CoronelBuendia · Oct 15, 2026 · Oct 15, 2026 · Oct 15, 2026 · Oct 15, 2026 · Oct 15, 2026
@@ -464,7 +464,7 @@ The critical current density *J*<sub>crit</sub> is a function of the temperature
 The temperature margin $\Delta$*T* is the difference between the current sharing temperature and the 
 operating temperature.  The current sharing temperature is the temperature at which *J*<sub>crit</sub> 
 is equal to the operating current density *J*<sub>op</sub>. The minimum allowed $\Delta$*T* can be 
-set using input parameter `tmargmin` together with constraint equation no. 60.
+set using input parameter `temp_cs_superconductor_margin_min` together with constraint equation no. 60.
 
 It is recommended that EITHER the temperature margin constraint (60), OR the current density 
 constraints (26 and 27) are activated.

@@ -241,7 +241,7 @@ Three constraints are relevant to the operating current density $J_{\mbox{op}}$
 
 - Temperature margin (`constraint 36`) -- The critical current density $J_{\mbox{crit}}$ falls with 
   the temperature of the superconductor. The temperature margin $\Delta T$ is the difference between the current sharing temperature (at which $J_{\mbox{crit}}$ would be equal to $J_{\mbox{op}}$) and the operating temperature. The minimum allowed $\Delta T$
-can be set using `tmargmin` together with constraint equation 36. Note that if the temperature margin is positive, $J_{\mbox{op}}$ is guaranteed to be lower than \jcrit, and so constraints 33 and 36 need not both be turned on. It is recommended that only one of these two constraints is activated.  
+can be set using `temp_tf_superconductor_margin_min` together with constraint equation 36. Note that if the temperature margin is positive, $J_{\mbox{op}}$ is guaranteed to be lower than \jcrit, and so constraints 33 and 36 need not both be turned on. It is recommended that only one of these two constraints is activated.  
 
 ---------
 

@@ -91,7 +91,7 @@ icc = 35
 *--------------------------*
 icc = 36
 * Minimum allowable temperature margin [K]
-tmargmin = 1.5
+temp_tf_superconductor_margin_min = 1.5
 
 * CS coil temp margin lower limit *
 *---------------------------------*

@@ -383,7 +383,7 @@ dr_tf_wp_with_insulation = 0.5153787768966674 * radial thickness of winding pack
 dx_tf_turn_steel = 0.008012110032981922 * TF coil conduit case thickness (m) (`iteration variable 58`)
 dx_tf_wp_insulation   = 0.008 * Thickness of the ground insulation layer surrounding (m)
 temp_cs_superconductor_margin_min = 1.5 * minimum allowable temperature margin ; CS (K)
-tmargmin = 1.5 * minimum allowable temperature margin ; TFC AND CS (K)
+temp_tf_superconductor_margin_min = 1.5 * minimum allowable temperature margin ; TF (K)
 v_tf_coil_dump_quench_max_kv    = 10.0 * max voltage across TF coil during quench (kV) (`iteration variable 52`)
 f_a_tf_turn_cable_space_extra_void     = 0.3 * coolant fraction of TFC 'cable' (`i_tf_sup=1`); or of TFC leg (`i_tf_sup=0`)
 flu_tf_neutron_fast_max = 1e22 * max fluence in the TF coil

@@ -95,7 +95,7 @@ icc = 35
 *--------------------------*
 icc = 36
 * Minimum allowable temperature margin [K]
-tmargmin = 1.5
+temp_tf_superconductor_margin_min = 1.5
 
 * CS coil temp margin lower limit *
 *---------------------------------*

@@ -96,7 +96,7 @@ icc = 35
 *--------------------------*
 icc = 36
 * Minimum allowable temperature margin [K]
-tmargmin = 1.5
+temp_tf_superconductor_margin_min = 1.5
 
 * CS coil temp margin lower limit *
 *---------------------------------*

@@ -102,7 +102,7 @@ icc = 35
 *--------------------------*
 icc = 36
 * Minimum allowable temperature margin [K]
-tmargmin = 1.5
+temp_tf_superconductor_margin_min = 1.5
 
 * CS coil temp margin lower limit *
 *---------------------------------*

@@ -483,6 +483,10 @@
     "temp_plasma_separatrix_kev": "temp_plasma_separatrix_electron_kev",
     "iohcl": "i_cs_use",
     "beta_total_vol_avg": None,
+    "tmargmin": [
+        "temp_tf_superconductor_margin_min",
+        "temp_cs_superconductor_margin_min",
+    ],
 }
 
 OBS_VARS_HELP = {

@@ -1218,27 +1218,6 @@ def check_process(inputs, data):  # noqa: ARG001
                 fsum=fsum,
             )
 
-    # Check that the temperature margins are not overdetermined
-    if data.tfcoil.tmargmin > 0.0001:
-        # This limit has been input and will be applied to both TFC and CS
-        if data.tfcoil.temp_tf_superconductor_margin_min > 0.0001:
-            logger.error(
-                "temp_tf_superconductor_margin_min and tmargmin should not both"
-                " be specified in IN.DAT"
-                " temp_tf_superconductor_margin_min has been ignored",
-                stacklevel=2,
-            )
-        if data.tfcoil.temp_cs_superconductor_margin_min > 0.0001:
-            logger.error(
-                "temp_cs_superconductor_margin_min and tmargmin should not both"
-                " be specified in IN.DAT"
-                " temp_cs_superconductor_margin_min has been ignored",
-                stacklevel=2,
-            )
-
-        data.tfcoil.temp_tf_superconductor_margin_min = data.tfcoil.tmargmin
-        data.tfcoil.temp_cs_superconductor_margin_min = data.tfcoil.tmargmin
-
     if (
         data.physics.tauee_in > 1e-10
         and data.physics.i_confinement_time != ConfinementTimeModel.NSTX_GYRO_BOHM

@@ -849,7 +849,6 @@ def bounds(self) -> tuple[NumberType | None, NumberType | None]:
     "dx_tf_wp_insulation": InputVariable("tfcoil", float, range=(0.0, 0.1)),
     "life_plant": InputVariable("costs", float, range=(1.0, 100.0)),
     "tmain": InputVariable("costs", float, range=(0.0, 100.0)),
-    "tmargmin": InputVariable("tfcoil", float, range=(0.0, 20.0)),
     "temp_cs_superconductor_margin_min": InputVariable(
         "tfcoil", float, range=(0.0, 20.0)
     ),

@@ -2,6 +2,7 @@
 
 from __future__ import annotations
 
+import re
 from typing import TYPE_CHECKING
 
 import numpy as np
@@ -15,6 +16,35 @@
 __all__ = ["plot_equality_constraint_equations", "plot_inequality_constraint_equations"]
 
 
+def _var_label_formatting(var_label: str) -> str:
+    """Format normalised-residue variable labels for display.
+
+    If ``var_label`` is a string ending with ``"_normalised_residue"``, the
+    suffix is removed, trailing underscores are stripped, and remaining
+    underscores are replaced with spaces. Underscores appearing within LaTeX
+    expressions delimited by ``$...$`` or ``$$...$$`` are preserved.
+
+    Parameters
+    ----------
+    var_label : str
+        Variable label to format. Non-string values, or strings that do not end
+        with ``"_normalised_residue"``, are returned unchanged.
+
+    Returns
+    -------
+    str
+        The formatted label if applicable, otherwise the original input value.
+    """
+    if isinstance(var_label, str) and var_label.endswith("_normalised_residue"):
+        var_label = var_label.removesuffix("_normalised_residue").rstrip("_")
+        parts = re.split(r"(\$\$.*?\$\$|\$[^$]*\$)", var_label)
+        var_label = "".join(
+            part.replace("_", " ") if i % 2 == 0 else part
+            for i, part in enumerate(parts)
+        )
+    return var_label
+
+
 def plot_equality_constraint_equations(axis: plt.Axes, m_file_data: MFile, scan: int):
     """Plot the equality constraints for a solution and their normalised residuals
 
@@ -45,6 +75,7 @@ def plot_equality_constraint_equations(axis: plt.Axes, m_file_data: MFile, scan:
 
         # Use the variable name if available, else fallback to "eq_conXXX"
         var_label = con_names.get(n, f"eq_con{n:03d}")
+        var_label = _var_label_formatting(var_label)
 
         # Normalized residual of the constraint
         con_norm_residual = m_file_data.data[f"eq_con{n:03d}"].get_scan(scan)
@@ -53,14 +84,6 @@ def plot_equality_constraint_equations(axis: plt.Axes, m_file_data: MFile, scan:
         con_units_raw = m_file_data.data[f"eq_units_con{n:03d}"].get_scan(scan)
         con_units = str(con_units_raw).strip("'`")
 
-        # Remove '_normalised_residue' from the label if present
-        if isinstance(var_label, str) and var_label.endswith("_normalised_residue"):
-            var_label = var_label.replace("_normalised_residue", "")
-
-            # Remove trailing underscores and replace underscores between words with
-            # spaces
-            var_label = var_label.rstrip("_").replace("_", " ")
-
         # Plot the normalised residual as a bar
         axis.barh(
             n_plot,
@@ -143,6 +166,7 @@ def plot_inequality_constraint_equations(axis: plt.Axes, m_file: MFile, scan: in
 
         # Use the variable name if available, else fallback to "ineq_conXXX"
         var_label = con_names.get(n, f"ineq_con{n:03d}")
+        var_label = _var_label_formatting(var_label)
 
         # Normalized residual of the constraint
         con_residual_norm = m_file.data[f"ineq_con{n:03d}"].get_scan(scan)
@@ -167,11 +191,6 @@ def plot_inequality_constraint_equations(axis: plt.Axes, m_file: MFile, scan: in
             zorder=0,
         )
 
-        # Remove '_normalised_residue' from the label if present
-        if isinstance(var_label, str) and var_label.endswith("_normalised_residue"):
-            var_label = var_label.replace("_normalised_residue", "")
-            var_label = var_label.rstrip("_").replace("_", " ")
-
         # Calculate the normalised constraint threshold depending if the constraint is an
         # upper
         # or lower limit

@@ -997,18 +997,19 @@ def constraint_equation_35(constraint_registration, data):
     )
 
 
-@ConstraintManager.register_constraint(36, "K", ">=")
+@ConstraintManager.register_constraint(36, "A/m²", "<=")
 def constraint_equation_36(constraint_registration, data):
     """Equation for TF coil s/c temperature margin lower limit (SCTF)
+    by means of the actual to critical current density
 
-    temp_tf_superconductor_margin:
-        TF coil temperature margin (K)
-    temp_tf_superconductor_margin_min:
-        minimum allowable temperature margin : TF coils (K)
+    j_tf_wp:
+        winding pack current density (A/m²)
+    j_tf_wp_temp_margin:
+        superconducting strand critical current density (A/m²)
     """
-    return geq(
-        data.tfcoil.temp_tf_superconductor_margin,
-        data.tfcoil.temp_tf_superconductor_margin_min,
+    return leq(
+        data.tfcoil.j_tf_wp,
+        data.tfcoil.j_tf_wp_temp_margin,
         constraint_registration,
     )
 

@@ -232,10 +232,10 @@ class NumericsData:
             "Plasma injected power (Pₐᵤₓ) upper limit      ",
             "TF coil case stress upper limit  ",
             "TF coil conduit stress upper limit ",
-            "TF coil superconductor critical current density upper limit  ",
+            r"TF coil superconductor $j_{\mathrm{crit}}$ upper limit (ratio) ",
             "TF quench dump voltage upper limit         ",
             "TF quench hotspot current density upper limit         ",
-            "TF coil superconductor temperature margin lower limit ",
+            r"TF coil superconductor $j_{\mathrm{crit}}$ upper limit (T margin) ",
             "HCD normalised current drive efficiency (γ) upper limit        ",  # noqa: RUF001
             "FW coolant temperature rise upper limit ",
             "FW peak temperature limit",
@@ -335,7 +335,8 @@ class NumericsData:
     * (33) I_op / I_critical (TF coil) (SCTF) (itv 50,56,57,58,59,60,24)
     * (34) Dump voltage upper limit (SCTF) (itv 51,52,56,57,58,59,60,24)
     * (35) TF Quench Hotspot J limit (SCTF) (itv 53,56,57,58,59,60,24)
-    * (36) TF coil temperature margin lower limit (SCTF) (itv 54,55,56,57,58,59,60,24)
+    * (36) TF coil superconductor critical current density upper limit (T margin) (SCTF)
+    (itv 54,55,56,57,58,59,60,24)
     * (37) Current drive gamma upper limit (itv 40,47)
     * (38) First wall coolant temperature rise upper limit (itv 62)
     * (39) First wall peak temperature upper limit (itv 63)

@@ -337,13 +337,16 @@ class TFData:
     """
 
     j_tf_bus: float = 1.25e6
-    """bussing current density (A/m2)"""
+    """bussing current density (A/m²)"""
 
     j_crit_str_tf: float = 0.0
     """j_crit_str : superconductor strand critical current density under operating
-    conditions (A/m2). Necessary for the cost calculation in $/kAm
+    conditions (A/m²).
     """
 
+    j_tf_wp_temp_margin: float = 0.0
+    """j_tf_wp_temp_margin : allowable TF coil winding pack current density, for specified temperature margin (A/m²)"""
+
     j_crit_str_0: list[float] = field(
         default_factory=lambda: np.array([
             596905475.80390120,
@@ -357,18 +360,18 @@ class TFData:
             865652122.9071957,
         ])
     )
-    """j_crit_str_pf_0 : superconductor strand critical current density at 6 T and 4.2 K (A/m2)
+    """j_crit_str_pf_0 : superconductor strand critical current density at 6 T and 4.2 K (A/m²)
     Necessary for the cost calculation in $/kAm
     """
 
     j_tf_wp_critical: float = 0.0
-    """critical current density for winding pack (A/m2)"""
+    """critical current density for winding pack (A/m²)"""
 
     j_tf_wp_quench_heat_max: float = 0.0
-    """allowable TF coil winding pack current density, for dump temperature rise protection (A/m2)"""
+    """allowable TF coil winding pack current density, for dump temperature rise protection (A/m²)"""
 
     j_tf_wp: float = 0.0
-    """winding pack engineering current density (A/m2)"""
+    """winding pack engineering current density (A/m²)"""
 
     j_tf_coil_full_area: float = 0.0
     """Inboard leg mid-plane full coil area current density (A/m²)
@@ -670,12 +673,6 @@ class TFData:
     temp_cs_superconductor_margin_min: float = 0.0
     """minimum allowable temperature margin : CS (K)"""
 
-    tmargmin: float = 0.0
-    """minimum allowable temperature margin : TFC AND CS (K)"""
-
-    temp_margin: float = 0.0
-    """temperature margin (K)"""
-
     temp_tf_superconductor_margin: float = 0.0
     """TF coil superconductor temperature margin (K)"""
 

@@ -737,7 +737,7 @@ def calc_u_unplanned_magnets(self, output: bool) -> float:
         This routine calculates the unplanned unavailability of the magnets,
         using the methodology outlined in the 2014 EUROfusion
         RAMI report.
-        2014 EUROfusion RAMI report, &quot;Availability in PROCESS&quot;
+        2014 EUROfusion RAMI report, "Availability in PROCESS";
 
         Parameters
         ----------
@@ -750,12 +750,11 @@ def calc_u_unplanned_magnets(self, output: bool) -> float:
             unplanned unavailability of magnets
         """
         # Magnet temperature margin limit (K)
-        # Use the lower of the two values.  Issue #526
+        # Use the lower of the two values.  Issue #527
         tmargmin = min(
             self.data.tfcoil.temp_tf_superconductor_margin_min,
             self.data.tfcoil.temp_cs_superconductor_margin_min,
         )
-        mag_temp_marg_limit = tmargmin
 
         # Magnet maintenance time (years)
         mag_main_time = 0.5e0
@@ -768,11 +767,11 @@ def calc_u_unplanned_magnets(self, output: bool) -> float:
         # Point at which risk of unplanned unavailability increases
         # conf_mag is the c factor, which determines the temperature margin at which
         # lifetime starts to decline.
-        start_of_risk = mag_temp_marg_limit / self.data.costs.conf_mag
+        start_of_risk = tmargmin / self.data.costs.conf_mag
 
         # Determine if temperature margin is in region with risk of
         # unplanned unavailability
-        if self.data.tfcoil.temp_margin >= start_of_risk:
+        if self.data.tfcoil.temp_tf_superconductor_margin >= start_of_risk:
             u_unplanned_magnets = mag_min_u_unplanned
         else:
             # Linear decrease in expected lifetime when approaching the limit
@@ -782,7 +781,7 @@ def calc_u_unplanned_magnets(self, output: bool) -> float:
                     self.data.costs.t_plant_operational_total_yrs
                     / (start_of_risk - tmargmin)
                 )
-                * (self.data.tfcoil.temp_margin - tmargmin),
+                * (self.data.tfcoil.temp_tf_superconductor_margin - tmargmin),
             )
             u_unplanned_magnets = mag_main_time / (t_life + mag_main_time)
 
@@ -792,7 +791,7 @@ def calc_u_unplanned_magnets(self, output: bool) -> float:
         if output:
             po.ocmmnt(self.outfile, "Magnets:")
             po.oblnkl(self.outfile)
-            po.ovarre(
+            po.ovarre(  # This is of questionable interest...
                 self.outfile, "Minimum temperature margin (K)", "(tmargmin)", tmargmin
             )
             po.ovarre(
@@ -804,8 +803,8 @@ def calc_u_unplanned_magnets(self, output: bool) -> float:
             po.ovarre(
                 self.outfile,
                 "Temperature Margin (K)",
-                "(temp_margin)",
-                self.data.tfcoil.temp_margin,
+                "(temp_tf_superconductor_margin_min)",
+                self.data.tfcoil.temp_tf_superconductor_margin,
                 "OP ",
             )
             po.ovarre(

@@ -417,15 +417,15 @@ def winding_pack_total_size(
         # jcrit for this bmax:
         jcrit_vector[k] = jcrit_from_material(
             b_max_k[k],
-            data.tfcoil.tftmp + data.tfcoil.tmargmin,
+            data.tfcoil.tftmp + data.tfcoil.temp_tf_superconductor_margin_min,
             data.tfcoil.i_tf_sc_mat,
             data.tfcoil.bcritsc,
             data.tfcoil.f_a_tf_turn_cable_copper,
             data.tfcoil.fhts,
             data.tfcoil.tcritsc,
             data.tfcoil.f_a_tf_turn_cable_space_extra_void,
             data.tfcoil.j_tf_wp,
-        )  # Get here a temperature margin from data.tfcoil.tmargtf.
+        )
 
     # The operation current density weighted with the global iop/icrit fraction
     lhs[:] = data.constraints.f_j_tf_wp_critical_max * jcrit_vector