From 280c4c2ce9030e9005db4fdebda498cb65f79746 Mon Sep 17 00:00:00 2001 From: Jonathan Citrin Date: Fri, 11 Sep 2026 02:38:36 -0700 Subject: [PATCH] Add local poloidal beta profile and beta_pol_prime derivative calculations Implement `calculate_beta_pol_profile` in `formulas.py` to calculate the local poloidal beta profile on the cell grid, defined as: beta_pol_local = P_total / ( / (2 * mu0)). Also implement `calc_beta_pol_prime` on the face grid to compute the derivative magnitude with respect to normalized poloidal flux: beta_pol_prime = -d(beta_pol_local) / d(psi_norm). Register BETA_POL_PROFILE and BETA_POL_PRIME as output keys in post-processing. Regenerate sim_tests with the new postprocessed outputs. Part of a chain of PRs related to setting Internal Boundary Conditions consistent with a user-set beta_pol_prime. PiperOrigin-RevId: 979698937 --- torax/_src/output_tools/output_keys.py | 8 ++ torax/_src/output_tools/post_processing.py | 17 ++++ torax/_src/physics/formulas.py | 72 ++++++++++++++++ torax/_src/physics/tests/formulas_test.py | 81 ++++++++++++++++++ .../test_all_transport_fusion_qlknn.nc | Bin 479226 -> 486326 bytes .../tests/test_data/test_bohmgyrobohm_all.nc | Bin 751400 -> 764419 bytes ...test_bremsstrahlung_time_dependent_Zimp.nc | Bin 234670 -> 239696 bytes .../test_data/test_changing_config_after.nc | Bin 351973 -> 355936 bytes .../test_data/test_changing_config_before.nc | Bin 390005 -> 394908 bytes torax/tests/test_data/test_chease.nc | Bin 324693 -> 330120 bytes .../test_data/test_combined_transport.nc | Bin 588243 -> 597831 bytes torax/tests/test_data/test_fixed_dt.nc | Bin 2053542 -> 2097222 bytes .../test_data/test_imas_profiles_and_geo.nc | Bin 658610 -> 668895 bytes torax/tests/test_data/test_implicit.nc | Bin 595311 -> 607621 bytes .../test_implicit_short_optimizer.nc | Bin 186121 -> 187393 bytes .../test_data/test_iterbaseline_mockup.nc | Bin 1024287 -> 1047973 bytes .../test_iterhybrid_lh_transition.nc | Bin 18632923 -> 19034396 bytes ..._transition_internal_boundary_condition.nc | Bin 1401783 -> 1433560 bytes .../tests/test_data/test_iterhybrid_mockup.nc | Bin 718139 -> 733591 bytes .../test_iterhybrid_predictor_corrector.nc | Bin 789518 -> 807028 bytes ...brid_predictor_corrector_Lmode_combined.nc | Bin 1545759 -> 1580261 bytes ...rhybrid_predictor_corrector_clip_inputs.nc | Bin 789517 -> 807027 bytes ...or_constant_fraction_impurity_radiation.nc | Bin 728133 -> 742873 bytes ...terhybrid_predictor_corrector_cyclotron.nc | Bin 769169 -> 784741 bytes ...terhybrid_predictor_corrector_ec_linliu.nc | Bin 838908 -> 857282 bytes ...st_iterhybrid_predictor_corrector_eqdsk.nc | Bin 990783 -> 1012165 bytes ...est_iterhybrid_predictor_corrector_imas.nc | Bin 810001 -> 827927 bytes ...tor_corrector_mavrin_impurity_radiation.nc | Bin 560726 -> 569494 bytes ...d_predictor_corrector_mavrin_n_e_ratios.nc | Bin 671347 -> 684775 bytes ...tor_corrector_mavrin_n_e_ratios_lengyel.nc | Bin 709832 -> 720672 bytes ...ictor_corrector_mavrin_n_e_ratios_z_eff.nc | Bin 751184 -> 765956 bytes ...hybrid_predictor_corrector_neoclassical.nc | Bin 809990 -> 827916 bytes ...iterhybrid_predictor_corrector_rotation.nc | Bin 566216 -> 576669 bytes ...ictor_corrector_set_pped_tpedratio_nped.nc | Bin 719096 -> 735294 bytes ...hybrid_predictor_corrector_tglfnn_ukaea.nc | Bin 1155542 -> 1182140 bytes ...edictor_corrector_tglfnn_ukaea_rotation.nc | Bin 1155856 -> 1182454 bytes ...dictor_corrector_timedependent_isotopes.nc | Bin 673912 -> 689246 bytes ...iterhybrid_predictor_corrector_tungsten.nc | Bin 830221 -> 848563 bytes ...rhybrid_predictor_corrector_zeffprofile.nc | Bin 791352 -> 808862 bytes .../test_iterhybrid_radiation_collapse.nc | Bin 627112 -> 742318 bytes .../tests/test_data/test_iterhybrid_rampup.nc | Bin 988440 -> 1008277 bytes .../test_iterhybrid_rampup_sawtooth.nc | Bin 3882024 -> 3960618 bytes .../test_data/test_ne_qlknn_deff_veff.nc | Bin 396765 -> 403599 bytes .../test_data/test_ne_qlknn_defromchie.nc | Bin 324498 -> 329925 bytes .../test_data/test_particle_sources_cgm.nc | Bin 313690 -> 319511 bytes .../test_prescribed_generic_current_source.nc | Bin 544490 -> 555307 bytes .../test_prescribed_timedependent_ne.nc | Bin 608395 -> 618935 bytes torax/tests/test_data/test_psi_and_heat.nc | Bin 229605 -> 234122 bytes torax/tests/test_data/test_psi_heat_dens.nc | Bin 318993 -> 324008 bytes .../test_psichease_ip_chease_vloop.nc | Bin 477624 -> 485292 bytes ...t_psichease_ip_parameters_vloop_varying.nc | Bin 481317 -> 488985 bytes .../test_psichease_prescribed_johm.nc | Bin 477623 -> 485291 bytes .../test_psichease_prescribed_jtot.nc | Bin 477622 -> 485290 bytes .../test_psichease_prescribed_jtot_vloop.nc | Bin 477621 -> 485289 bytes .../test_data/test_semiimplicit_convection.nc | Bin 472760 -> 481676 bytes .../tests/test_data/test_step_flattop_bgb.nc | Bin 3525011 -> 3593712 bytes torax/tests/test_data/test_timedependence.nc | Bin 645311 -> 657080 bytes 57 files changed, 178 insertions(+) diff --git a/torax/_src/output_tools/output_keys.py b/torax/_src/output_tools/output_keys.py index 556cecda0..e381bf20b 100644 --- a/torax/_src/output_tools/output_keys.py +++ b/torax/_src/output_tools/output_keys.py @@ -870,6 +870,14 @@ def T_fast_ion_key(source_key: str) -> str: # pylint: disable=invalid-name BETA_N: Final[OutputKey] = OutputKey( "beta_N", units=Units.DIMENSIONLESS, grid_type=GridType.SCALAR ) +BETA_POL_PROFILE: Final[OutputKey] = OutputKey( + "beta_pol_profile", + units=Units.DIMENSIONLESS, + grid_type=GridType.FACE, +) +BETA_POL_PRIME: Final[OutputKey] = OutputKey( + "beta_pol_prime", units=Units.DIMENSIONLESS, grid_type=GridType.FACE +) # --------------------------------------------------------------------------- # Edge model outputs. diff --git a/torax/_src/output_tools/post_processing.py b/torax/_src/output_tools/post_processing.py index a81504d5d..404f3692b 100644 --- a/torax/_src/output_tools/post_processing.py +++ b/torax/_src/output_tools/post_processing.py @@ -200,6 +200,11 @@ class PostProcessedOutputs: beta_tor: Volume-averaged toroidal plasma beta (thermal) [dimensionless] beta_pol: Volume-averaged poloidal plasma beta (thermal) [dimensionless] beta_N: Normalized toroidal plasma beta (thermal) [dimensionless]. + beta_pol_profile: Local poloidal beta profile on the face grid + [dimensionless] + beta_pol_prime: Derivative of local poloidal beta with respect to normalized + poloidal flux on the face grid: -d(beta_pol_local) / d(psi_norm) + [dimensionless] impurity_species: Dictionary of outputs for each impurity species. poloidal_velocity: Poloidal velocity [m/s] radial_electric_field: Radial electric field [V/m] @@ -315,6 +320,8 @@ class PostProcessedOutputs: beta_tor: array_typing.FloatScalar beta_pol: array_typing.FloatScalar beta_N: array_typing.FloatScalar + beta_pol_profile: array_typing.FloatVector + beta_pol_prime: array_typing.FloatVector S_total: array_typing.FloatScalar impurity_species: dict[str, impurity_radiation.ImpuritySpeciesOutput] poloidal_velocity: array_typing.FloatVector @@ -428,6 +435,8 @@ def zeros(cls, geo: geometry.Geometry) -> typing_extensions.Self: beta_tor=jnp.array(0.0, dtype=jax_utils.get_dtype()), beta_pol=jnp.array(0.0, dtype=jax_utils.get_dtype()), beta_N=jnp.array(0.0, dtype=jax_utils.get_dtype()), + beta_pol_profile=jnp.zeros(geo.rho_face.shape), + beta_pol_prime=jnp.zeros(geo.rho_face.shape), S_total=jnp.array(0.0, dtype=jax_utils.get_dtype()), impurity_species={}, poloidal_velocity=jnp.zeros(geo.rho_face.shape), @@ -927,6 +936,12 @@ def cumulative_values(): beta_tor, beta_pol, beta_N = formulas.calculate_betas( # pyrefly: ignore[not-iterable] sim_state.core_profiles, sim_state.geometry ) + beta_pol_profile = formulas.calculate_beta_pol_profile( + sim_state.core_profiles, sim_state.geometry + ) + beta_pol_prime = formulas.calculate_beta_pol_prime( + sim_state.core_profiles, sim_state.geometry + ) rotation_output = rotation.calculate_rotation( T_i=sim_state.core_profiles.T_i, @@ -1019,6 +1034,8 @@ def cumulative_values(): beta_tor=beta_tor, beta_pol=beta_pol, beta_N=beta_N, + beta_pol_profile=beta_pol_profile.face_value(), + beta_pol_prime=beta_pol_prime, impurity_species=impurity_radiation_outputs, poloidal_velocity=rotation_output.poloidal_velocity.face_value(), # pyrefly: ignore[bad-argument-type] radial_electric_field=rotation_output.Er.face_value(), # pyrefly: ignore[bad-argument-type] diff --git a/torax/_src/physics/formulas.py b/torax/_src/physics/formulas.py index a0d11968b..a4b0c8a63 100644 --- a/torax/_src/physics/formulas.py +++ b/torax/_src/physics/formulas.py @@ -30,6 +30,10 @@ averaged electron density (can be line-averaged or volume-averaged). - calculate_beta_volume_avg: Calculates the volume-averaged plasma beta based on thermal pressure. + - calculate_beta_pol_profile: Calculates local poloidal beta profile as a + CellVariable. + - calc_beta_pol_prime: Calculates + beta_pol_prime = -d(beta_pol) / d(psi_norm) on the face grid. """ from jax import numpy as jnp from torax._src import array_typing @@ -38,6 +42,7 @@ from torax._src import state from torax._src.fvm import cell_variable from torax._src.geometry import geometry +from torax._src.physics import psi_calculations # pylint: disable=invalid-name @@ -264,3 +269,70 @@ def calculate_betas( ) return beta_tor, beta_pol, beta_N # pyrefly: ignore[bad-return] + + +def calculate_beta_pol_profile( + core_profiles: state.CoreProfiles, + geo: geometry.Geometry, +) -> cell_variable.CellVariable: + """Calculates the local poloidal beta profile on the cell grid. + + beta_pol_local(psi) = P_total(psi) / ( / (2 * mu0)) + + Args: + core_profiles: CoreProfiles object. + geo: Geometry object. + + Returns: + beta_pol_profile: CellVariable of local poloidal beta profile. + """ + bpol2_face = psi_calculations.calc_bpol_squared(geo, core_profiles.psi) + bpol2_cell = geometry.face_to_cell(bpol2_face) + denom_cell = ( + bpol2_cell / (2.0 * constants.CONSTANTS.mu_0) + constants.CONSTANTS.eps + ) + denom_right = ( + bpol2_face[-1] / (2.0 * constants.CONSTANTS.mu_0) + + constants.CONSTANTS.eps + ) + right_face_constraint = ( + core_profiles.pressure_total.right_face_constraint / denom_right + if core_profiles.pressure_total.right_face_constraint is not None + else None + ) + return cell_variable.CellVariable( + value=core_profiles.pressure_total.value / denom_cell, + face_centers=core_profiles.pressure_total.face_centers, + right_face_constraint=right_face_constraint, + right_face_grad_constraint=None, + ) + + +def calculate_beta_pol_prime( + core_profiles: state.CoreProfiles, + geo: geometry.Geometry, +) -> array_typing.FloatVectorFace: + r"""Calculates beta_pol_prime on the face grid. + + Defined as: + beta_pol_prime = -d(beta_pol_local) / d(psi_norm) + where beta_pol_local is the local poloidal beta CellVariable and psi_norm is + the normalized poloidal flux in [0, 1]. In normal confinement, pressure + decreases toward the edge, making d(beta_pol)/d(psi_norm) negative, so + beta_pol_prime represents the positive gradient magnitude. + + Args: + core_profiles: CoreProfiles object. + geo: Geometry object. + + Returns: + beta_pol_prime: Face-grid array of the derivative magnitude [dimensionless]. + """ + beta_pol = calculate_beta_pol_profile(core_profiles, geo) + return -calc_dvar_dpsi( + var=beta_pol, + psi=core_profiles.psi, + normalized=True, + ) + + diff --git a/torax/_src/physics/tests/formulas_test.py b/torax/_src/physics/tests/formulas_test.py index 2870088f8..c6a73275d 100644 --- a/torax/_src/physics/tests/formulas_test.py +++ b/torax/_src/physics/tests/formulas_test.py @@ -16,11 +16,14 @@ from absl.testing import absltest from absl.testing import parameterized import numpy as np +from torax._src import constants from torax._src import jax_utils from torax._src import math_utils from torax._src.fvm import cell_variable from torax._src.geometry import circular_geometry +from torax._src.geometry import geometry from torax._src.physics import formulas +from torax._src.physics import psi_calculations from torax._src.test_utils import core_profile_helpers @@ -154,6 +157,84 @@ def test_calc_dvar_dpsi_against_analytical_solution(self): dvar_dpsi_norm, expected_dvar_dpsi_norm, rtol=1e-6 ) + def test_calculate_beta_pol_profile_and_derivative_analytical_circular(self): + geo = circular_geometry.CircularConfig( + n_rho=50, a_minor=1.0, R_major=10.0, B_0=2.0 + ).build_geometry() + Ip = 1e6 + mu0 = constants.CONSTANTS.mu_0 + R0 = geo.R_major + + psi_face = 0.5 * mu0 * Ip * R0 * (geo.rho_face / geo.rho_face[-1]) ** 2 + psi_cell = 0.5 * mu0 * Ip * R0 * (geo.rho / geo.rho_face[-1]) ** 2 + psi_var = cell_variable.CellVariable( + value=psi_cell, + face_centers=geo.rho_face, + left_face_constraint=psi_face[0], + right_face_constraint=psi_face[-1], + left_face_grad_constraint=None, + right_face_grad_constraint=None, + ) + + # Compute magnetic pressure denominator: / (2 * mu0) + bpol2_face = psi_calculations.calc_bpol_squared(geo, psi_var) + bpol2_cell = geometry.face_to_cell(bpol2_face) + denom_cell = bpol2_cell / (2.0 * mu0) + denom_right = bpol2_face[-1] / (2.0 * mu0) + + # Define a linear profile in normalized psi space: + # beta_pol_target = beta_0 + beta_prime * (1 - psi_N) + # Then d(beta_pol) / d(psi_N) = -beta_prime everywhere. + psi_range = psi_var.right_face_value - psi_var.left_face_value + psi_N_cell = (psi_var.value - psi_var.left_face_value) / psi_range + beta_0 = 0.5 + beta_prime = 1.2 + target_beta_pol_cell = beta_0 + beta_prime * (1.0 - psi_N_cell) + + P_tot_cell = target_beta_pol_cell * denom_cell + P_tot_right = beta_0 * denom_right + + # Construct T_e and n_e so that pressure_total equals P_tot: + # With n_i = 0, n_impurity = 0, fast_ions = (): + # P_tot = P_el = n_e * T_e * keV_to_J. + # Set n_e = 1.0 / keV_to_J, and T_e = P_tot. + n_e_val = cell_variable.CellVariable( + value=np.ones_like(geo.rho) / constants.CONSTANTS.keV_to_J, + face_centers=geo.rho_face, + right_face_constraint=1.0 / constants.CONSTANTS.keV_to_J, + right_face_grad_constraint=None, + ) + T_e_val = cell_variable.CellVariable( + value=P_tot_cell, + face_centers=geo.rho_face, + left_face_constraint=None, + left_face_grad_constraint=0.0, + right_face_constraint=P_tot_right, + right_face_grad_constraint=None, + ) + + core_profiles = core_profile_helpers.make_zero_core_profiles(geo) + core_profiles = dataclasses.replace( + core_profiles, + psi=psi_var, + n_e=n_e_val, + T_e=T_e_val, + ) + + with self.subTest('beta_pol_profile'): + beta_pol_prof = formulas.calculate_beta_pol_profile(core_profiles, geo) + np.testing.assert_allclose( + beta_pol_prof.value, target_beta_pol_cell, rtol=1e-6 + ) + self.assertIsNotNone(beta_pol_prof.right_face_constraint) + np.testing.assert_allclose( + beta_pol_prof.right_face_constraint, beta_0, rtol=1e-6 + ) + + with self.subTest('beta_pol_prime'): + beta_pol_prime = 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