linescaling.h File Reference

Constains various line scaling functions. More...

#include "absorption.h"
#include "arts_conversions.h"

Go to the source code of this file.

Functions
Numeric	single_partition_function (const Numeric &T, const Species::IsotopeRecord &ir)
	Computes the partition function at one temperature.
Numeric	dsingle_partition_function_dT (const Numeric &T, const Species::IsotopeRecord &ir)
	Computes the partition function temperature derivative.
Numeric	stimulated_emission (Numeric T, Numeric F0)
	Computes exp(-hf/kT)
Numeric	dstimulated_emissiondT (Numeric T, Numeric F0)
	Computes temperature derivative of exp(-hf/kT)
Numeric	dstimulated_emissiondF0 (Numeric T, Numeric F0)
	Computes frequency derivative of exp(-hf/kT)
Numeric	stimulated_relative_emission (const Numeric F0, const Numeric T0, const Numeric T) noexcept
	Computes.
Numeric	dstimulated_relative_emission_dT (const Numeric F0, const Numeric T0, const Numeric T) noexcept
	Computes.
Numeric	dstimulated_relative_emission_dF0 (const Numeric F0, const Numeric T0, const Numeric T) noexcept
	Computes.
Numeric	stimulated_relative_emission (const Numeric &gamma, const Numeric &gamma_ref)
	Computes (1 - gamma) / (1 - gamma_ref)
Numeric	dstimulated_relative_emission_dT (const Numeric &gamma, const Numeric &gamma_ref, const Numeric &F0, const Numeric &T)
	Computes temperature derivative of (1 - gamma) / (1 - gamma_ref)
Numeric	dstimulated_relative_emission_dF0 (const Numeric &gamma, const Numeric &gamma_ref, const Numeric &T, const Numeric &T0)
	Computes frequency derivative of (1 - gamma) / (1 - gamma_ref)
Numeric	boltzman_ratio (const Numeric &T, const Numeric &T0, const Numeric &E0)
	Computes exp(E0/c (T - T0) / (T * T0))
Numeric	dboltzman_ratio_dT (const Numeric &boltzmann_ratio, const Numeric &T, const Numeric &E0)
	Computes temperature derivatives exp(E0/k (T - T0) / (T * T0))
constexpr Numeric	dboltzman_ratio_dT_div_boltzmann_ratio (Numeric T, Numeric E0)
	Computes temperature derivatives exp(E0/k (T - T0) / (T * T0)) / exp(E0/c (T - T0) / (T * T0))
Numeric	boltzman_factor (Numeric T, Numeric E0)
	Computes exp(- E0/kT)
Numeric	dboltzman_factordT (Numeric T, Numeric E0)
	Computes temperature derivatives exp(- E0/kT)
Numeric	dboltzman_factordE0 (Numeric T, Numeric E0)
	Computes lower state energy derivatives exp(- E0/kT)
Numeric	absorption_nlte_ratio (const Numeric &gamma, const Numeric &r_upp=1.0, const Numeric &r_low=1.0) noexcept
	Computes (r_low - r_upp * gamma) / (1 - gamma)
Numeric	dabsorption_nlte_rate_dT (const Numeric &gamma, const Numeric &T, const Numeric &F0, const Numeric &El, const Numeric &Eu, const Numeric &r_upp=1.0, const Numeric &r_low=1.0)
	Computes temperature derivatives of (r_low - r_upp * gamma) / (1 - gamma)
Numeric	dabsorption_nlte_rate_dF0 (const Numeric &gamma, const Numeric &T, const Numeric &r_upp=1.0, const Numeric &r_low=1.0)
	Computes frequency derivative of (r_low - r_upp * gamma) / (1 - gamma)
Numeric	dabsorption_nlte_rate_dTl (const Numeric &gamma, const Numeric &T, const Numeric &Tl, const Numeric &El, const Numeric &r_low=1.0)
	Computes lower state temperature derivative of (r_low - r_upp * gamma) / (1 - gamma)
Numeric	dabsorption_nlte_rate_dTu (const Numeric &gamma, const Numeric &T, const Numeric &Tu, const Numeric &Eu, const Numeric &r_upp=1.0)
	Computes upper state temperature derivative of (r_low - r_upp * gamma) / (1 - gamma)

Detailed Description

Constains various line scaling functions.

Author

Richard Larsson

Date

2015-06-25

Headers for line scaling functions

Helps to solve line scaling and derivatives for lbl calculations

Definition in file linescaling.h.

Function Documentation

absorption_nlte_ratio()

Numeric absorption_nlte_ratio ( const Numeric &  gamma, const Numeric &  r_upp = 1.0, const Numeric &  r_low = 1.0  )

noexcept

Computes (r_low - r_upp * gamma) / (1 - gamma)

Parameters

[in]	gamma	Stimulated emission at temperature
[in]	r_upp	Relative ratio NLTE/LTE in upper ratio
[in]	r_low	Relative ratio NLTE/LTE in lower ratio

Returns

(r_low - r_upp * gamma) / (1 - gamma)

Definition at line 110 of file linescaling.cc.

boltzman_factor()

Numeric boltzman_factor	(	Numeric	T,
		Numeric	E0
	)

Computes exp(- E0/kT)

Parameters

[in]	T	Temperature
[in]	E0	Lower state energy

Returns

exp(- E0/kT)

Definition at line 90 of file linescaling.cc.

References Constant::k.

Referenced by lm_hitran_2017::convtp(), Absorption::Lines::F_mean(), lm_hitran_2017::hitran_lm_eigenvalue_approximation(), and Absorption::LineMixing::PopulationAndDipole::PopulationAndDipole().

boltzman_ratio()

Numeric boltzman_ratio	(	const Numeric &	T,
		const Numeric &	T0,
		const Numeric &	E0
	)

Computes exp(E0/c (T - T0) / (T * T0))

Parameters

[in]	T	Temperature
[in]	T0	Reference temperature
[in]	E0	Lower state energy

Returns

exp(E0/c (T - T0) / (T * T0))

Definition at line 75 of file linescaling.cc.

References c, and Constant::k.

Referenced by lm_hitran_2017::convtp(), Absorption::Lines::F_mean(), lm_hitran_2017::hitran_lm_eigenvalue_approximation(), and Absorption::LineMixing::PopulationAndDipole::PopulationAndDipole().

dabsorption_nlte_rate_dF0()

Numeric dabsorption_nlte_rate_dF0	(	const Numeric &	gamma,
		const Numeric &	T,
		const Numeric &	r_upp = 1.0,
		const Numeric &	r_low = 1.0
	)

Computes frequency derivative of (r_low - r_upp * gamma) / (1 - gamma)

Parameters

[in]	gamma	Stimulated emission at temperature
[in]	T	Temperature
[in]	r_upp	Relative ratio NLTE/LTE in upper ratio
[in]	r_low	Relative ratio NLTE/LTE in lower ratio

Returns

d[(r_low - r_upp * gamma) / (1 - gamma)] / dF0

Definition at line 138 of file linescaling.cc.

References c, Constant::h, Constant::k, and Math::pow2().

dabsorption_nlte_rate_dT()

Numeric dabsorption_nlte_rate_dT	(	const Numeric &	gamma,
		const Numeric &	T,
		const Numeric &	F0,
		const Numeric &	El,
		const Numeric &	Eu,
		const Numeric &	r_upp = 1.0,
		const Numeric &	r_low = 1.0
	)

Computes temperature derivatives of (r_low - r_upp * gamma) / (1 - gamma)

Parameters

[in]	gamma	Stimulated emission at temperature
[in]	T	Temperature
[in]	F0	Central frequency
[in]	El	Lower state energy
[in]	Eu	Upper state energy
[in]	r_upp	Relative ratio NLTE/LTE in upper ratio
[in]	r_low	Relative ratio NLTE/LTE in lower ratio

Returns

d[(r_low - r_upp * gamma) / (1 - gamma)] / dT

Definition at line 116 of file linescaling.cc.

References ARTS_USER_ERROR_IF, c, Constant::h, and Constant::k.

dabsorption_nlte_rate_dTl()

Numeric dabsorption_nlte_rate_dTl	(	const Numeric &	gamma,
		const Numeric &	T,
		const Numeric &	Tl,
		const Numeric &	El,
		const Numeric &	r_low = 1.0
	)

Computes lower state temperature derivative of (r_low - r_upp * gamma) / (1 - gamma)

Parameters

[in]	gamma	Stimulated emission at temperature
[in]	T	Temperature
[in]	Tl	Temperature of lower level
[in]	El	Lower state energy
[in]	r_low	Relative ratio NLTE/LTE in lower ratio

Returns

d[(r_low - r_upp * gamma) / (1 - gamma)] / dTl

Definition at line 147 of file linescaling.cc.

References Constant::k.

dabsorption_nlte_rate_dTu()

Numeric dabsorption_nlte_rate_dTu	(	const Numeric &	gamma,
		const Numeric &	T,
		const Numeric &	Tu,
		const Numeric &	Eu,
		const Numeric &	r_upp = 1.0
	)

Computes upper state temperature derivative of (r_low - r_upp * gamma) / (1 - gamma)

Parameters

[in]	gamma	Stimulated emission at temperature
[in]	T	Temperature
[in]	Tu	Temperature of lower level
[in]	Eu	Lower state energy
[in]	r_upp	Relative ratio NLTE/LTE in upper ratio

Returns

d[(r_low - r_upp * gamma) / (1 - gamma)] / dTu

Definition at line 158 of file linescaling.cc.

References Constant::k.

dboltzman_factordE0()

Numeric dboltzman_factordE0	(	Numeric	T,
		Numeric	E0
	)

Computes lower state energy derivatives exp(- E0/kT)

Parameters

[in]	T	Temperature
[in]	E0	Lower state energy

Returns

dexp(- E0/kT) / dE0

Definition at line 104 of file linescaling.cc.

dboltzman_factordT()

Numeric dboltzman_factordT	(	Numeric	T,
		Numeric	E0
	)

Computes temperature derivatives exp(- E0/kT)

Parameters

[in]	T	Temperature
[in]	E0	Lower state energy

Returns

dexp(- E0/kT) / dT

Definition at line 96 of file linescaling.cc.

dboltzman_ratio_dT()

Numeric dboltzman_ratio_dT	(	const Numeric &	boltzmann_ratio,
		const Numeric &	T,
		const Numeric &	E0
	)

Computes temperature derivatives exp(E0/k (T - T0) / (T * T0))

Parameters

[in]	boltzmann_ratio	Output of boltzmann_ratio(...)
[in]	T	Temperature
[in]	E0	Lower state energy

Returns

exp(E0/k (T - T0) / (T * T0))

Definition at line 81 of file linescaling.cc.

References c, and Constant::k.

dboltzman_ratio_dT_div_boltzmann_ratio()

constexpr Numeric dboltzman_ratio_dT_div_boltzmann_ratio ( Numeric  T, Numeric  E0  )

constexpr

Computes temperature derivatives exp(E0/k (T - T0) / (T * T0)) / exp(E0/c (T - T0) / (T * T0))

Parameters

[in]	T	Temperature
[in]	E0	Lower state energy

Returns

E0 k / T^2

Definition at line 173 of file linescaling.h.

References Constant::k.

dsingle_partition_function_dT()

Numeric dsingle_partition_function_dT	(	const Numeric &	T,
		const Species::IsotopeRecord &	ir
	)

Computes the partition function temperature derivative.

Parameters

[in]	T	Temperature
[in]	partition_type	Switch for partition type of line
[in]	partition_data	Partition data of line

Returns

partition function derivative wrt temperature

Definition at line 9 of file linescaling.cc.

References PartitionFunctions::dQdT().

Referenced by LineShape::compute().

dstimulated_emissiondF0()

Numeric dstimulated_emissiondF0	(	Numeric	T,
		Numeric	F0
	)

Computes frequency derivative of exp(-hf/kT)

Parameters

[in]	T	Temperatures
[in]	F0	Frequency

Returns

dexp(-hf/kT) / dF0

Definition at line 27 of file linescaling.cc.

dstimulated_emissiondT()

Numeric dstimulated_emissiondT	(	Numeric	T,
		Numeric	F0
	)

Computes temperature derivative of exp(-hf/kT)

Parameters

[in]	T	Temperatures
[in]	F0	Frequency

Returns

dexp(-hf/kT) / dT

Definition at line 20 of file linescaling.cc.

dstimulated_relative_emission_dF0() [1/2]

Numeric dstimulated_relative_emission_dF0	(	const Numeric &	gamma,
		const Numeric &	gamma_ref,
		const Numeric &	T,
		const Numeric &	T0
	)

Computes frequency derivative of (1 - gamma) / (1 - gamma_ref)

Parameters

[in]	gamma	Stimulated emission at temperature
[in]	gamma_ref	Stimulated emission at reference temperature
[in]	T	Temperature
[in]	T0	Reference temperature

Returns

d[(1 - gamma) / (1 - gamma_ref)] / dF0

Definition at line 62 of file linescaling.cc.

References c, Constant::h, and Constant::k.

dstimulated_relative_emission_dF0() [2/2]

Numeric dstimulated_relative_emission_dF0 ( const Numeric  F0, const Numeric  T0, const Numeric  T  )

noexcept

Computes.

\[ \frac{h\left(T\left[1 -e^{h f_0/k T}\right] e^{h f_0 / k T_0} - T_0 \left[1 -e^{h f_0/k T_0}\right] e^{h f_0 / k T} \right)}{kTT_0 \left(1 -e^{h f_0/k T_0}\right)^2} \]

using std::expm1 for increased low number accuracies

Parameters

[in]	gamma	Stimulated emission at temperature
[in]	gamma_ref	Stimulated emission at reference temperature

Returns

\( \frac{h\left(T\left[1 -e^{h f_0/k T}\right] e^{h f_0 / k T_0} - T_0 \left[1 -e^{h f_0/k T_0}\right] e^{h f_0 / k T} \right)}{kTT_0 \left(1 -e^{h f_0/k T_0}\right)^2} \)

Definition at line 42 of file linescaling.cc.

References Constant::h, Conversion::hz2joule(), Constant::k, Conversion::kelvin2joule(), and Math::pow2().

dstimulated_relative_emission_dT() [1/2]

Numeric dstimulated_relative_emission_dT	(	const Numeric &	gamma,
		const Numeric &	gamma_ref,
		const Numeric &	F0,
		const Numeric &	T
	)

Computes temperature derivative of (1 - gamma) / (1 - gamma_ref)

Parameters

[in]	gamma	Stimulated emission at temperature
[in]	gamma_ref	Stimulated emission at reference temperature
[in]	F0	Frequency
[in]	T	Temperature

Returns

d[(1 - gamma) / (1 - gamma_ref)] / dT

Definition at line 53 of file linescaling.cc.

References c, Constant::h, and Constant::k.

dstimulated_relative_emission_dT() [2/2]

Numeric dstimulated_relative_emission_dT ( const Numeric  F0, const Numeric  T0, const Numeric  T  )

noexcept

Computes.

\[ \frac{1}{T} \frac{h f_0}{k T} \frac{e^{h f_0/k T}}{1 - e^{h f_0 / k T_0}} \]

using std::expm1 for increased low number accuracies

Parameters

[in]	gamma	Stimulated emission at temperature
[in]	gamma_ref	Stimulated emission at reference temperature

Returns

\( \frac{1}{T} \frac{h f_0}{k T} \frac{e^{h f_0/k T}}{1 - e^{h f_0 / k T_0}} \)

Definition at line 37 of file linescaling.cc.

References Conversion::hz2joule(), and Conversion::kelvin2joule().

single_partition_function()

Numeric single_partition_function	(	const Numeric &	T,
		const Species::IsotopeRecord &	ir
	)

Computes the partition function at one temperature.

Parameters

[in]	T	Temperature
[in]	partition_type	Switch for partition type of line
[in]	partition_data	Partition data of line

Returns

partition function

Definition at line 4 of file linescaling.cc.

References PartitionFunctions::Q().

Referenced by LineShape::compute(), lm_hitran_2017::convtp(), Absorption::LineMixing::ecs_eigenvalue_approximation(), Absorption::Lines::F_mean(), lm_hitran_2017::hitran_lm_eigenvalue_approximation(), and Absorption::LineMixing::PopulationAndDipole::PopulationAndDipole().

stimulated_emission()

Numeric stimulated_emission	(	Numeric	T,
		Numeric	F0
	)

Computes exp(-hf/kT)

Parameters

[in]	T	Temperatures
[in]	F0	Frequency

Returns

exp(-hf/kT)

Definition at line 14 of file linescaling.cc.

stimulated_relative_emission() [1/2]

Numeric stimulated_relative_emission	(	const Numeric &	gamma,
		const Numeric &	gamma_ref
	)

Computes (1 - gamma) / (1 - gamma_ref)

Parameters

[in]	gamma	Stimulated emission at temperature
[in]	gamma_ref	Stimulated emission at reference temperature

Returns

(1 - gamma) / (1 - gamma_ref)

Definition at line 48 of file linescaling.cc.

stimulated_relative_emission() [2/2]

Numeric stimulated_relative_emission ( const Numeric  F0, const Numeric  T0, const Numeric  T  )

noexcept

Computes.

\[ \frac{1 - e^{h f_0/k T}}{1 - e^{h f_0 / k T_0}} \]

using std::expm1 for increased low number accuracies

Parameters

[in]	gamma	Stimulated emission at temperature
[in]	gamma_ref	Stimulated emission at reference temperature

Returns

\( \frac{1 - e^{h f_0/k T}}{1 - e^{h f_0 / k T_0}} \)

Definition at line 33 of file linescaling.cc.

References Conversion::hz2joule(), and Conversion::kelvin2joule().