Implements the weak screening model based on the Debye-Hückel approximation. More...
#include <screening_weak.h>
Public Member Functions | |
| std::vector< double > | calculateScreeningFactors (const reaction::ReactionSet &reactions, const std::vector< fourdst::atomic::Species > &species, const std::vector< double > &Y, double T9, double rho) const override |
| Calculates weak screening factors for a set of reactions. | |
| std::vector< CppAD::AD< double > > | calculateScreeningFactors (const reaction::ReactionSet &reactions, const std::vector< fourdst::atomic::Species > &species, const std::vector< CppAD::AD< double > > &Y, CppAD::AD< double > T9, CppAD::AD< double > rho) const override |
| Calculates weak screening factors using CppAD types. | |
 Public Member Functions inherited from gridfire::screening::ScreeningModel | |
| virtual | ~ScreeningModel ()=default |
| Virtual destructor. | |
Private Member Functions | |
| template<IsArithmeticOrAD T> | |
| std::vector< T > | calculateFactors_impl (const reaction::ReactionSet &reactions, const std::vector< fourdst::atomic::Species > &species, const std::vector< T > &Y, T T9, T rho) const |
| Template implementation for calculating weak screening factors. | |
Private Attributes | |
| quill::Logger * | m_logger = fourdst::logging::LogManager::getInstance().getLogger("log") |
| Logger instance for recording trace and debug information. | |
Additional Inherited Members | |
| Public Types inherited from gridfire::screening::ScreeningModel | |
| using | ADDouble = CppAD::AD< double > |
| Alias for CppAD Automatic Differentiation type for double precision. | |
Detailed Description
Implements the weak screening model based on the Debye-Hückel approximation.
This class provides a concrete implementation of the ScreeningModel interface for the weak screening regime, following the formulation of Salpeter (1954). This approach applies the Debye-Hückel theory to model the electrostatic shielding of nuclei in a plasma. It is applicable to non-degenerate, non-relativistic plasmas where thermal energy dominates the electrostatic potential energy.
Member Function Documentation
◆ calculateFactors_impl()
|
private |
Template implementation for calculating weak screening factors.
Core implementation of the weak screening calculation (Debye-Hückel model).
This private helper function contains the core logic for calculating weak screening factors. It is templated to handle both double and CppAD::AD<double> numeric types, avoiding code duplication.
- Template Parameters
-
T The numeric type, either doubleorCppAD::AD<double>.
- Parameters
-
reactions The set of reactions. species A vector of all species in the network. Y The composition object with current molar abundances. T9 The temperature in 10^9 K. rho The density in g/cm^3.
- Returns
- A vector of screening factors of type
T.
This function calculates the screening factor exp(H_12) for each reaction, based on the Debye-Hückel approximation as formulated by Salpeter (1954).
- Template Parameters
-
T The numeric type ( doubleorCppAD::AD<double>).
- Parameters
-
reactions The set of reactions to be screened. species The list of all species in the network. Y The composition object providing current molar abundances. T9 The temperature in 10^9 K. rho The density in g/cm^3.
- Returns
- A vector of screening factors, one for each reaction.
Algorithm
- Low-Temperature Cutoff: If T9 is below a small threshold (1e-9), screening is effectively turned off to prevent numerical instability.
- Zeta Factor (ζ): A composition-dependent term is calculated:
ζ = ∑(Z_i² + Z_i) * Y_i, where Z_i is the charge and Y_i is the molar abundance of species i. - Prefactor: A key prefactor is computed:
prefactor = 0.188 * sqrt(ρ / T₇³) * sqrt(ζ), where T₇ is the temperature in units of 10^7 K. - Screening Term (H_12): For each reaction, the term H_12 is calculated:
- For a two-body reaction (reactants Z₁ and Z₂):
H_12 = prefactor * Z₁ * Z₂. - For the triple-alpha reaction (3 * He4):
H_12 = 3 * (prefactor * Z_α * Z_α). - For one-body reactions (decays), H_12 is 0, so the factor is 1.
- For a two-body reaction (reactants Z₁ and Z₂):
- Capping: The value of H_12 is capped at 2.0 to prevent excessively large and unphysical screening factors (exp(2) ≈ 7.4).
- Final Factor: The screening factor for the reaction is
exp(H_12).
◆ calculateScreeningFactors() [1/2]
|
overridevirtual |
Calculates weak screening factors using CppAD types.
This is the automatic differentiation-compatible version of the method. It allows the derivatives of the screening factors to be computed with respect to plasma conditions.
- Parameters
-
reactions The set of logical reactions in the network. species A vector of all atomic species involved in the network. Y The composition object giving the current molar abundances. T9 The temperature as an AD type. rho The plasma density as an AD type.
- Returns
- A vector of screening factors as AD types.
Implements gridfire::screening::ScreeningModel.
◆ calculateScreeningFactors() [2/2]
|
overridevirtual |
Calculates weak screening factors for a set of reactions.
This method computes the screening enhancement factor for each reaction based on the Salpeter (1954) formula.
- Parameters
-
reactions The set of logical reactions in the network. species A vector of all atomic species involved in the network. Y The composition object giving the current molar abundances. T9 The temperature in units of 10^9 K. rho The plasma density in g/cm^3.
- Returns
- A vector of screening factors (dimensionless), one for each reaction.
Usage
Implements gridfire::screening::ScreeningModel.
Member Data Documentation
◆ m_logger
|
private |
Logger instance for recording trace and debug information.
The documentation for this class was generated from the following files:
- src/include/gridfire/screening/screening_weak.h
- src/lib/screening/screening_weak.cpp
