Increase profile class verbosity

documentation/source/physics-models/profiles/plasma_density_profile.md

@@ -1,4 +1,4 @@
-# Density Profile | `NeProfile(Profile)`
+# Density Profile | `ElectronDensityProfile(Profile)`
 
 The density profile class is organised around a central runner function that is called each time the plasma is parameterised by the parent [`PlasmaProfile()`](./plasma_profiles.md) class. It is called by [`pedestal_parameterisation()`](plasma_profiles.md#pedestal_parameterisation) and [`parabolic parameterisation()`](./plasma_profiles.md#parabolic_parameterisation). The sequence of the runner function can be seen below along with explanation of the following calculations.
 
@@ -19,7 +19,7 @@ $$
 n_{\text{i0}} = \left(\frac{n_\text{i}}{n_\text{e}}\right)n_{\text{e0}}
 $$
 
-#### Electron core density of a pedestalised profile | `ncore()`
+#### Electron core density of a pedestalised profile | `calculate_pedestal_profile_on_axis_density()`
 
 This function calculates the core electron density for a pedestalsied profile (`i_plasma_pedestal == 1`). It takes in values of
 
@@ -110,6 +110,70 @@ $\blacksquare$
 
 4. The y profile is then calculated using [`calculate_profile_y()`](plasma_density_profile.md#calculate-density-at-each-radius-position-calculate_profile_y). This routine calculates the density at each normalised minor radius position $\rho$ for a HELIOS-type density pedestal profile[^1]
 
+
+---------------
+
+#### Electron core density of a parabolic profile | `calculate_parabolic_profile_on_axis_density()`
+
+###### Derivation
+
+We calculate the volume integrated profile and then divide by the volume of integration to get the volume average density $\langle n \rangle$. If we assume the plasma to be a torus of circular cross-section then we can use spherical coordinates. We can simplify the problem by representing the torus as a cylinder of height equal to the circumference of the torus equal to $2\pi R$ where $R$ is the major radius of the torus.
+
+The cylindrical volume element is given by:
+
+$$
+V = \int \int \int dV = \int^{2\pi R}_0 \int^{2\pi}_0 \int^a_0 r \ dr \ d\theta \ dz
+$$
+
+Inserting our density function in the form where $\rho$ is expanded as $\rho = r/a$ we get:
+
+$$
+\int^{2\pi R}_0 \int^{2\pi}_0 \int^a_0     r  \left(n_0(1-r^2/a^2)^{\alpha_n}\right) \ dr \ d\theta \ dz
+$$
+
+Since our density function is only a function of $r$, and the torus is symmetric around its center, the integration simplifies to integrating over $r$ and the $d\theta ,\ dz$ integrals are solved to give values for the full poloidal angle and cylindrical height and torus length, leading to:
+
+$$
+4\pi^2R \int^a_0     r  \left(n_0(1-r^2/a^2)^{\alpha_n}\right) \ dr  
+$$
+
+In the form of volume average density where the volume integrated density function has to be divided by the volume of the cylinder / torus we get:
+
+$$
+\langle n \rangle =  \frac{4\pi^2R \int^a_0     r  \left(n_0(1-r^2/a^2)^{\alpha_n}\right) \ dr}{2\pi^2Ra^2}  
+$$
+
+Simplify:
+
+$$
+\langle n \rangle =  \frac{2 \int^a_0     r  \left(n_0(1-r^2/a^2)^{\alpha_n}\right) \ dr}{a^2}  
+$$
+
+Integrate:
+
+$$
+\langle n \rangle =  \frac{2}{a^2} \frac{a^2n_0}{2(\alpha_n+1)}
+$$
+
+$$
+\therefore \langle n \rangle =   \frac{n_0}{\alpha_n+1}
+$$
+
+This is in agreement with the derivation from the ITER Physics Design 1989. [^iter_design_89]
+
+Since all parabolic profiles are of the same form this proof holds for the density and temperature.
+
+A similar derivation is found in normalised coordinates, $\rho$ if the line averaged integral is swept around the poloidal circumference then divided by the poloidal area.
+
+$$
+\langle n \rangle =  \frac{2\pi \int^1_0     \rho  \left(n_0(1-\rho^2)^{\alpha_n}\right) \ d\rho}{\pi\rho^2}  
+$$
+
+$\blacksquare$
+
+------
+
+
 ### Calculate density at each radius position | `calculate_profile_y()`
 
 A table of the input variables can be found below
@@ -176,3 +240,5 @@ and `ixc = 152` respectively
 
 
 [^1]: Jean, J. (2011). *HELIOS: A Zero-Dimensional Tool for Next Step and Reactor Studies*. Fusion Science and Technology, 59(2), 308–349. <https://doi.org/10.13182/FST11-A11650>
+
+[^iter_design_89]: N.A. Uckan and ITER Physics Group, 'ITER Physics Design Guidelines: 1989',

documentation/source/physics-models/profiles/plasma_profiles.md

@@ -4,7 +4,7 @@
 
 In `PROCESS` the density, temperature and current profiles of the plasma for electrons and ions can take two forms depending on the switch value for `i_plasma_pedestal`. Either without a [pedestal](http://fusionwiki.ciemat.es/wiki/Pedestal), `i_plasma_pedestal == 0` or with a pedestal `i_plasma_pedestal == 1`.  `i_plasma_pedestal == 0` is better suited for modelling L-mode plasmas, while `i_plasma_pedestal == 1` is better suited for modelling [H-mode](https://en.wikipedia.org/wiki/High-confinement_mode) plasmas.
 
-The files responsible for calculating and storing the profiles are `plasma_profiles.py` and `profiles.py`. A central plasma profile object is created from the [`PlasmaProfile`](plasma_profiles.md#plasma-profile-class-plasmaprofile) class that contains attributes for the plasma density and temperature. The density and temperature profiles are in themselves objects of the [`Profile`](./plasma_profiles_abstract_class.md) abstract base class. [`Profile`](./plasma_profiles_abstract_class.md), [`NeProfile`](plasma_density_profile.md) and [`TeProfile`](./plasma_temperature_profile.md) are all defined in `profiles.py`. [`PlasmaProfile`](plasma_profiles.md#plasma-profile-class-plasmaprofile) is exclusively in `plasma_profiles.py`
+The files responsible for calculating and storing the profiles are `plasma_profiles.py` and `profiles.py`. A central plasma profile object is created from the [`PlasmaProfile`](plasma_profiles.md#plasma-profile-class-plasmaprofile) class that contains attributes for the plasma density and temperature. The density and temperature profiles are in themselves objects of the [`Profile`](./plasma_profiles_abstract_class.md) abstract base class. [`Profile`](./plasma_profiles_abstract_class.md), [`ElectronDensityProfile`](plasma_density_profile.md) and [`ElectronTemperatureProfile`](./plasma_temperature_profile.md) are all defined in `profiles.py`. [`PlasmaProfile`](plasma_profiles.md#plasma-profile-class-plasmaprofile) is exclusively in `plasma_profiles.py`
 
 <figure markdown>
 ![UML of profiles](./uml_classes_PlasmaProfile.png){height="1000px"}
@@ -238,7 +238,7 @@ The graph below is for a standard pedestal profile. You can vary its attributes
 
 ## Plasma Profile Class | `PlasmaProfile`
 ### Initialization | `__init__()`
-The parent plasma profile class is `PlasmaProfile`. Initialization sets the profile class size and `neprofile` and `teprofile` to [`NeProfile`](plasma_density_profile.md) & [`TeProfile`](plasma_temperature_profile.md) objects from `profiles.py`
+The parent plasma profile class is `PlasmaProfile`. Initialization sets the profile class size and `neprofile` and `teprofile` to [`ElectronDensityProfile`](plasma_density_profile.md) & [`ElectronTemperatureProfile`](plasma_temperature_profile.md) objects from `profiles.py`
 
 ???+ Note
 
@@ -266,7 +266,7 @@ Depending on the value of `i_plasma_pedestal` different functions will be ran, t
 
 If pedestal profile values are set they are reset to have values that agree with the original form of the parabolic profiles. Such that $\rho_{\text{ped}} = 1$ and that pedestal and separatrix densities and temperatures are zero. This will then warn the user in the terminal.
 
-The density and temperature profile runner function [`TeProfile/NeProfile.run()`](plasma_density_profile.md#runner-function-run) is then called to re-calculate the profile and core values.
+The density and temperature profile runner function [`ElectronTemperatureProfile/ElectronDensityProfile.run()`](plasma_density_profile.md#runner-function-run) is then called to re-calculate the profile and core values.
 
 Ratio of density-weighted to volume-averaged temperature factor is calculated:
 
@@ -593,7 +593,7 @@ $$
 
 ##### `pedestal_parameterisation()`
 
-The density and temperature profile runner function [`TeProfile/NeProfile.run()`](plasma_density_profile.md#runner-function-run) is firstly called to re-calculate the profile and core values.
+The density and temperature profile runner function [`ElectronTemperatureProfile/ElectronDensityProfile.run()`](plasma_density_profile.md#runner-function-run) is firstly called to re-calculate the profile and core values.
 
  Perform integrations to calculate ratio of density-weighted to volume-averaged temperature, etc. Density-weighted temperature = $\frac{\int{nT \ dV}}{\int{n \ dV}}$,  which is approximately equal to the ratio $\frac{\int{\rho \ n(\rho) T(\rho) \ d\rho}}{\int{\rho \ n(\rho) \ d\rho}}$
 

documentation/source/physics-models/profiles/plasma_temperature_profile.md

@@ -1,4 +1,4 @@
-# Temperature Profile | `TeProfile(Profile)`
+# Temperature Profile | `ElectronTemperatureProfile(Profile)`
 
 The temperature profile class is organised around a central runner function that is called each time the plasma is parameterised by the parent [`PlasmaProfile()`](plasma_profiles.md#plasma-profile-class-plasmaprofile) class. It is called by [`pedestal_parameterisation()`](plasma_profiles.md#pedestal_parameterisation) and [`parabolic parameterisation()`](plasma_profiles.md#parabolic_parameterisation). The sequence of the runner function can be seen below along with explanation of the following calculations.
 
@@ -14,15 +14,15 @@ The temperature profile class is organised around a central runner function that
 
 The core electron temperature is calculated using the [`tcore`](plasma_temperature_profile.md#electron-core-density-of-a-pedestalised-profile--tcore) method.
 
-#### Electron core density of a pedestalised profile | `tcore()`
+#### Electron core temperature of a pedestalised profile | `calculate_pedestal_profile_on_axis_temperature()`
 
-This function calculates the core electron density for a pedestalsied profile in $\text{keV}$. The inclusion of a new $\beta_T$ exponent term allows a more accurate description of temperature profiles with a triangular shape or a strong gradient near the pedestal (characteristic of regimes with an [internal transport barrier](https://wiki.fusion.ciemat.es/wiki/Internal_Transport_Barrier)).
+This function calculates the core electron temperature for a pedestalsied profile in $\text{keV}$. The inclusion of a new $\beta_T$ exponent term allows a more accurate description of temperature profiles with a triangular shape or a strong gradient near the pedestal (characteristic of regimes with an [internal transport barrier](https://wiki.fusion.ciemat.es/wiki/Internal_Transport_Barrier)).
 
 A list of input parameters for calculating the core plasma temperature can be found below.
 
 | Profile parameter / Input               | Temperature   |
 |----------------------------------|-----------|
-| Pedestal radius (r/a)            | `radius_plasma_pedestal_density_norm`, $\rho_{\text{ped,T}}$ |
+| Pedestal radius (r/a)            | `radius_plasma_pedestal_temp_norm`, $\rho_{\text{ped,T}}$ |
 | Pedestal value                   | `nd_plasma_pedestal_electron`, $T_{\text{ped}}$ |
 | Separatrix value                 | `nd_plasma_separatrix_electron`, $T_{\text{sep}}$ |
 | Average temperature             | `nd_plasma_electrons_vol_avg`, $\langle T_\text{e} \rangle$ |
@@ -39,7 +39,7 @@ Where $\text{B}$ is the [Beta function](https://en.wikipedia.org/wiki/Beta_funct
 
 ##### Derivation
 
-We calculate the volume integrated profile and then divide by the volume of integration to get the volume average density $\langle T_{\text{e}} \rangle$. If we assume the plasma to be a torus of circular cross-section then we can use spherical coordinates. We can simplify the problem by representing the torus as a cylinder of height equal to the circumference of the torus equal to $2\pi R$ where $R$ is the major radius of the torus, and $a$ is the plasma minor radius in the poloidal plane.
+We calculate the volume integrated profile and then divide by the volume of integration to get the volume average temperature $\langle T_{\text{e}} \rangle$. If we assume the plasma to be a torus of circular cross-section then we can use spherical coordinates. We can simplify the problem by representing the torus as a cylinder of height equal to the circumference of the torus equal to $2\pi R$ where $R$ is the major radius of the torus, and $a$ is the plasma minor radius in the poloidal plane.
 
 The cylindrical volume element is given by:
 
@@ -97,6 +97,68 @@ $\blacksquare$
 
 -----
 
+#### Electron core temperature of a parabolic profile | `calculate_parabolic_profile_on_axis_temperature()`
+
+###### Derivation
+
+We calculate the volume integrated profile and then divide by the volume of integration to get the volume average temperature $\langle T \rangle$. If we assume the plasma to be a torus of circular cross-section then we can use spherical coordinates. We can simplify the problem by representing the torus as a cylinder of height equal to the circumference of the torus equal to $2\pi R$ where $R$ is the major radius of the torus.
+
+The cylindrical volume element is given by:
+
+$$
+V = \int \int \int dV = \int^{2\pi R}_0 \int^{2\pi}_0 \int^a_0 r \ dr \ d\theta \ dz
+$$
+
+Inserting our temperature function in the form where $\rho$ is expanded as $\rho = r/a$ we get:
+
+$$
+\int^{2\pi R}_0 \int^{2\pi}_0 \int^a_0     r  \left(T_0(1-r^2/a^2)^{\alpha_T}\right) \ dr \ d\theta \ dz
+$$
+
+Since our temperature function is only a function of $r$, and the torus is symmetric around its center, the integration simplifies to integrating over $r$ and the $d\theta ,\ dz$ integrals are solved to give values for the full poloidal angle and cylindrical height and torus length, leading to:
+
+$$
+4\pi^2R \int^a_0     r  \left(T_0(1-r^2/a^2)^{\alpha_T}\right) \ dr  
+$$
+
+In the form of volume average temperature where the volume integrated temperature function has to be divided by the volume of the cylinder / torus we get:
+
+$$
+\langle n \rangle =  \frac{4\pi^2R \int^a_0     r  \left(T_0(1-r^2/a^2)^{\alpha_T}\right) \ dr}{2\pi^2Ra^2}  
+$$
+
+Simplify:
+
+$$
+\langle n \rangle =  \frac{2 \int^a_0     r  \left(T_0(1-r^2/a^2)^{\alpha_T}\right) \ dr}{a^2}  
+$$
+
+Integrate:
+
+$$
+\langle T \rangle =  \frac{2}{a^2} \frac{a^2 T_0}{2(\alpha_T+1)}
+$$
+
+$$
+\therefore \langle T \rangle =   \frac{T_0}{\alpha_T+1}
+$$
+
+This is in agreement with the derivation from the ITER Physics Design 1989. [^iter_design_89]
+
+Since all parabolic profiles are of the same form this proof holds for the density and temperature.
+
+A similar derivation is found in normalised coordinates, $\rho$ if the line averaged integral is swept around the poloidal circumference then divided by the poloidal area.
+
+$$
+\langle T \rangle =  \frac{2\pi \int^1_0     \rho  \left(T_0(1-\rho^2)^{\alpha_T}\right) \ d\rho}{\pi\rho^2}  
+$$
+
+$\blacksquare$
+
+------
+
+
+
 The core ion temperature is then set such as:
 
 $$
@@ -115,7 +177,7 @@ A table of the input variables can be found below
 |----------------------------------|-----------|
 | Normalised plasma radii            | `profile_x` |
 | Pedestal radius (r/a)            | `radius_plasma_pedestal_temp_norm`, $\rho_{\text{ped,T}}$ |
-| Core density                | `temp_plasma_electron_on_axis_kev`, $T_{\text{e0}}$ |
+| Core temperature                | `temp_plasma_electron_on_axis_kev`, $T_{\text{e0}}$ |
 | Pedestal value                   | `temp_plasma_pedestal_kev`, $T_{\text{ped}}$ |
 | Separatrix value                 | `temp_plasma_separatrix_kev`, $T_{\text{sep}}$ |
 | Profile index/ peaking parameter | `alphat`, $\alpha_T$ |
@@ -130,7 +192,7 @@ $$
 The central temperature ($T_0$) is then checked to make sure it is not less than the pedestal temperature, $T_{\text{ped}}$.
 If it is less than a logger warning is pushed to the terminal at runtime.
 
-Values of the profile temperature are then assigned based on the density function below across bounds from 0 to `radius_plasma_pedestal_density_norm` and `radius_plasma_pedestal_density_norm` to 1.  
+Values of the profile temperature are then assigned based on the temperature function below across bounds from 0 to `radius_plasma_pedestal_temp_norm` and `radius_plasma_pedestal_temp_norm` to 1.  
 
 $$\begin{aligned}
 \mbox{Temperature:} \ \ T(\rho) = \left\{
@@ -146,3 +208,5 @@ $$\begin{aligned}
 5. Profile is then integrated with `integrate_profile_y()` using Simpsons integration from the profile abstract base class
 
 [^1]: Jean, J. (2011). *HELIOS: A Zero-Dimensional Tool for Next Step and Reactor Studies*. Fusion Science and Technology, 59(2), 308–349. <https://doi.org/10.13182/FST11-A11650>
+
+[^iter_design_89]: N.A. Uckan and ITER Physics Group, 'ITER Physics Design Guidelines: 1989',

process/main.py

@@ -99,7 +99,10 @@
 from process.models.physics.plasma_fields import PlasmaFields
 from process.models.physics.plasma_geometry import PlasmaGeom
 from process.models.physics.plasma_profiles import PlasmaProfile
-from process.models.physics.profiles import NeProfile, TeProfile
+from process.models.physics.profiles import (
+    ElectronDensityProfile,
+    ElectronTemperatureProfile,
+)
 from process.models.physics.scrape_off_layer import ScrapeOffLayer
 from process.models.power import Power
 from process.models.pulse import Pulse
@@ -664,8 +667,8 @@ def __init__(self, data: DataStructure):
         self.pulse = Pulse()
         self.shield = Shield()
         self.ife = IFE(availability=self.availability, costs=self.costs)
-        self.ne_profile = NeProfile()
-        self.te_profile = TeProfile()
+        self.ne_profile = ElectronDensityProfile()
+        self.te_profile = ElectronTemperatureProfile()
         self.plasma_profile = PlasmaProfile(self.ne_profile, self.te_profile)
         self.fw = FirstWall()
         self.blanket_library = BlanketLibrary(fw=self.fw)

process/models/physics/plasma_profiles.py

@@ -29,8 +29,10 @@ def __init__(self, ne_profile, te_profile):
         Args:
             profile_size (int): The size of the plasma profile.
             outfile (str): The output file path.
-            neprofile (NeProfile): An instance of the NeProfile class.
-            teprofile (TeProfile): An instance of the TeProfile class.
+            neprofile (ElectronDensityProfile): An instance of the ElectronDensityProfile
+            class.
+            teprofile (ElectronTemperatureProfile): An instance of the
+            ElectronTemperatureProfile class.
         """
         # Default profile_size = 201, but it's possible to experiment with this value.
         # See `n_plasma_profile_elements`
@@ -195,7 +197,7 @@ def pedestal_parameterisation(self):
         `temp_plasma_electron_density_weighted_kev` and
         `temp_plasma_ion_density_weighted_kev`.
         """
-        #  Run TeProfile and NeProfile class methods:
+        #  Run ElectronTemperatureProfile and ElectronDensityProfile class methods:
         #  Re-calculate core and profile values
 
         self.teprofile.run()