &	energy_J,
		const std::vector< double > &	sigma_m2,
		const std::vector< double > &	Te,
		double	x_max = 20.0,
		int	N = 1000 )

static

Tabulated variant of meanCrossSection, evaluated at each Te in the input vector.

Parameters

energy_J	Tabulated cross-section energy abscissa [J]
sigma_m2	Tabulated momentum-transfer cross section [m^2]
Te	Electron temperatures at which to evaluate Qbar, one per output entry [K]
x_max	Upper limit of the reduced-energy integration variable \(x = E / (k_B T_e)\)
N	Number of trapezoid points spanning [0, x_max]

Definition at line 109 of file CollisionModel.cpp.

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

/home/runner/work/rizer/rizer/rizer/cantera_ext/src/CollisionModel.h
/home/runner/work/rizer/rizer/rizer/cantera_ext/src/CollisionModel.cpp

Classes

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ CollisionModel() [1/2]

◆ CollisionModel() [2/2]

Member Function Documentation

◆ conductivity()

◆ electronElectronCollisionFrequency()

◆ empty()

◆ evaluate()

◆ meanCrossSection()

◆ meanCrossSectionTable()