Updated tprofile to teprofile and nprofile to neprofile.

documentation/proc-pages/eng-models/heating_and_current_drive/RF/culham_electron_cyclotron.md

@@ -1,13 +1,11 @@
 # Culham Electron Cyclotron Model | `culecd()`
 
-
-- `iefrf/iefrffix` = 7 
+- `iefrf/iefrffix` = 7
 
 This routine calculates the current drive parameters for a electron cyclotron system, based on the AEA FUS 172 model[^1]
 
-
-1. Local electron temperature $(\mathtt{tlocal})$ is calculated using the `tprofile` method  
-2. Local electron density $(\mathtt{dlocal})$ is calculated using the `nprofile` method
+1. Local electron temperature $(\mathtt{tlocal})$ is calculated using the `teprofile` method  
+2. Local electron density $(\mathtt{dlocal})$ is calculated using the `neprofile` method
 
 3. Calculate the inverse aspect ratio `epsloc`.
 
@@ -47,7 +45,7 @@ Uses the `eccdef` model found [here](ec_overview.md)
 
 $$
 \mathtt{ecgam} = 0.25(\mathtt{ecgam1} + \mathtt{ecgam2} +\mathtt{ecgam3} + \mathtt{ecgam4})
- $$      
+ $$
 
 7. Calculate the current drive efficiency by dividing `ecgam` by `(dlocal * physics_variables.rmajor)`.
 
@@ -57,8 +55,6 @@ $$
 
 Note: The `eccdef` method is called to calculate the current drive efficiency at each poloidal angle.
 
-
-
 [^1]: Hender, T.C., Bevir, M.K., Cox, M., Hastie, R.J., Knight, P.J., Lashmore-Davies, C.N., Lloyd, B., Maddison, G.P., Morris, A.W., O’Brien, M.R. and Turner, M.F., 1992. *"Physics assessment for the European reactor study."* AEA FUS, 172.
 
-[^2]: Wesson, J. and Campbell, D.J., 2011. *"Tokamaks"* (Vol. 149). Oxford university press.
+[^2]: Wesson, J. and Campbell, D.J., 2011. *"Tokamaks"* (Vol. 149). Oxford university press.

documentation/proc-pages/eng-models/heating_and_current_drive/RF/culham_lower_hybrid.md

@@ -2,18 +2,15 @@
 
 - `iefrf/iefrffix` = 6
 
-
-
 This routine calculates the current drive parameters for a
 lower hybrid system, based on the AEA FUS 172 model.
 AEA FUS 251: A User's Guide to the PROCESS Systems Code
 AEA FUS 172: Physics Assessment for the European Reactor Study[^1]
 
-
 1. Call the [`lhrad()`](#lower-hybrid-wave-absorption-radius--lhrad) method to calculate the lower hybrid wave absorption radius, `rratio`.
 2. Calculate the penetration radius, `rpenet`, by multiplying `rratio` with the minor radius of the plasma.
-3. Calculate the local density, `dlocal`, using the `nprofile()` function from the `profiles_module` module. This function takes into account various plasma parameters such as the density profile, electron density at the edge, pedestal density, separatrix density, and the value of the parameter `alphan`.
-4. Similarly, calculate the local temperature, `tlocal`, using the `tprofile()` function from the `profiles_module` module. This function considers parameters such as the temperature profile, electron temperature at the edge, pedestal temperature, separatrix temperature, `alphat`, and `tbeta`.
+3. Calculate the local density, `dlocal`, using the `neprofile()` function from the `profiles_module` module. This function takes into account various plasma parameters such as the density profile, electron density at the edge, pedestal density, separatrix density, and the value of the parameter `alphan`.
+4. Similarly, calculate the local temperature, `tlocal`, using the `teprofile()` function from the `profiles_module` module. This function considers parameters such as the temperature profile, electron temperature at the edge, pedestal temperature, separatrix temperature, `alphat`, and `tbeta`.
 5. Calculate the local toroidal magnetic field, `blocal`, using the formula `bt * rmajor / (rmajor - rpenet)`. Here, `bt` is the toroidal magnetic field at the magnetic axis, and `rmajor` is the major radius of the plasma.
 6. Calculate the parallel refractive index, `nplacc`, which is needed for plasma access. It uses the local density `dlocal` and the local magnetic field `blocal` to calculate a fraction `frac`. `nplacc` is then obtained by adding `frac` to the square root of `1.0 + frac * frac`.
 7. Calculate the local inverse aspect ratio, `epslh`, by dividing `rpenet` by `rmajor`.
@@ -46,5 +43,3 @@ Iterate over the following steps to find the minor radius ratio:
     - Update $\mathtt{rat0}$ with the new approximation, $\mathtt{rat1}$.
 3. If the loop completes all 100 iterations without finding a satisfactory solution, report an error and set $\mathtt{rat0}$ to 0.8.
 4. Return the final value of $\mathtt{rat0}$.
-
-[^1]: T. C. Hender, M. K. Bevir, M. Cox, R. J. Hastie, P. J. Knight, C. N. Lashmore-Davies, B. Lloyd, G. P. Maddison, A. W. Morris, M. R. O'Brien, M.F. Turner abd H. R. Wilson, *"Physics Assessment for the European Reactor Study"*, AEA Fusion Report AEA FUS 172 (1992)

documentation/proc-pages/physics-models/profiles/plasma_density_profile.md

@@ -1,4 +1,4 @@
-# Density Profile | `NProfile(Profile)`
+# Density Profile | `NeProfile(Profile)`
 
 The desnity 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_paramterisation). The sequence of the runner function can be seen below along with explanation of the following calculations.
 
@@ -8,21 +8,20 @@ The desnity profile class is organised around a central runner function that is
 
 2. The steps between the normalized points is then done by [`calculate_profile_dx()`](./plasma_profiles_abstract_class.md#calculate-the-profile-steps-in-x--calculate_profile_dx) which divides the max x-dimension by the number of points.
 
-3. The core electron and ion temperatures are claculated via [`set_physics_variables()`]() 
+3. The core electron and ion temperatures are claculated via [`set_physics_variables()`]()
 
-
-    ### Calculate core values | `set_physics_variables()`
+   ### Calculate core values | `set_physics_variables()`
 
     The core electron density is calculated using the [`ncore`](plasma_density_profile.md#electron-core-density-of-a-pedestalised-profile--ncore) method.
     The core ion density is then set from $n_{\text{i}}$ (`nd_ions_total`) which is the total ion density such as:
 
     $$
     n_{\text{i0}} = \left(\frac{n_\text{i}}{n_\text{e}}\right)n_{\text{e0}}
     $$
-
-    #### Electron core density of a pedestalised profile | `ncore()`
 
-    This function calculates the core electron density for a pedestalsied profile (`ipedestal == 1`). It takes in values of 
+   #### Electron core density of a pedestalised profile | `ncore()`
+
+    This function calculates the core electron density for a pedestalsied profile (`ipedestal == 1`). It takes in values of
 
     | Profile parameter / Input               | Density   |
     |----------------------------------|-----------|
@@ -32,7 +31,6 @@ The desnity profile class is organised around a central runner function that is
     | Average density             | `dene`, $\langle n \rangle$ |
     | Profile index/ peaking parameter | `alphan`, $\alpha_n$ |
 
-
     $$
     n_0  =  \frac{1}{3\rho_{\text{ped,n}}^2}\left[3\langle n_{\text{e}} \rangle (1+\alpha_n)
     + n_{\text{sep}} (1+\alpha_n) \left(-2 + \rho_{\text{ped,n}} + \rho_{\text{ped,n}}^2\right) \\
@@ -42,7 +40,7 @@ The desnity profile class is organised around a central runner function that is
 
     If `ncore` is returned as being less than 0, it is forced into a state of `ncore = 1E-6` in order to help convergence. This will also give a warning to the user to raise the lower bound of the average electron density `dene`.
 
-    ##### Derivation
+   ##### Derivation
 
     We calculate the volume integrated profile and then divide by the volume of integration to get the volume average density $\langle n_{\text{e}} \rangle$. 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.
 
@@ -71,26 +69,26 @@ The desnity profile class is organised around a central runner function that is
     \frac{\rho^2}{\rho_{\text{ped},n}^2}\right)^{\alpha_n}\right) \ d\rho \\
     +\int^1_{\rho_{\text{ped,n}}}     \rho\left(n_{\text{sep}} + (n_{\text{ped}} - n_{\text{sep}})\left( \frac{1- \rho}{1-\rho_{\text{ped},n}}\right)\right)\right] \ d\rho
     $$
-        
+
     Integrating each part within its bounds:
-    
+
     $$
     4\pi^2R\left[ \frac{\left(n_{\text{ped}} {\alpha}_{n} + n_{0}\right) {\rho}_{\text{ped,n}}^{2}}{2{\alpha}_{n} + 2} \\
-    +\frac{\left(1-{\rho}_{\text{ped,n}}\right) \left(\left(n_{\text{sep}} + 2n_{\text{ped}}\right) {\rho}_{\text{ped,n}} + 2n_{\text{sep}} + n_{\text{ped}}\right)}{6}\right] 
+    +\frac{\left(1-{\rho}_{\text{ped,n}}\right) \left(\left(n_{\text{sep}} + 2n_{\text{ped}}\right) {\rho}_{\text{ped,n}} + 2n_{\text{sep}} + n_{\text{ped}}\right)}{6}\right]
     $$
 
     In the form of volume average density where the volume integrated density function has to be divided by the volume of the cylinder / torus, within the volume bounded by that pedestal position we get:
 
     $$
     \langle n_{\text{e}} \rangle = 4\pi^2R\left[ \frac{\frac{\left(n_{\text{ped}} {\alpha}_{n} + n_{0}\right) {\rho}_{\text{ped,n}}^{2}}{2{\alpha}_{n} + 2}
-    +\frac{\left(1-{\rho}_{\text{ped,n}}\right) \left(\left(n_{\text{sep}} + 2n_{\text{ped}}\right) {\rho}_{\text{ped,n}} + 2n_{\text{sep}} + n_{\text{ped}}\right)}{6}}{2\pi^2 R \rho^2}\right] 
+    +\frac{\left(1-{\rho}_{\text{ped,n}}\right) \left(\left(n_{\text{sep}} + 2n_{\text{ped}}\right) {\rho}_{\text{ped,n}} + 2n_{\text{sep}} + n_{\text{ped}}\right)}{6}}{2\pi^2 R \rho^2}\right]
     $$
 
     In this case, the value of $\rho$ is equal to 1 as we integrated over the full profile.
 
     $$
     \langle n_{\text{e}} \rangle = 2\left[\frac{\left(n_{\text{ped}} {\alpha}_{n} + n_{0}\right) {\rho}_{\text{ped,n}}^{2}}{2{\alpha}_{n} + 2} \\
-    +\frac{\left(1-{\rho}_{\text{ped,n}}\right) \left(\left(n_{\text{sep}} + 2n_{\text{ped}}\right) {\rho}_{\text{ped,n}} + 2n_{\text{sep}} + n_{\text{ped}}\right)}{6}\right] 
+    +\frac{\left(1-{\rho}_{\text{ped,n}}\right) \left(\left(n_{\text{sep}} + 2n_{\text{ped}}\right) {\rho}_{\text{ped,n}} + 2n_{\text{sep}} + n_{\text{ped}}\right)}{6}\right]
     $$
 
     $$
@@ -105,16 +103,16 @@ The desnity profile class is organised around a central runner function that is
     - n_{\text{ped}}\left( (1 + \alpha_n)(1+ \rho_{\text{ped,n}}) + (\alpha_n -2)
     \rho_{\text{ped,n}}^2\right)\right]
     $$
-    
+
     $\blacksquare$
 
     ------
 
 4. The y profile is then calculated using [`calculate_profile_y()`](plasma_density_profile.md#calculate-desnity-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]
 
-    ### Calculate desnity at each radius position | `calculate_profile_y()`
+   ### Calculate desnity at each radius position | `calculate_profile_y()`
 
-    A table of the input variables can be found below 
+    A table of the input variables can be found below
 
     | Profile parameter / Input               | Density   |
     |----------------------------------|-----------|
@@ -128,18 +126,16 @@ The desnity profile class is organised around a central runner function that is
     If `ipedestal == 0` then the original parabolic profile form is used
 
     $$
-    n(\rho) = n_0(1 - \rho^2)^{\alpha_n} 
+    n(\rho) = n_0(1 - \rho^2)^{\alpha_n}
     $$
 
     The central density ($n_0$) is then checked to make sure it is not less than the pedestal density, $n_{\text{ped}}$.
     If it is less than a logger warning is pushed to the terminal at runtime.
 
     Values of the profile density are then assigned based on the density function below across bounds from 0 to `rhopedn` and `rhopedn` to 1.  
 
-
-
     $$\begin{aligned}
-    \mbox{Density:} \ n(\rho) = \left\{ 
+    \mbox{Density:} \ n(\rho) = \left\{
     \begin{aligned}
         & n_{\text{ped}} + (n_0 - n_{\text{ped}}) \left( 1 -
         \frac{\rho^2}{\rho_{\text{ped,n}}^2}\right)^{\alpha_n}
@@ -149,8 +145,7 @@ The desnity profile class is organised around a central runner function that is
     \end{aligned}
     \right.
     \end{aligned}$$
-
 
 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
+[^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>