3873 beta profiles and new average values

documentation/physics-models/plasma_beta/plasma_beta.md

@@ -5,9 +5,19 @@
 The efficiency of confinement of plasma pressure by the magnetic field is represented by the ratio:
 
 $$
-\beta = \frac{2\mu_0p}{B^2}
+\beta(\rho) = \frac{2\mu_0p(\rho)}{\left(B(\rho)\right)^2}
 $$
 
+Where $\beta$ is a function of normalised minor radius across the plasma ($\rho$), due to the change in pressure and magnetic field strength. 
+
+The standard $\beta$ term used for comparison and to represent the plasma as a whole in many calculations is the volume averaged value given by:
+
+$$
+\langle \beta \rangle = \frac{2\mu_0 \langle p \rangle}{\langle B \rangle^2}
+$$
+
+Where $\langle p \rangle$ is the volume averaged plasma pressure and $\langle B \rangle$ is the average field.
+
 There are several different measures of this type, arising from different choices of definition and from the need to quantify different equilibrium properties.
 
 In its expanded form of magnetic field components:
@@ -92,6 +102,20 @@ $$
 
 ------------------------
 
+## Definitions
+
+### Volume averaged thermal toroidal beta
+
+$$
+\overbrace{\langle \beta_t \rangle}^{\texttt{beta_toroidal_thermal_vol_avg}} = \frac{2\mu_0 \langle p_{\text{thermal}} \rangle}{\underbrace{B_{\text{T,on-axis}}^2}_{\texttt{b_plasma_toroidal_on_axis}}}
+$$
+
+### Volume averaged thermal poloidal beta
+
+$$
+\langle \beta_p \rangle = \frac{2\mu_0 \langle p_{\text{thermal}} \rangle}{\langle B_{\text{P,average}} \rangle^2}
+$$
+
 ## Troyon Beta Limit
 
 The Troyon plasma beta limit is given by[^0][^1]:

examples/data/large_tokamak_nof_2_MFILE.DAT

@@ -231,8 +231,8 @@
  Volume_averaged_electron_number_density_(/m3)____________________________ (nd_plasma_electrons_vol_avg)_________________________ 7.79622390002983731e+19
  Electron_number_density_on_axis_(/m3)____________________________________ (nd_plasma_electron_on_axis)__________________________ 1.02466460344915771e+20 OP
  Line-averaged_electron_number_density_(/m3)______________________________ (nd_electron_line)_________________________ 8.63127495812675338e+19 OP
- Plasma_pressure_on_axis_(Pa)_____________________________________________ (pres_plasma_on_axis)___________________________ 7.82668759018785902e+05 OP
- Volume_averaged_plasma_pressure_(Pa)_____________________________________ (pres_plasma_vol_avg)_____________ 2.26860509860517632e+05 OP
+ Plasma_pressure_on_axis_(Pa)_____________________________________________ (pres_plasma_thermal_on_axis)___________________________ 7.82668759018785902e+05 OP
+ Volume_averaged_plasma_pressure_(Pa)_____________________________________ (pres_plasma_thermal_vol_avg)_____________ 2.26860509860517632e+05 OP
  Line-averaged_electron_density_/_Greenwald_density_______________________ (dnla_gw)______________________ 1.19833068191158598e+00 OP
  Total_Ion_number_density_(/m3)___________________________________________ (nd_ions_total)________________ 7.06084473006886912e+19 OP
  Fuel_ion_number_density_(/m3)____________________________________________ (nd_fuel_ions)_________________ 6.58453241268011663e+19 OP

examples/data/large_tokamak_nof_MFILE.DAT

@@ -303,8 +303,8 @@
  Volume_averaged_electron_number_density_(/m3)____________________________ (nd_plasma_electrons_vol_avg)_________________________ 8.50078961768999158e+19
  Electron_number_density_on_axis_(/m3)____________________________________ (nd_plasma_electron_on_axis)__________________________ 1.11814263037413868e+20 OP
  Line-averaged_electron_number_density_(/m3)______________________________ (nd_electron_line)_________________________ 9.41418090734859715e+19 OP
- Plasma_pressure_on_axis_(Pa)_____________________________________________ (pres_plasma_on_axis)___________________________ 9.10652371594472905e+05 OP
- Volume_averaged_plasma_pressure_(Pa)_____________________________________ (pres_plasma_vol_avg)_____________ 2.63957209157818230e+05 OP
+ Plasma_pressure_on_axis_(Pa)_____________________________________________ (pres_plasma_thermal_on_axis)___________________________ 9.10652371594472905e+05 OP
+ Volume_averaged_plasma_pressure_(Pa)_____________________________________ (pres_plasma_thermal_vol_avg)_____________ 2.63957209157818230e+05 OP
  Line-averaged_electron_density_/_Greenwald_density_______________________ (dnla_gw)______________________ 1.19999999999999951e+00 OP
  Total_Ion_number_density_(/m3)___________________________________________ (nd_ions_total)________________ 7.34892735750798868e+19 OP
  Fuel_ion_number_density_(/m3)____________________________________________ (nd_fuel_ions)_________________ 6.49714589130413015e+19 OP

process/data_structure/physics_variables.py

@@ -244,6 +244,14 @@
 beta_toroidal: float = None
 """toroidal beta"""
 
+beta_toroidal_profile: list[float] = None
+"""toroidal beta profile"""
+
+beta_poloidal_profile: list[float] = None
+"""poloidal beta profile"""
+
+beta_total_profile: list[float] = None
+"""total beta profile"""
 
 beta_thermal: float = None
 """thermal beta"""
@@ -284,10 +292,24 @@
 b_plasma_poloidal_average: float = None
 """Plasma average poloidal field (T)"""
 
+b_plasma_poloidal_edge: float = None
+"""Plasma poloidal field at plasma edge (T)"""
 
 b_plasma_toroidal_on_axis: float = None
 """Plasma toroidal field on axis (T) (`iteration variable 2`)"""
 
+b_plasma_toroidal_profile: list[float] = None
+"""toroidal field profile in plasma (T)"""
+
+b_plasma_poloidal_profile: list[float] = None
+"""poloidal field profile in plasma (T)"""
+
+b_plasma_circular_poloidal_profile: list[float] = None
+"""poloidal field profile in circular plasma (T)"""
+
+b_plasma_total_profile: list[float] = None
+"""total field profile in plasma (T)"""
+
 
 b_plasma_total: float = None
 """Sum of plasma total toroidal + poloidal field (T)"""
@@ -803,7 +825,7 @@
 """margin to vertical stability"""
 
 
-pres_plasma_on_axis: float = None
+pres_plasma_thermal_on_axis: float = None
 """central total plasma pressure (Pa)"""
 
 pres_plasma_total_profile: list[float] = None
@@ -821,11 +843,14 @@
 j_plasma_on_axis: float = None
 """Central plasma current density (A/m2)"""
 
+j_plasma_circular_on_axis: float = None
+"""Central plasma current density for a circular plasma (A/m2)"""
+
 n_plasma_profile_elements: int = None
 """Number of elements in plasma profile"""
 
-pres_plasma_vol_avg: float = None
-"""Volume averaged plasma pressure (Pa)"""
+pres_plasma_thermal_vol_avg: float = None
+"""Volume averaged thermal plasma pressure (Pa)"""
 
 
 f_dd_branching_trit: float = None
@@ -951,6 +976,9 @@
 plasma_current: float = None
 """plasma current (A)"""
 
+c_plasma_circular: float = None
+"""Plasma current for circular plasma (A)"""
+
 
 p_plasma_neutron_mw: float = None
 """Neutron fusion power from just the plasma [MW]"""
@@ -1097,6 +1125,11 @@
 qstar: float = None
 """cylindrical safety factor"""
 
+q_95_circular: float = None
+"""Safety factor at 95% flux surface for circular plasma"""
+
+q_circular_profile: list[float] = None
+"""safety factor profile for circular plasma"""
 
 rad_fraction_sol: float = None
 """SoL radiation fraction"""
@@ -1380,6 +1413,9 @@ def init_physics_variables():
     global beta_poloidal
     global beta_poloidal_eps
     global beta_toroidal
+    global beta_toroidal_profile
+    global beta_total_profile
+    global beta_poloidal_profile
     global beta_thermal
     global beta_thermal_poloidal
     global beta_thermal_toroidal
@@ -1390,7 +1426,12 @@ def init_physics_variables():
     global beta_norm_toroidal
     global betbm0
     global b_plasma_poloidal_average
+    global b_plasma_poloidal_edge
     global b_plasma_toroidal_on_axis
+    global b_plasma_toroidal_profile
+    global b_plasma_poloidal_profile
+    global b_plasma_circular_poloidal_profile
+    global b_plasma_total_profile
     global b_plasma_total
     global burnup
     global burnup_in
@@ -1488,12 +1529,13 @@ def init_physics_variables():
     global nd_plasma_electron_on_axis
     global nd_plasma_ions_on_axis
     global m_s_limit
-    global pres_plasma_on_axis
+    global pres_plasma_thermal_on_axis
     global pres_plasma_total_profile
     global pres_plasma_electron_profile
     global pres_plasma_ion_total_profile
     global pres_plasma_fuel_profile
     global j_plasma_on_axis
+    global j_plasma_circular_on_axis
     global n_plasma_profile_elements
     global f_dd_branching_trit
     global pden_plasma_alpha_mw
@@ -1526,6 +1568,7 @@ def init_physics_variables():
     global pflux_fw_rad_mw
     global pden_ion_electron_equilibration_mw
     global plasma_current
+    global c_plasma_circular
     global p_plasma_neutron_mw
     global p_neutron_total_mw
     global pden_neutron_total_mw
@@ -1556,6 +1599,8 @@ def init_physics_variables():
     global tauratio
     global q95_min
     global qstar
+    global q_95_circular
+    global q_circular_profile
     global rad_fraction_sol
     global rad_fraction_total
     global f_nd_alpha_electron
@@ -1632,6 +1677,9 @@ def init_physics_variables():
     beta_poloidal = 0.0
     beta_poloidal_eps = 0.0
     beta_toroidal = 0.0
+    beta_toroidal_profile = []
+    beta_poloidal_profile = []
+    beta_total_profile = []
     beta_thermal = 0.0
     beta_thermal_poloidal = 0.0
     beta_thermal_toroidal = 0.0
@@ -1642,7 +1690,12 @@ def init_physics_variables():
     beta_norm_toroidal = 0.0
     betbm0 = 1.5
     b_plasma_poloidal_average = 0.0
+    b_plasma_poloidal_edge = 0.0
     b_plasma_toroidal_on_axis = 5.68
+    b_plasma_toroidal_profile = []
+    b_plasma_poloidal_profile = []
+    b_plasma_circular_poloidal_profile = []
+    b_plasma_total_profile = []
     b_plasma_total = 0.0
     burnup = 0.0
     burnup_in = 0.0
@@ -1740,12 +1793,13 @@ def init_physics_variables():
     nd_plasma_electron_on_axis = 0.0
     nd_plasma_ions_on_axis = 0.0
     m_s_limit = 0.3
-    pres_plasma_on_axis = 0.0
+    pres_plasma_thermal_on_axis = 0.0
     pres_plasma_total_profile = []
     pres_plasma_electron_profile = []
     pres_plasma_ion_total_profile = []
     pres_plasma_fuel_profile = []
     j_plasma_on_axis = 0.0
+    j_plasma_circular_on_axis = 0.0
     n_plasma_profile_elements = 500
     f_dd_branching_trit = 0.0
     pden_plasma_alpha_mw = 0.0
@@ -1778,6 +1832,7 @@ def init_physics_variables():
     pflux_fw_rad_mw = 0.0
     pden_ion_electron_equilibration_mw = 0.0
     plasma_current = 0.0
+    c_plasma_circular = 0.0
     p_plasma_neutron_mw = 0.0
     p_neutron_total_mw = 0.0
     pden_neutron_total_mw = 0.0
@@ -1808,6 +1863,8 @@ def init_physics_variables():
     tauratio = 1.0
     q95_min = 0.0
     qstar = 0.0
+    q_95_circular = 0.0
+    q_circular_profile = []
     rad_fraction_sol = 0.8
     rad_fraction_total = 0.0
     f_nd_alpha_electron = 0.1