ukaea · timothy-nunn · Oct 22, 2025 · Oct 21, 2025 · Oct 22, 2025 · Nov 5, 2025
diff --git a/documentation/development/standards.md b/documentation/development/standards.md
@@ -506,11 +506,6 @@ If a variable is intended to represent an engineering efficiency then it should
 
 ---------------------
 
-##### F-values
-
-Variables used within constraint equations to scale iteration variables (f-values) should start with the `f` prefix without an underscore before the next word.
-
----------------------
 
 ### Variable Length
 

diff --git a/documentation/eng-models/central-solenoid.md b/documentation/eng-models/central-solenoid.md
@@ -299,22 +299,20 @@ using `f_j_cs_start_pulse_end_flat_top` (iteration variable no. 41). The current
 calculated by taking into account the flux swing necessary to initiate and maintain plasma current.
 
 The current density in the central solenoid can be limited at BOP and at EOF. To limit the current 
-density at BOP, constraint equation no. 27 is used with iteration variable no. 39 (`fjohc0`). To 
-limit the current density at the EOF, constraint equation no. 26 should be turned on with iteration 
-variable no. 38 (`fjohc`).
+density at BOP, use constraint equation no. 27 (with a margin set by `fjohc0`). To 
+limit the current density at the EOF, constraint equation no. 26 should be turned on (with a margin set by `fjohc`).
 
 The critical current density *J*<sub>crit</sub> is a function of the temperature of the superconductor. 
 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 and iteration variable 
-no. 106 (`ftmargoh`).
+set using input parameter `tmargmin` 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.
 
 !!! tip "Recommended maximum current ratio"
-    For engineering feasibility, the centrepost currents at end of flat-top and beginning of pulse (`fjohc` and `fjohc0` respectively) shouldn't be set above 0.7.
+    For engineering feasibility, the currents at end of flat-top and beginning of pulse (set by the `fjohc` and `fjohc0` margins, respectively) shouldn't be set above 0.7.
 
 !!! note "Central solenoid current over time"
     A plot of how the central solenoid current varies over time can be found [here](../physics-models/pulsed-plant.md#burn-time)

diff --git a/documentation/eng-models/heating_and_current_drive/NBI/nbi_overview.md b/documentation/eng-models/heating_and_current_drive/NBI/nbi_overview.md
@@ -7,7 +7,7 @@
 
 If present, a neutral beam injection system needs sufficient space between the TF coils to be able to intercept the plasma tangentially. The major radius `radius_beam_tangency` at which the centre-line of the beam is tangential to the toroidal direction is user-defined using input parameter `f_radius_beam_tangency_rmajor`, which is the ratio of `radius_beam_tangency` to the plasma major radius `rmajor`.
 
-The maximum possible tangency radius `radius_beam_tangency_max` is determined by the geometry of the TF coils - see Figure 1, and this can be enforced using `icc = 20` with `ixc = 33` (`fradius_beam_tangency`). The thickness of the beam duct walls may be set using input parameter `dx_beam_shield`.
+The maximum possible tangency radius `radius_beam_tangency_max` is determined by the geometry of the TF coils - see Figure 1, and this can be enforced using `icc = 20`. The thickness of the beam duct walls may be set using input parameter `dx_beam_shield`.
 
 
 <figure markdown>

diff --git a/documentation/eng-models/power-conversion-and-heat-dissipation-systems.md b/documentation/eng-models/power-conversion-and-heat-dissipation-systems.md
@@ -31,7 +31,7 @@ This performs calculations on the first wall of the machine. Evaluations of the
 thermal stresses on this component lead to a measure of the maximum number of cycles to which the 
 first wall can be subjected, and hence to the minimum allowable length of each reactor cycle for a 
 specified first wall lifetime. The cycle time can be constrained to be at least the minimum value 
-by turning on constraint equation no. 42 with iteration variable no 67 (`ft_cycle_min`).
+by turning on constraint equation no. 42.
 
 # Power conversion cycle
 

diff --git a/documentation/eng-models/tf-coil-superconducting.md b/documentation/eng-models/tf-coil-superconducting.md
@@ -237,15 +237,11 @@ The toroidal field falls off at a rate $1/R$, with the peak value occurring at t
 
 Three constraints are relevant to the operating current density $J_{\mbox{op}}$ in the TF coils.
 
-- Criticial current (`constraint 33`): $J_{\mbox{op}}$ must not exceed the critical value $J_{\mbox{crit}}$.  Iteration variable 50 must be active (`fiooic`).  The current density margin can be set using the upper bound of `fiooic`:
-
-$$
-  J_{\mbox{op}} < \texttt{fiooic} \cdot J_{\mbox{crit}}
-$$
+- Criticial current (`constraint 33`): $f_{\text{iooic}}J_{\mbox{op}}$ must not exceed the critical value $J_{\mbox{crit}}$ where `fiooic` is a margin on the constraint that defaults to `0.7`.
 
 - 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 and iteration variable 54 (`ftmargtf`). 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 `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.  
 
 ---------
 
@@ -281,7 +277,7 @@ $$
 $$
 
 
-- `Constraint 35` -- To ensure that $J_{\mbox{op}}$ does not exceed the quench protection current density limit, $J_{TF,\mathrm{quench}}$, constraint equation no.\ 35 should be turned on with iteration variable 53 ( `fjprot`).
+- `Constraint 35` -- To ensure that $J_{\mbox{op}}$ does not exceed the quench protection current density limit, $J_{TF,\mathrm{quench}}$, turn on constraint equation no.\ 35.
 
 -----------------------
 

diff --git a/documentation/eng-models/tf-coil.md b/documentation/eng-models/tf-coil.md
@@ -983,7 +983,6 @@ $$
 | `n_tf_wp_pancakes`          | Number of turns in the toroidal direction (`i_tf_turns_integer = 1` only)                                                   | -                  | 10            | -    |
 | `dx_tf_turn_general`          | TF turn squared size                                                                                                        | -                  | No default    | m    |
 | `dx_tf_turn_cable_space_general`         | TF cable diameter size                                                                                                      | -                  | No default    | m    |
-| `f_t_turn_tf`        | f-value for TF turn squared size constraint (icc = 86)                                                                      | 175                | 1.            | m    |
 | `t_turn_tf_max`      | Maximum turn squared size for constraint (icc = 86)                                                                         | -                  | 0.05          | m    |
 | `c_tf_turn`              | Current per turn <br> Overwitten if `dx_tf_turn_general` is set by the user                                                          | ixc = 60           | $70.10^3$     | A    |
 | `dx_tf_turn_insulation`           | Turn insulation layer thickness                                                                                             | -                  | $0.8.10^{-3}$ | m    |

diff --git a/documentation/eng-models/vacuum-vessel.md b/documentation/eng-models/vacuum-vessel.md
@@ -9,8 +9,7 @@ A model has been implemented, based on
 
 This model takes account of the currents induced in both the vacuum vessel and the steel TF coil structures.
 
-Constraint 65 implements this model, by applying a maximum permitted stress in the vacuum vessel.  
-`fmaxvvstress` f-value for constraint 65. Iteration variable 113.   
+Constraint 65 implements this model, by applying a maximum permitted stress in the vacuum vessel.   
 `theta1_coil` An angle, shown as $\theta_1$ in Figure 1, relating to the shape of the TF coil conductor centre-line (degrees).   
 `theta1_vv` An angle, shown as $\theta_1$ in Figure 1, relating to the shape of the vacuum vessel centre-line (degrees).   
 `max_vv_stress` The maximum permissible maximum shear stress in the vacuum vessel (Pa) (as used in the Tresca criterion).    

diff --git a/documentation/fusion-devices/inertial.md b/documentation/fusion-devices/inertial.md
@@ -28,7 +28,7 @@ Switch `ifetyp` defines the type of device that is assumed; this varies widely b
 
 Switch `ifedrv` defines how the code calculates the drivers efficiency and target gain - these are the primary outputs required from the physics part of the model. For the SOMBRERO and OSIRIS cases (`ifedrv = 1` and `ifedrv = 2`, respectively) the driver efficiency and gain are calculated from curves of these parameters as functions of the driver energy, via the two arrays`etaxe(1:10)` and `gainve(1:10)` respectively; the element number corresponds to the driver energy in MJ, and outside the range 1-10 MJ the curves are extrapolated linearly. Finally, for the `ifedrv = 0` case, the user inputs single values for the driver efficiency (`drveff`) and target gain (`tgain`).
 
-Constraint equation no. 50 can be turned on to enable the ignition repetition rate to remain below a user-specified upper limit (`rrmax`); iteration variable no. 86 (`frrmax`) is the associated f-value. The other iteration variables relevant for the IFE model are nos. 81-85 (`edrive`, `drveff`, `tgain`, `chrad` and `pdrive`).
+Constraint equation no. 50 can be turned on to enable the ignition repetition rate to remain below a user-specified upper limit (`rrmax`). The other iteration variables relevant for the IFE model are nos. 81-85 (`edrive`, `drveff`, `tgain`, `chrad` and `pdrive`).
 
 [^1]: P. J. Knight, *"PROCESS 3009: Incorporation of Inertial Fusion Energy Model"*, Work File Note F/MI/PJK/PROCESS/CODE/032
 [^2]: Bourque et al., *"Overview of the OSIRIS IFE Reactor Conceptual Design"*, Fusion Technology **21** (1992) 1465

diff --git a/documentation/fusion-devices/spherical-tokamak.md b/documentation/fusion-devices/spherical-tokamak.md
@@ -18,9 +18,9 @@
 
 2. Spherical tokamaks have resistive TF coils that combine into a single centrepost at the centre of the machine. The centrepost is constructed from copper (as are the outboard TF coil sections), and tapered length ways so that it is narrowest at the midplane of the device. Routine `CNTRPST` calculates various parameters relevant to the centrepost, including the pump pressure, maximum temperature and pip radius, and these may be limited using constraint equations 43 to 45 of required:
     * Equation 43 is a consistency equation for the average centrepost temperature.
-    * Equation 44 can be used to limit the peak centrepost temperature to a maximum value (`temp_cp_max`) using iteration variable no. 68 (`fptemp`).
-    * Equation 45 can be used to force a lower; limit to the edge safety factor *q$_{lim}$* using iteration variable no. 71 (`fq95_min`).
-    Equation 46 can be used to apply an upper limit to the ratio of plasma current to TF coil ("rod") current , using iteration variable no. 72 (`fipir`)<br></br>
+    * Equation 44 can be used to limit the peak centrepost temperature to a maximum value (`temp_cp_max`).
+    * Equation 45 can be used to force a lower; limit to the edge safety factor *q$_{lim}$*.
+    Equation 46 can be used to apply an upper limit to the ratio of plasma current to TF coil ("rod") current.<br></br>
 
 3. A gaseous divertor model is used, and a simple divertor heat load calculation is employed, rather than the more complex divertor model assumed for conventional aspect ratio tokamaks. <br></br>
 

diff --git a/documentation/fusion-devices/stellarator.md b/documentation/fusion-devices/stellarator.md
@@ -63,7 +63,7 @@ icc = 83 * Radial build at critical location
 icc = 91 * ECRH ignitability (checks critical density at ignition point)
 ```
 
-A reasonable start for iteration variables (next to the required f-values) are:
+A reasonable start for iteration variables are:
 
 ```
 ixc = 2 * Toroidal Magnetic field strength
@@ -123,15 +123,15 @@ Stellarators try to achieve zero plasma current in order to allow safe divertor
 ### Beta limit
 
 The stellarator version calculates the plasma beta based on the input parameter and it is thus not necessary to Differently to the tokamak version, 
-The beta limit is assumed to be 5%, based on 3-D MHD calculations[^7]. To apply the beta limit, constraint equation no. 24 should be turned on with iteration variable no. 36 (`fbeta_max`).
+The beta limit is assumed to be 5%, based on 3-D MHD calculations[^7]. To apply the beta limit, constraint equation no. 24 should be turned on.
 
 ### Density limit
 
 The density limit relevant to certain stellarators experiments has been proposed to be[^8]
 
 $n_{max} = 0.25(PB_0/R_0a^2_p)^{1/2}$
 
-where $n$ is the line-averaged electron density in units of $10^{20} m^{-3}$, $p$ is the absorbed heating power (MW), $B_0$ is the on-axis field (t), $R_0$ is the major radius (m), and $a_p$ is the plasma minor radius (m). To enforce the Sudo density limit, turn on constraint equation no. 5 with iteration variable no. 9 (`fdene`).
+where $n$ is the line-averaged electron density in units of $10^{20} m^{-3}$, $p$ is the absorbed heating power (MW), $B_0$ is the on-axis field (t), $R_0$ is the major radius (m), and $a_p$ is the plasma minor radius (m). To enforce the Sudo density limit, turn on constraint equation no. 5 (`fdene != 1` can be used to scale the constraint bound).
 
 Note that the Sudo limit is a radiation based density limit and it is unclear how well this limit extrapolates to reactor parameters, especially as no impurity dependence e.g. is present in the Sudo model.
 PROCESS features an impurity dependent radiation module already which can be used with `icc=17` and by setting the `f_nd_impurity_electrons` vector.
@@ -226,7 +226,7 @@ f_a_tf_turn_cable_copper = 0.7 *Copper fraction of cable conductor (TF coils), S
 tftmp = 4.75 *Peak helium coolant temperature in TF coils and PF coils (K)
 temp_tf_cryo = 4.75 * Temperature in TF coils, required for plant efficiency (K)
 f_a_tf_turn_cable_space_extra_void = 0.3 *Coolant fraction of TF coil leg (itfsup=0) this is the same for conductor and strand!
-fiooic = 0.78 *Fraction TF coil critical current to operation current (should be iteration variable!)
+fiooic = 0.78 * Fraction TF coil critical current to operation current (constraint margin)
 v_tf_coil_dump_quench_max_kv = 12.64 * Max voltage across tf coil during quench (kV)
 t_tf_superconductor_quench = 20 * Dump time (should be iteration variable)
 dr_tf_nose_case = 0.1 * Thickness TF Coil case (for stellarators: Also for toroidal direction)

diff --git a/documentation/io/input-guide.md b/documentation/io/input-guide.md
@@ -44,9 +44,6 @@ equation 2. A comment on the same line is recommended:
 icc = 2 * Global power balance (consistency equation)
 ```
 
-Some constraints have `f-value` variables. These must be set as iteration variables, 
-which are discussed below.
-
 
 !!! Info "Constraints"  
     A full list of constraints is given on the variable description page in the row labelled 

diff --git a/documentation/physics-models/fusion_reactions/plasma_reactions.md b/documentation/physics-models/fusion_reactions/plasma_reactions.md
@@ -222,15 +222,15 @@ If the plasma is classed as ignited then the injected heating power density is n
 
 This constraint can be activated by stating `icc = 9` in the input file.
 
-The value of `p_fusion_total_max_mw` can be set to the desired maximum fusion power. The scaling value `fp_fusion_total_max_mw` can be varied also.
+The value of `p_fusion_total_max_mw` can be set to the desired maximum fusion power.
 
 ---------------------------------
 
 ### Q value lower limit
 
 This constraint can be activated by stating `icc = 28` in the input file.
 
-The value of `big_q_plasma_min` can be set to the minimum desired $Q_{\text{plasma}}$ value. The scaling value `fbig_q_plasma_min` can be varied also.
+The value of `big_q_plasma_min` can be set to the minimum desired $Q_{\text{plasma}}$ value.
 
 -------------------------
 

diff --git a/documentation/physics-models/plasma_beta/plasma_beta.md b/documentation/physics-models/plasma_beta/plasma_beta.md
@@ -405,8 +405,6 @@ This constraint can be activated by stating `icc = 6` in the input file [^6].
 
 The limiting value of $\epsilon\beta_p$ is be set using input parameter `beta_poloidal_eps_max`.
 
-The scaling value `fbeta_poloidal_eps` can be varied also.
-
 !!! note "Origin of the $\epsilon\beta_p$ limit"
 
     High poloidal beta shots in TFTR were performed[^6] and it was found that as $\beta_p$,
@@ -427,8 +425,6 @@ It is the general setting of the $\beta$ limit depending on the $\beta_{\text{N}
 The upper limit value of beta is calculated by `calculate_beta_limit()`. The beta
 coefficient $g$ can be set using `beta_norm_max`, depending on the setting of [`i_beta_norm_max`](#setting-the-beta--coefficient). It can be set directly or follow some relation.
 
-The scaling value `fbeta_max` can be varied also.
-
 **It is recommended to have this constraint on as it is a plasma stability model**
 
 --------------------
@@ -437,15 +433,15 @@ The scaling value `fbeta_max` can be varied also.
 
 This constraint can be activated by stating `icc = 48` in the input file.
 
-The value of `beta_poloidal_max` can be set to the desired maximum poloidal beta. The scaling value `fbeta_poloidal` can be varied also.
+The value of `beta_poloidal_max` can be set to the desired maximum poloidal beta.
 
 -------------------
 
 ### Beta lower limit
 
 This constraint can be activated by stating `icc = 84` in the input file.
 
-The value of `beta_vol_avg_min` can be set to the desired minimum total beta. The scaling value `fbeta_min` can be varied also.
+The value of `beta_vol_avg_min` can be set to the desired minimum total beta.
 
 [^0]: F. Troyon et.al,  “Beta limit in tokamaks. Experimental and computational status,” Plasma Physics and Controlled Fusion, vol. 30, no. 11, pp. 1597–1609, Oct. 1988, doi: https://doi.org/10.1088/0741-3335/30/11/019.
 

diff --git a/documentation/physics-models/plasma_composition.md b/documentation/physics-models/plasma_composition.md
@@ -236,7 +236,5 @@ This constraint can be activated by stating `icc = 78` in the input file.
 
 The minimum impurity fraction required from the Reinke module can be set with, `fzmin`
 
-The scaling value `freinke` can be varied also.
-
 
 [^1]: H. Lux, R. Kemp, D.J. Ward, M. Sertoli, Impurity radiation in DEMO systems modelling, Fusion Engineering and Design, Volume 101, 2015, Pages 42-51, ISSN 0920-3796, https://doi.org/10.1016/j.fusengdes.2015.10.002.
diff --git a/documentation/physics-models/plasma_confinement.md b/documentation/physics-models/plasma_confinement.md
@@ -707,9 +707,6 @@ This constraint can be activated by stating `icc = 62` in the input file.
 
 The value of `f_alpha_energy_confinement_min` can be set to the desired minimum total ratio between the alpha confinement and energy confinement times.
 
- The scaling value `falpha_energy_confinement` can be varied also.
-
-
 [^1]: N. A. Uckan, International Atomic Energy Agency, Vienna (Austria) and ITER Physics Group, "ITER physics design guidelines: 1989", no. No. 10. Feb. 1990.
 [^2]: T.C. Hender et al., 'Physics Assessment of the European Reactor Study', AEA FUS 172, 1992.
 [^3]: J. P. Christiansen et al., “Global energy confinement H-mode database for ITER,” Nuclear Fusion, vol. 32, no. 2, pp. 291-338, Feb. 1992, doi: https://doi.org/10.1088/0029-5515/32/2/i11.

diff --git a/documentation/physics-models/plasma_current/plasma_current.md b/documentation/physics-models/plasma_current/plasma_current.md
@@ -677,7 +677,7 @@ $$
 
 This constraint can be activated by stating `icc = 41` in the input file.
 
-The value of `tohsm` can be set to the required minimum plasma current ramp up time at the start of a pulse. The scaling value `ft_current_ramp_up` can be varied also
+The value of `tohsm` can be set to the required minimum plasma current ramp up time at the start of a pulse.
 
 The calculated plasma current ramp up time `t_plant_pulse_plasma_current_ramp_up` is dictated by the [pulsed plant operation configuration](../pulsed-plant.md).
 
@@ -696,7 +696,7 @@ $$
 $$
 
 In this case $I_{\text{cp}}$ is the total current going up the centrepost in a spherical tokamak.
-This constraint was initially though to prevent instabilities and act as a guideline to limit power dissipation when generating new designs. The scaling value for the constraint, `fipir` can be varied also.
+This constraint was initially though to prevent instabilities and act as a guideline to limit power dissipation when generating new designs.
 
  The origins of the relation should be seen in early spherical tokamak papers not yet referenced here.
-Original file line number
+Diff line change
@@ Expand Up @@
     ---------------------
-    ##### F-values
-    Variables used within constraint equations to scale iteration variables (f-values) should start with the `f` prefix without an underscore before the next word.
-    ---------------------
     ### Variable Length
@@ Expand Down @@
Original file line number	Diff line number	Diff line change
Expand Up		@@ -236,7 +236,5 @@ This constraint can be activated by stating `icc = 78` in the input file.

		The minimum impurity fraction required from the Reinke module can be set with, `fzmin`

		The scaling value `freinke` can be varied also.


		[^1]: H. Lux, R. Kemp, D.J. Ward, M. Sertoli, Impurity radiation in DEMO systems modelling, Fusion Engineering and Design, Volume 101, 2015, Pages 42-51, ISSN 0920-3796, https://doi.org/10.1016/j.fusengdes.2015.10.002.