Output-profiles.md

@@ -12,7 +12,7 @@ The content of each column in the file is given here below.
 
 | Column | Label    |      Variable      | Units  | Description                     |
 |   ---: | :---     |        :---:       | :---:  | :----------------------   |
-|      1 | `rhop `  | $`\rho_{\rm pol}`$ |   -    | Normalized poloidal flux  |
+|      1 | `rhop `  | $`\rho_{\rm pol}`$ |   -    | Normalized minor radius   |
 |      2 | `rhot`   | $`\rho_{\rm tor}`$ |   -    | Normalized minor radius   |
 |      3 | `Jphi`   | $`J_\phi`$     | MA/m$`^2`$ | Driven toroidal current density        |
 |      4 | `Jcdb`   | $`J_{\rm cd}`$ | MA/m$`^2`$ | Driven current density, JETTO definition     |
@@ -24,6 +24,18 @@ The content of each column in the file is given here below.
 
 ## Definitions
 
+- Normalized minor radii
+    ```math
+    \rho_{\rm pol} = \sqrt{\frac{\psi - \psi_0}{\psi_a - \psi_0}} \\
+    \rho_{\rm tor} = \sqrt{\frac{\Phi}{\Phi_a}}
+    ```
+
+- Flux surface average
+
+    ```math
+    \langle x \rangle = \frac{\oint x \frac{dl}{B_p}}
+                             {\oint \frac{dl}{B_p}}
+    ```
 - Flux-averaged parallel current density
 
     ```math
@@ -58,4 +70,15 @@ The content of each column in the file is given here below.
     P_{\mathrm{ins}}(\rho) = \int_0^\rho \frac{dP}{dV} \frac{dV}{d\rho'} d\rho'
     ```
 
-where $`V(\rho)`$ is the volume enclosed by the flux surface at $`\rho`$ and $`A(\rho)`$ is its cross-section area.
+Where:
\ No newline at end of file
+- $`\Phi`$ and $`\psi`$ are the toroidal and poloidal magnetic flux respectively
+- $`\Phi_a`$ and $`\psi_a`$ their values at the last closed flux surface
+- $`\Phi_0=0`$ and $`\psi_0`$ their values value at the plasma magnetic axis
+- $`R`$ the major radius
+- $`\phi`$ the toroidal angle
+- $`{\bf J}`$ the EC driven current density vector
+- $`{\bf B}`$ the magnetic field
+- $`B_\phi`$ and $`B_p`$ its toroidal and poloidal components
+- $`f(\psi) = B_\phi R`$ the poloidal flux function
+- $`V(\rho)`$ the volume enclosed by the flux surface at $`\rho`$
+- $`A(\rho)`$ its cross-section area
\ No newline at end of file