Analysis of edge profile inference results

The pedinf.analysis module provides tools for analysis and post-processing of inferred electron temperature and density profiles.

Inferring the separatrix given a temperature

If the separatrix temperature has been estimated, for example via power-balance analysis, the separatrix_given_temperature function can be used to infer the separatrix radius, density and pressure.

pedinf.analysis.separatrix_given_temperature(ne_profile_samples: ndarray, te_profile_samples: ndarray, model: ProfileModel, te_sep: float = None, te_sep_error: float = None, te_sep_samples: ndarray = None) → dict

Given an estimated separatrix electron temperature (and optionally an associated uncertainty) this function estimates the separatrix major radius, electron density and electron pressure.

Parameters

ne_profile_samples – A set of sampled parameters of a profile model from pedinf.models representing possible electron density edge profiles. The samples should be given as a numpy.ndarray of shape (n, m) where n is the number of samples and m is the number of model parameters.
te_profile_samples – A set of sampled parameters of a profile model from pedinf.models representing possible electron temperature edge profiles. The samples should be given as a numpy.ndarray of shape (n, m) where n is the number of samples and m is the number of model parameters.
model – An instance of one of the model classes from pedinf.models.
te_sep – The electron temperature value for which the corresponding major radius, electron density and electron pressure will be estimated.
te_sep_error – The Gaussian uncertainty on the given value of te_sep.
te_sep_samples – Samples of the separatrix temperature value. This allows non-gaussian uncertainties on the separatrix temperature to included in the analysis. Specifying te_sep_samples overrides any values given to the te_sep or te_sep_error arguments, which will be ignored. The number of separatrix temperature samples given must be equal to the number of profile samples.

Returns

A dictionary containing the mean and standard-deviation for the separatrix major radius, separatrix electron density, and separatrix electron pressure. The keys are R_mean, ne_mean, pe_mean for the means, and R_std, ne_std, pe_std for the standard-deviations.

Inferring the separatrix given a scaling

Given a scaling which predicts the separatrix electron temperature as a function of the separatrix electron density (e.g. from modelling), the separatrix_given_scaling function can be used to infer the separatrix radius, temperature, density and pressure.

pedinf.analysis.separatrix_given_scaling(ne_profile_samples: ndarray, te_profile_samples: ndarray, model: ProfileModel, separatrix_scaling: callable, radius_limits=(1.2, 1.6))

Given a scaling function which specifies the separatrix temperature as a function of the separatrix density, estimate the mean and standard-deviation of the separatrix radius and separatrix electron density, temperature and pressure.

Parameters

ne_profile_samples – A set of sampled parameters of a profile model from pedinf.models representing possible electron density edge profiles. The samples should be given as a numpy.ndarray of shape (n, m) where n is the number of samples and m is the number of model parameters.
te_profile_samples – A set of sampled parameters of a profile model from pedinf.models representing possible electron temperature edge profiles. The samples should be given as a numpy.ndarray of shape (n, m) where n is the number of samples and m is the number of model parameters.
model – An instance of one of the model classes from pedinf.models.
separatrix_scaling (callable) – A callable which maps a given separatrix density to a corresponding separatrix temperature. It must take an array of electron density values as its only argument.
radius_limits – A tuple specifying the range of radius values used to search for the separatrix position in the form (lower_limit, upper_limit).

Returns

A dictionary containing the mean and standard-deviation for the separatrix major radius, and separatrix electron temperature, density and pressure. The keys are R_mean, te_mean, ne_mean, pe_mean for the means, and R_std, te_std, ne_std, pe_std for the standard-deviations.

Inferring the pressure profile

The pressure_profile_and_gradient function generates a sample of pressure and pressure gradient profiles and associated means and highest-density intervals.

pedinf.analysis.pressure_profile_and_gradient(radius: ndarray, ne_profile_samples: ndarray, te_profile_samples: ndarray, model: ProfileModel) → Tuple[PlasmaProfile, PlasmaProfile]

Calculates the electron pressure and pressure gradient profiles at specified major radius positions, given samples of the edge electron temperature and density profiles.

It is assumed that the electron temperatures and densities have units of \(eV\) and \(m^{-3}\) respectively, and the returned electron pressure will have units of \(N / m^2\).

Parameters

radius – Major radius values at which to evaluate the pressure profiles as a numpy.ndarray.
ne_profile_samples – A set of sampled parameters of a profile model from pedinf.models representing possible electron density edge profiles. The samples should be given as a numpy.ndarray of shape (n, m) where n is the number of samples and m is the number of model parameters.
te_profile_samples – A set of sampled parameters of a profile model from pedinf.models representing possible electron temperature edge profiles. The samples should be given as a numpy.ndarray of shape (n, m) where n is the number of samples and m is the number of model parameters.
model – An instance of one of the model classes from pedinf.models.

Returns

A tuple of two PlasmaProfile objects, the first corresponding to the electron pressure profile, and the second to the electron pressure gradient profile.

Estimating pressure profile parameters

The pressure_parameters function estimates the parameters of the electron pressure for a given edge profile model and corresponding set of temperature and density parameters.

pedinf.analysis.pressure_parameters(ne_parameters: ndarray, te_parameters: ndarray, model: ProfileModel, return_diagnostics=False)

Approximates the electron pressure profile parameters by re-fitting the profile model to the predicted pressure profile obtained from the product of the predicted temperature and density profiles.

Parameters

ne_parameters – The density parameter vector for the given profile model.
te_parameters – The temperature parameter vector for the given profile model.
model – An instance of either the mtanh` or ``lpm model classes from pedinf.models.
return_diagnostics – If set as True, a dictionary containing diagnostic information about the fit to the pressure will be returned alongside the fit parameters.

Returns

The fitted pressure profile parameters.

The PlasmProfile class

PlasmaProfile is a data class which packages all the data associated with a given estimate of a plasma profile.

class pedinf.analysis.PlasmaProfile(axis: ndarray, profile_samples: ndarray, axis_label: str = None, profile_label: str = None, axis_units: str = None, profile_units: str = None)

Class for representing the estimate of a plasma profile derived from samples of possible profiles produced by uncertainty quantification.

Parameters

axis – The axis values at which the profile samples were evaluated as a 1D numpy.ndarray.
profile_samples – The profile samples as a 2D numpy.ndarray of shape (axis.size, n_samples).
axis_label – A description of the axis on which the profiles have been evaluated, e.g. ‘major radius’.
profile_label – A description of the quantity represented by the profile, e.g. ‘electron temperature’.
axis_units – The units of the axis values, e.g. ‘m’ for metres.
profile_units – The units of the profile values, e.g. ‘eV’ for electron temperature.

classmethod from_parameters(axis: ndarray, parameter_samples: ndarray, model: ProfileModel, gradient: bool = False, axis_label: str = None, profile_label: str = None, axis_units: str = None, profile_units: str = None)

Class for representing the estimate of a plasma profile derived from samples of possible profiles produced by uncertainty quantification.

Parameters

axis – The axis values at which the profile samples are to be evaluated as a 1D numpy.ndarray.
parameter_samples – The model parameter samples as a 2D numpy.ndarray of shape (model.n_parameters, n_samples).
model – An instance of a profile model class from the pedinf.models module.
gradient – If given True the profile samples will be the gradient of the model prediction instead of the prediction itself. Default is False.
axis_label – A description of the axis on which the profiles have been evaluated, e.g. ‘major radius’.
profile_label – A description of the quantity represented by the profile, e.g. ‘electron temperature’.
axis_units – The units of the axis values, e.g. ‘m’ for metres.
profile_units – The units of the profile values, e.g. ‘eV’ for electron temperature.

plot(axis=None, color: str = None)

Plot the profile.

Parameters

axis – A matplotlib axis object on which the profile will be plotted.
color – A valid matplotlib color string which will be used to plot the profile.