❇️ ♻️ Create Beta class

documentation/physics-models/plasma_beta/plasma_beta.md

@@ -170,7 +170,7 @@ beta_norm_max = 3.0
 
 ---------
 
-#### Wesson Relation
+#### Wesson Relation | `calculate_beta_norm_max_wesson()`
 
 This can be activated by stating `i_beta_norm_max = 1` in the input file.
 
@@ -188,7 +188,7 @@ This is only recommended for high aspect ratio tokamaks[^3].
 
 ---------
 
-#### Original Scaling Law
+#### Original Scaling Law | `calculate_beta_norm_max_original()`
 
 This can be activated by stating `i_beta_norm_max = 2` in the input file.
 
@@ -263,7 +263,7 @@ $$
 
 ---------
 
-#### Menard Beta Relation
+#### Menard Beta Relation | `calculate_beta_norm_max_menard()`
 
 This can be activated by stating `i_beta_norm_max = 3` in the input file.
 
@@ -345,7 +345,7 @@ Found as a reasonable fit to the computed no wall limit at $f_{\text{BS}} \appro
 
 ---------
 
-#### Tholerus Relation
+#### Tholerus Relation | `calculate_beta_norm_max_thloreus()`
 
 This can be activated by stating `i_beta_norm_max = 4` in the input file.
 
@@ -362,7 +362,7 @@ where $F_p$ is the pressure peaking, $F_p = p_{\text{ax}} / \langle p \rangle$ a
 
 -------------
 
-#### Stambaugh Relation
+#### Stambaugh Relation | `calculate_beta_norm_max_stambaugh()`
 
 This can be activated by stating `i_beta_norm_max = 5` in the input file.
 
@@ -377,13 +377,24 @@ This fit was done for $A = 1.2 -7.0, \kappa = 1.5-6.0$ with $\delta = 0.5$ for n
 
 ---------
 
+## Stored energy | `calculate_plasma_energy_from_beta()`
+
+As the $\beta$ metric is simply the ratio between the kinetic pressure of the plasma and the magnetic pressure, $\beta$ can be used to get the total kinetic energy of the plasma (assuming the total $\beta$ is used).
+
+
+$$
+E_{\text{plasma}} \approx \frac{3}{2}\frac{\beta B^2}{2\mu_0}V_{\text{plasma}}
+$$
+
+---------------
+
 ## Key Constraints
 
 ### Beta consistency
 
 This constraint can be activated by stating `icc = 1` in the input file.
 
-Ensures the relationship between $\beta$, density, temperature and total magnetic field is withheld by checking the fixed input or iteration variable $\mathtt{beta}$ is consistent in value with the rest of the physics parameters
+Ensures the relationship between $\beta$, density, temperature and total magnetic field is withheld by checking the fixed input or iteration variable $\texttt{beta}$ is consistent in value with the rest of the physics parameters
 
 $$
 \texttt{beta_total_vol_avg} \equiv \frac{2\mu_0 \langle n_{\text{e}}T_{\text{e}}+n_{\text{i}}T_{\text{i}}\rangle}{B^2} + \beta_{\alpha} + \beta_{\text{beam}}

documentation/physics-models/plasma_current/plasma_current.md

@@ -92,7 +92,7 @@ Instead of $q_a$, $q_{95}$ is used as in plasma configurations with divertors th
 
 ## Plasma Current Calculation | `calculate_plasma_current()`
 
-This function calculates the plasma current shaping factor ($f_q$), plasma current ($I_{\text{p}}$), qstar ($q^*$), normalized beta ($\beta_{\text{N}}$) and then poloidal field and the profile settings for $\mathtt{alphaj}$ ($\alpha_J$) and $\mathtt{ind_plasma_internal_norm}$ ($l_{\mathtt{i}}$). This is done in 5 separate steps which are shown in the following numbered sections.
+This function calculates the plasma current shaping factor ($f_q$), plasma current ($I_{\text{p}}$), qstar ($q^*$) and then poloidal field and the profile settings for $\texttt{alphaj}$ ($\alpha_J$) and $\texttt{ind_plasma_internal_norm}$ ($l_{\text{i}}$). This is done in 5 separate steps which are shown in the following numbered sections.
 
 
 $$\begin{aligned}
@@ -118,7 +118,7 @@ The formula for calculating `fq` is:
 
 $$f_q = \left(\frac{{1.22 - 0.68  \epsilon}}{{(1.0 - \epsilon^2)^2}}\right)  \left(\frac{L_{\text{poloidal}}}{2\pi a}\right)^2$$
 
-Where $\epsilon$ is the inverse [aspect ratio](../plasma_geometry.md) ($\mathtt{eps}$) and $L_{\text{poloidal}}$ is the poloidal perimeter of the plasma.
+Where $\epsilon$ is the inverse [aspect ratio](../plasma_geometry.md) ($\texttt{eps}$) and $L_{\text{poloidal}}$ is the poloidal perimeter of the plasma.
 
 -----------
 
@@ -523,23 +523,13 @@ $$
 
 --------------
 
-### 3. Calculate the normalized beta
 
-The total normalized beta is calculated as per:
-
-$$
-\beta_N = \beta\frac{1\times10^8  a B_{\text{T}}}{I_{\text{P}}}
-$$
-
-
------------------
-
-### 4. Plasma Current Poloidal Field
+### 3. Plasma Current Poloidal Field
 
 For calculating the poloidal magnetic field created due to the presence of the plasma current, [Ampere's law](https://en.wikipedia.org/wiki/Amp%C3%A8re%27s_circuital_law) can be used. In this case the poloidal field is simply returned as:
 
 $$
-B_{\text{p}} = \frac{\mu_0 I_{\text{p}}}{\mathtt{len_plasma_poloidal}}
+B_{\text{p}} = \frac{\mu_0 I_{\text{p}}}{\texttt{len_plasma_poloidal}}
 $$
 
 Where `len_plasma_poloidal` is the plasma poloidal perimeter calculated [here](../plasma_geometry.md#poloidal-perimeter).

process/main.py

@@ -93,7 +93,7 @@
 )
 from process.log import logging_model_handler, show_errors
 from process.pfcoil import PFCoil
-from process.physics import DetailedPhysics, Physics
+from process.physics import DetailedPhysics, Physics, PlasmaBeta
 from process.plasma_geometry import PlasmaGeom
 from process.plasma_profiles import PlasmaProfile
 from process.power import Power
@@ -682,8 +682,11 @@ def __init__(self):
             neutral_beam=NeutralBeam(plasma_profile=self.plasma_profile),
             electron_bernstein=ElectronBernstein(plasma_profile=self.plasma_profile),
         )
+        self.plasma_beta = PlasmaBeta()
         self.physics = Physics(
-            plasma_profile=self.plasma_profile, current_drive=self.current_drive
+            plasma_profile=self.plasma_profile,
+            current_drive=self.current_drive,
+            plasma_beta=self.plasma_beta,
         )
         self.physics_detailed = DetailedPhysics(
             plasma_profile=self.plasma_profile,
@@ -700,6 +703,7 @@ def __init__(self):
             current_drive=self.current_drive,
             physics=self.physics,
             neoclassics=self.neoclassics,
+            plasma_beta=self.plasma_beta,
         )
         self.dcll = DCLL(fw=self.fw)