Replace iterative beta idempotence with an explicit fixed-point solve
PROCESS previously relied on repeated model evaluations and the optimisation problem to obtain a self-consistent value of the total plasma beta. In particular, beta_total_vol_avg was included as an iteration variable (ixc = 5) and equality constraint 1 enforced consistency between the total beta and its thermal, fast-alpha and beam components.
This change makes that coupling explicit by solving plasma beta internally as a fixed-point problem.
PROCESS now solves
$$
\beta =
\beta_{\mathrm{fast\ alpha}}
+
\beta_{\mathrm{beam}}
+
\beta_{\mathrm{thermal}}
$$
using scipy.optimize.fixed_point, with a maximum of 20 iterations.
The thermal beta is calculated using the existing PlasmaBeta.calculate_plasma_beta() method from process.models.physics.physics.
The implementation adds two small methods to Caller:
_calculate_beta() evaluates the PROCESS models at a trial value of beta_total_vol_avg and returns the corresponding calculated total beta._solve_beta_fixed_point() repeatedly evaluates this mapping until a self-consistent beta is obtained.
The trial beta is applied after the optimisation variables are set in _call_models_once(). This is important because it prevents set_scaled_iteration_variable() from overwriting the beta being tested by the fixed-point solver.
The existing final-output/MFILE idempotence machinery has otherwise been retained; this change is intended specifically to replace the implicit iterative treatment of plasma beta rather than remove unrelated idempotence handling.
Validation
The low_aspect_ratio_DEMO.IN.DAT regression case was run with beta_total_vol_avg removed as an optimisation iteration variable while retaining beta consistency constraint 1.
beta_total_vol_avg is absent from the optimisation solution vector, confirming that VMCON is no longer directly varying beta.
Nevertheless, beta consistency constraint 1 is satisfied exactly:
⟨β⟩ consistency = 0.03718848552085542, with a constraint residual of 0.0.
The final total plasma beta is
beta_total_vol_avg = 0.03718848552085542, composed of a thermal beta of 0.03250787755343900, a fast-alpha beta of 0.004680607967416424, and zero beam beta.
The resulting solution is essentially the same as the corresponding main solution in which beta_total_vol_avg is retained as ixc = 5.
This demonstrates that the beta closure is now being supplied internally by the fixed-point calculation rather than by the optimiser varying beta_total_vol_avg.
impact
At this stage, constraint 1 has deliberately been retained as an independent validation of the new fixed-point calculation.
Because beta_total_vol_avg is now solved internally by the fixed-point calculation, it no longer needs to be exposed to the optimiser as iteration variable ixc = 5. Once the fixed-point implementation is validated, beta consistency constraint icc = 1 can also be removed, since the same closure is already enforced internally during every model evaluation.
Replace iterative beta idempotence with an explicit fixed-point solve
PROCESS previously relied on repeated model evaluations and the optimisation problem to obtain a self-consistent value of the total plasma beta. In particular,
beta_total_vol_avgwas included as an iteration variable (ixc = 5) and equality constraint 1 enforced consistency between the total beta and its thermal, fast-alpha and beam components.This change makes that coupling explicit by solving plasma beta internally as a fixed-point problem.
PROCESS now solves
using
scipy.optimize.fixed_point, with a maximum of 20 iterations.The thermal beta is calculated using the existing
PlasmaBeta.calculate_plasma_beta()method fromprocess.models.physics.physics.The implementation adds two small methods to
Caller:_calculate_beta()evaluates the PROCESS models at a trial value ofbeta_total_vol_avgand returns the corresponding calculated total beta._solve_beta_fixed_point()repeatedly evaluates this mapping until a self-consistent beta is obtained.The trial beta is applied after the optimisation variables are set in
_call_models_once(). This is important because it preventsset_scaled_iteration_variable()from overwriting the beta being tested by the fixed-point solver.The existing final-output/MFILE idempotence machinery has otherwise been retained; this change is intended specifically to replace the implicit iterative treatment of plasma beta rather than remove unrelated idempotence handling.
Validation
The
low_aspect_ratio_DEMO.IN.DATregression case was run withbeta_total_vol_avgremoved as an optimisation iteration variable while retaining beta consistency constraint 1.beta_total_vol_avgis absent from the optimisation solution vector, confirming that VMCON is no longer directly varying beta.Nevertheless, beta consistency constraint 1 is satisfied exactly:
⟨β⟩ consistency = 0.03718848552085542, with a constraint residual of0.0.The final total plasma beta is
beta_total_vol_avg = 0.03718848552085542, composed of a thermal beta of0.03250787755343900, a fast-alpha beta of0.004680607967416424, and zero beam beta.The resulting solution is essentially the same as the corresponding
mainsolution in whichbeta_total_vol_avgis retained asixc = 5.This demonstrates that the beta closure is now being supplied internally by the fixed-point calculation rather than by the optimiser varying
beta_total_vol_avg.impact
At this stage, constraint 1 has deliberately been retained as an independent validation of the new fixed-point calculation.
Because
beta_total_vol_avgis now solved internally by the fixed-point calculation, it no longer needs to be exposed to the optimiser as iteration variableixc = 5. Once the fixed-point implementation is validated, beta consistency constrainticc = 1can also be removed, since the same closure is already enforced internally during every model evaluation.