vaughan module

Create the Vaughan model, to compute TEEY.

TEEY at non-normal incidence will not be taken into account into the fit (FIXME).

Todo

Make this more robust. Especially the _vaughan_func.

Model parameters

Parameter	Name	Unit	Initial	Description
\(E_0\)	E_0	\(\mathrm{eV}\)	\(12.5\)	Threshold energy. By default, locked to \(12.5\mathrm{\,eV}\). If unlocked, will be fitted to retrieve \(E_{\mathrm{c,\,1}}\).
\(E_\mathrm{max}\)	E_max	\(\mathrm{eV}\)	\(100.0\)	Energy at maximum TEEY.
\(\Delta E_{tr}\)	delta_E_transition	\(\mathrm{eV}\)	\(1.0\)	Energy over which we switch from \(\sigma_\mathrm{low}\) to actual Vaughan TEEY. Useful for smoothing the transition. Currently not implemented.
\(\sigma_\mathrm{low}\)	teey_low	\(\mathrm{1}\)	\(0.5\)	TEEY below \(E_0\).
\(\sigma_\mathrm{max}\)	teey_max	\(\mathrm{1}\)	\(1.5\)	Maximum TEEY, directly taken from the measurement.
\(k_s\)	k_s	\(\mathrm{1}\)	\(1.0\)	Roughness factor (\(\sigma_\mathrm{max}\)). Locked by default, but could be used for more precise fits.
\(k_{se}\)	k_se	\(\mathrm{1}\)	\(1.0\)	Roughness factor (\(E_\mathrm{max}\)). Locked by default, but could be used for more precise fits.
\(E_{\mathrm{c,\,1}}\)	E_c1	\(\mathrm{eV}\)	\(25.0\)	First crossover energy. Must be provided instead of \(E_0\) for SPARK3D Vaughan.

class VaughanParameters

Bases: TypedDict

E_0: Parameter

E_max: Parameter

delta_E_transition: Parameter

teey_low: Parameter

teey_max: Parameter

k_s: Parameter

k_se: Parameter

E_c1: Parameter

class Vaughan(implementation='original', parameters_values=None)

Bases: Model

Define the classic Vaughan model.

Instantiate the object.

Note

Parameter values set by implementation have priority over values given in parameters_values.

Parameters:

• implementation (Literal['original', 'CST', 'SPARK3D'], default: 'original') – Modifies certain presets to match different interpretations of the model by calling set_implementation(). These parameter modifications have precedence over the ones set in parameters_values.

• parameters_values (dict[str, Any] | None, default: None) – Contains name of parameters and associated value. If provided, will override the default values set in initial_parameters.

emission_data_types: list[Literal['Emission Yield', 'Emission Energy', 'Emission Angle']] = ['Emission Yield']

populations: list[Literal['SE', 'EBE', 'IBE', 'all']] = ['all']

considers_energy: bool = True

is_3d: bool = True

is_dielectrics_compatible: bool = False

model_config: ModelConfig = ModelConfig(emission_yield_files=('all',), emission_energy_files=(), emission_angle_files=())

initial_parameters: dict[str, dict[str, str | float | bool]] = {'E_0': {'description': 'Threshold energy. By default, locked to :math:`12.5\\mathrm{\\,eV}`. If unlocked, will be fitted to retrieve :math:`E_{\\mathrm{c,\\,1}}`.', 'is_locked': True, 'markdown': 'E_0', 'unit': 'eV', 'value': 12.5}, 'E_c1': {'description': 'First crossover energy. Must be provided instead of :math:`E_0` for SPARK3D Vaughan.', 'is_locked': False, 'markdown': 'E_{\\mathrm{c,\\,1}}', 'unit': 'eV', 'value': 25.0}, 'E_max': {'description': 'Energy at maximum TEEY.', 'lower_bound': 0.0, 'markdown': 'E_\\mathrm{max}', 'unit': 'eV', 'value': 100.0}, 'delta_E_transition': {'description': 'Energy over which we switch from :math:`\\sigma_\\mathrm{low}` to actual Vaughan TEEY. Useful for smoothing the transition. Currently not implemented.', 'is_locked': True, 'markdown': '\\Delta E_{tr}', 'unit': 'eV', 'value': 1.0}, 'k_s': {'description': 'Roughness factor (:math:`\\sigma_\\mathrm{max}`).  Locked by default, but could be used for more precise fits.', 'is_locked': True, 'lower_bound': 0.0, 'markdown': 'k_s', 'unit': '1', 'upper_bound': 2.0, 'value': 1.0}, 'k_se': {'description': 'Roughness factor (:math:`E_\\mathrm{max}`).  Locked by default, but could be used for more precise fits.', 'is_locked': True, 'lower_bound': 0.0, 'markdown': 'k_{se}', 'unit': '1', 'upper_bound': 2.0, 'value': 1.0}, 'teey_low': {'description': 'TEEY below :math:`E_0`.', 'is_locked': True, 'lower_bound': 0.0, 'markdown': '\\sigma_\\mathrm{low}', 'unit': '1', 'value': 0.5}, 'teey_max': {'description': 'Maximum TEEY, directly taken from the measurement.', 'lower_bound': 0.0, 'markdown': '\\sigma_\\mathrm{max}', 'unit': '1', 'value': 1.5}}

implementations: tuple[str, ...] | None = ('original', 'CST', 'SPARK3D')

parameters: VaughanParameters

A TypedDict specific to every model.Model. Keys are parameters names, values are Parameter.

_func: Callable

current_implementation: Literal['original', 'CST', 'SPARK3D']

set_implementation(implementation)

Update some parameters to reproduce a specific implementation.

Vaughan CST:

• \(\sigma_\mathrm{low}\) is set to 0.

Vaughan SPARK3D:

• \(\sigma_\mathrm{low}\) is set to 0.

• \(E_0\) is unlocked, so that it will be fitted to match \(E_{c,\,1}\).

• Below \(10\) \(\mathrm{eV}\), TEEY is 0.

Note

If the implementation is changed after the creation of the object, some parameters will be reset to their default value defined in initial_parameters, not to the values defined in the parameters_values argument of __init__ method.

Return type:

None

get_data(population, emission_data_type, energy, theta, *args, **kwargs)

Return desired data according to current model.

Will return a dataframe only if the TEEY is asked.

Todo

This method could be so much simpler and efficient.

Return type:

DataFrame | None

find_optimal_parameters(data_matrix, **kwargs)

Match with position of first crossover and maximum.

Return type:

None

find_e_0()

Find E_0 with error handling.

Return type:

None

_E_0_matching(*, E_c1)

Fit E_0 to retrieve E_c1 (SPARK3D)

Return type:

float

evaluate(data_matrix)

Evaluate the quality of the model using Fil criterions.

Fil criterions [FBHP16, FBHP20] are adapted to TEEY models.

Return type:

dict[str, float]

vaughan_func(ene, the, E_0, E_max, teey_max, teey_low, k_se, k_s, delta_E_transition, **parameters)

Compute the TEEY for incident energy E.

Return type:

float | ndarray[tuple[Any, ...], dtype[float64]]

vaughan_spark3d(ene, the, E_0, E_max, teey_max, teey_low, k_se, k_s, delta_E_transition, **parameters)

Compute TEEY as SPARK3D would.

This is a classic Vaughan, but TEEY is null for energies below E_0_SPARK3D=10.0. This parameter is different from the classic E_0 that appears in the expression of \(\xi\).

Return type:

float | ndarray[tuple[Any, ...], dtype[float64]]