Update README.md to include finite beta explanation and example code

README.md

@@ -550,6 +550,8 @@ size_categories:
 
 A dataset of diverse quasi-isodynamic (QI) stellarator boundary shapes with corresponding performance metrics and ideal magneto-hydrodynamic (MHD) equilibria, as well as settings for their generation.
 
+The performance metrics and ideal MHD equilibria were evaluated under vacuum (default) and with plasma inside (finite beta).
+
 ## Dataset Details
 
 ### Dataset Description
@@ -557,6 +559,7 @@ A dataset of diverse quasi-isodynamic (QI) stellarator boundary shapes with corr
 <!-- Provide a longer summary of what this dataset is. -->
 
 Stellarators are magnetic confinement devices that are being pursued to deliver steady-state carbon-free fusion energy. Their design involves a high-dimensional, constrained optimization problem that requires expensive physics simulations and significant domain expertise. Specifically, QI-stellarators are seen as a promising path to commercial fusion due to their intrinsic avoidance of current-driven disruptions. 
+
 With the release of this dataset, we aim to lower the barrier for optimization and machine learning researchers to contribute to stellarator design, and to accelerate cross-disciplinary progress toward bringing fusion energy to the grid.
 
 - **Curated by:** Proxima Fusion
@@ -576,8 +579,46 @@ With the release of this dataset, we aim to lower the barrier for optimization a
 
 <!-- This section provides a description of the dataset fields, and additional information about the dataset structure such as criteria used to create the splits, relationships between data points, etc. -->
 
-The dataset consists of 2 tabular parts. Both parts have a column `plasma_config_id` in common which can be used to associate respective entries:
-
+There are 6 tuples of datasets, one for each percentage of volume-averaged plasma inside the boundary:
+<table>
+  <tr>
+    <th>Condition</th>
+    <th>Boundaries, Metrics, Generation Settings, Misc</th>
+    <th>Ideal MHD Equilibira</th>
+  </tr>
+  <tr>
+    <th>Vacuum</th>
+    <th>default</th>
+    <th>vmecpp_wout</th>
+  </tr>
+  <tr>
+    <th>1% Beta</th>
+    <th>finte_beta_1pct</th>
+    <th>vmecpp_wout_finite_beta_1pct</th>
+  </tr>
+  <tr>
+    <th>2% Beta</th>
+    <th>finte_beta_2pct</th>
+    <th>vmecpp_wout_finite_beta_2pct</th>
+  </tr>
+  <tr>
+    <th>3% Beta</th>
+    <th>finte_beta_3pct</th>
+    <th>vmecpp_wout_finite_beta_3pct</th>
+  </tr>
+  <tr>
+    <th>4% Beta</th>
+    <th>finte_beta_4pct</th>
+    <th>vmecpp_wout_finite_beta_4pct</th>
+  </tr>
+  <tr>
+    <th>5% Beta</th>
+    <th>finte_beta_5pct</th>
+    <th>vmecpp_wout_finite_beta_5pct</th>
+  </tr>
+</table>
+<br>
+Contents of datasets:
 <table>
   <tr>
     <th style="border-right: 1px solid gray;">default</th>
@@ -585,22 +626,59 @@ The dataset consists of 2 tabular parts. Both parts have a column `plasma_config
   </tr>
   <tr>
     <td style="border-right: 1px solid gray;">
-        Contains information about:
-        <ul>
-            <li>Plasma boundaries</li>
-            <li>Ideal MHD metrics</li>
-            <li>Omnigenous field and targets, used as input for sampling of plasma boundaries</li>
-            <li>Sampling settings for various methods (DESC, VMEC, QP initialization, Near-axis expansion)</li>
-            <li>Miscellaneous information about errors that might have occurred during sampling or metrics computation.</li>
-        </ul>
-        For each of the components above there is an identifier column (ending with `.id`), a JSON column containing a JSON-string representation, as well as one column per leaf in the nested JSON structure (with `.` separating the keys on the JSON path to the respective leaf).
-</td>
-    <td>Contains, for each plasma boundary, a JSON-string representations of the "WOut" file as obtained when running VMEC, initialized on the boundary.<br>The JSON representation can be converted to a VMEC2000 output file.
-</td>
+      Contains information about:
+      <ul>
+        <li>Plasma boundaries</li>
+        <li>Ideal MHD metrics in vacuum</li>
+        <li>Omnigenous field and targets, used as input for sampling of plasma boundaries</li>
+        <li>Sampling settings for various methods (DESC, VMEC, QP initialization, Near-axis expansion)</li>
+        <li>Miscellaneous information about errors that might have occurred during sampling or metrics computation.</li>
+        <li>Miscellaneous information
+          <ul>
+            <li>the corresponding ideal MHD equilibrium ID in <b>vmecpp_wout</b></li>
+            <li>errors that might have occurred during sampling or metrics computation.</li>
+          </ul>
+        </li>
+      </ul>
+    </td>
+    <td>
+      Contains:
+      <ul>
+        <li>For each plasma boundary in <b>default</b>, a JSON-string representation of the "WOut" file as obtained when running VMEC, initialized on the boundary.<br>The JSON representation can be converted to a VMEC2000 output file.</li>
+        <li>The corresponding plasma configuration ID in <b>default</b></li>
+      </ul>
+    </td>
+  </tr>
+  <tr>
+    <td colspan="2">
+      The <b>default</b> (vacuum) subset above is special in the sense that it contains more information than the other subsets (finite betas) below. Those are derived from the <b>default</b> (vacuum) subset by setting for each plasma boundary the respective volume-averaged beta percentage and re-computing the performance metrics and ideal MHD equilibria:
+    </td>
+  </tr>
+  <tr>
+    <th style="border-right: 1px solid gray;">finite_beta_*pct</th>
+    <th>vmecpp_wout_finite_beta_*pct</th>
+  </tr>
+  <tr>
+    <td style="border-right: 1px solid gray;">
+      Contains information about:
+      <ul>
+        <li>Ideal MHD metrics with plasma</li>
+        <li>Miscellaneous information
+          <ul>
+            <li>the corresponding source plasma configuration ID in <b>default</b></li>
+            <li>the corresponding ideal MHD equilibrium ID in <b>vmecpp_wout_finite_beta_*pct</b></li>
+            <li>errors that might have occurred metrics computation.</li>
+          </ul>
+        </li>
+      </ul>
+    </td>
+    <td>
+      Same as <b>vmecpp_wout</b> above, corresponding to <b>finite_beta_*pct</b>
+    </td>
   </tr>
 </table>
 
-The columns `plasma_config_id` and `vmecpp_wout_id` are present in both parts and link the two in both directions.
+For each of the components above there is an identifier column (ending with `.id`), a JSON column containing a JSON-string representation, as well as one column per leaf in the nested JSON structure (with `.` separating the keys on the JSON path to the respective leaf).
 
 ## Uses
 
@@ -806,6 +884,7 @@ from constellaration.utils import visualization
 visualization.plot_flux_surfaces(vmecpp_wout, boundary)
 ```
 ![Plot of flux surfaces](assets/flux_surfaces.png)
+
 Save ideal MHD equilibrium to *VMEC2000 WOut* file:
 ```python
 import pathlib
@@ -813,6 +892,43 @@ from constellaration.utils import file_exporter
 
 file_exporter.to_vmec2000_wout_file(vmecpp_wout, pathlib.Path("vmec2000_wout.nc"))
 ```
+Match the boundaries from the **default** dataset to the corresponding metrics under a certain plasma condition:
+```python
+import datasets
+
+# Load default dataset to get the boundaries
+default_ds = datasets.load_dataset(
+    "proxima-fusion/constellaration",
+    split="train",
+    num_proc=4,
+)
+
+# Load finite beta 3% dataset
+finite_beta_3pct_ds = datasets.load_dataset(
+    "proxima-fusion/constellaration",
+    name="finite_beta_3pct",
+    split="train",
+    num_proc=4,
+)
+
+# Join the two datasets on plasma_config_id <-> misc.source_plasma_config_id
+default_df = (
+    default_ds
+    .to_pandas()
+    .set_index("plasma_config_id")
+    .filter(like="boundary.")
+)
+finite_beta_3pct_df = (
+    finite_beta_3pct_ds
+    .to_pandas()
+    .set_index("misc.source_plasma_config_id")
+)
+finite_beta_3pct_with_boundaries_df = (
+    finite_beta_3pct_df
+    .join(default_df, how="inner")  # joins on index
+    .reset_index(names="misc.source_plasma_config_id")
+)
+```
 
 ## Dataset Creation