From 63d8590fcb0248b7a1c4dda796d69c89d5be2d35 Mon Sep 17 00:00:00 2001 From: Jonathan Citrin Date: Mon, 25 Nov 2024 14:59:44 -0800 Subject: [PATCH] Add H98, H20, H98L confinement quality factors. These are the ratios between predicted thermal confinement time and various empirical confinement times derived from database scalings. Does not include the dW/dt term yet, so their interpretations are restricted to quasi-stationary cases, which is anyway their main use case. Regenerate all tests to incorporate new post-processed outputs. PiperOrigin-RevId: 700110838 --- docs/output.rst | 25 ++++ torax/physics.py | 140 ++++++++++++++++-- torax/post_processing.py | 31 ++++ torax/state.py | 15 ++ torax/tests/physics.py | 133 ++++++++++++++++- .../test_all_transport_crank_nicolson.nc | Bin 297044 -> 301639 bytes .../test_all_transport_fusion_qlknn.nc | Bin 699125 -> 703352 bytes .../tests/test_data/test_bohmgyrobohm_all.nc | Bin 924082 -> 931059 bytes torax/tests/test_data/test_bootstrap.nc | Bin 253794 -> 257255 bytes torax/tests/test_data/test_bremsstrahlung.nc | Bin 171713 -> 176188 bytes torax/tests/test_data/test_cgmheat.nc | Bin 268658 -> 271349 bytes .../test_data/test_changing_config_after.nc | Bin 169049 -> 171266 bytes .../test_data/test_changing_config_before.nc | Bin 215207 -> 217288 bytes torax/tests/test_data/test_chease.nc | Bin 315738 -> 317741 bytes torax/tests/test_data/test_eqdsk.nc | Bin 1321960 -> 1330922 bytes torax/tests/test_data/test_explicit.nc | Bin 277145 -> 284860 bytes torax/tests/test_data/test_fixed_dt.nc | Bin 810194 -> 817451 bytes torax/tests/test_data/test_fusion_power.nc | Bin 251993 -> 256204 bytes torax/tests/test_data/test_implicit.nc | Bin 253794 -> 257255 bytes .../test_implicit_short_optimizer.nc | Bin 105012 -> 108019 bytes .../test_data/test_iterbaseline_mockup.nc | Bin 484317 -> 489265 bytes .../tests/test_data/test_iterhybrid_mockup.nc | Bin 429772 -> 433083 bytes .../tests/test_data/test_iterhybrid_newton.nc | Bin 155065 -> 157272 bytes .../test_iterhybrid_predictor_corrector.nc | Bin 377983 -> 379938 bytes ...rhybrid_predictor_corrector_clip_inputs.nc | Bin 377983 -> 379938 bytes ...terhybrid_predictor_corrector_ec_linliu.nc | Bin 400677 -> 406878 bytes ...st_iterhybrid_predictor_corrector_eqdsk.nc | Bin 366735 -> 370746 bytes ...rhybrid_predictor_corrector_zeffprofile.nc | Bin 312943 -> 317538 bytes .../tests/test_data/test_iterhybrid_rampup.nc | Bin 392687 -> 394626 bytes .../test_data/test_ne_qlknn_deff_veff.nc | Bin 297044 -> 301639 bytes .../test_data/test_ne_qlknn_defromchie.nc | Bin 261722 -> 264405 bytes torax/tests/test_data/test_ohmic_power.nc | Bin 302414 -> 304417 bytes .../test_data/test_particle_sources_cgm.nc | Bin 407873 -> 411184 bytes .../test_particle_sources_constant.nc | Bin 412193 -> 417504 bytes torax/tests/test_data/test_pc_method_ne.nc | Bin 643565 -> 649840 bytes torax/tests/test_data/test_pedestal.nc | Bin 253794 -> 257255 bytes .../test_prescribed_generic_current_source.nc | Bin 924082 -> 931059 bytes .../test_prescribed_timedependent_ne.nc | Bin 252331 -> 255022 bytes torax/tests/test_data/test_psi_and_heat.nc | Bin 336570 -> 338621 bytes torax/tests/test_data/test_psi_heat_dens.nc | Bin 392866 -> 398177 bytes .../test_data/test_psichease_ip_chease.nc | Bin 711355 -> 718564 bytes .../test_data/test_psichease_ip_parameters.nc | Bin 711355 -> 718564 bytes .../test_psichease_prescribed_johm.nc | Bin 711355 -> 718564 bytes .../test_psichease_prescribed_jtot.nc | Bin 711355 -> 718564 bytes torax/tests/test_data/test_psiequation.nc | Bin 589610 -> 595885 bytes torax/tests/test_data/test_qei.nc | Bin 253794 -> 257255 bytes .../test_data/test_qei_chease_highdens.nc | Bin 295811 -> 297814 bytes torax/tests/test_data/test_qlknnheat.nc | Bin 308499 -> 310534 bytes .../test_data/test_semiimplicit_convection.nc | Bin 639907 -> 644134 bytes .../test_time_dependent_circular_geo.nc | Bin 1057771 -> 1070420 bytes torax/tests/test_data/test_timedependence.nc | Bin 258667 -> 261366 bytes 51 files changed, 330 insertions(+), 14 deletions(-) diff --git a/docs/output.rst b/docs/output.rst index ecd4d05a..5ed06c71 100644 --- a/docs/output.rst +++ b/docs/output.rst @@ -241,6 +241,31 @@ analysis and inspection. ``W_thermal_tot`` (time) [J]: Total thermal stored energy. +``tauE`` (time) [s]: + Thermal confinement time defined as ``W_thermal_tot`` / ``P_heating``, where + ``P_heating`` is the total heating power into the plasma, including external + contributions and fusion heating. Radiative losses are not subtracted from + heating power. + +``H98`` (time) [dimensionless]: + H-mode confinement quality factor with respect to the ITER98y2 scaling law, + defined as ``tauE`` / ``tau98_scaling``, where ``tau98_scaling`` is the + confinement time defined by the ITER98y2 scaling law, derived from the ITER + H-mode confinement database. As for ``tauE``, radiative losses are not + subtracted from the ``P_loss`` term used to calculate the empirical scaling + law confinement time. + +``H97L`` (time) [dimensionless]: + L-mode confinement quality factor with respect to the ITER97L scaling law + derived from the ITER L-mode confinement database. Defined similarly to ``H98`` + above, but using the ITER97L scaling law for the confinement time. + +``H20`` (time) [dimensionless]: + H-mode confinement quality factor with respect to the ITER20 scaling law + derived from the updated (2020) ITER confinement database. Defined similarly + to ``H98`` above, but using the updated ITER20 scaling law law for the + confinement time. + ``FFprime_face`` (time, rho_face) [m^2 T^2 / Wb]: :math:`FF'` on the face grid, where F is the toroidal flux function, and F' is its derivative with respect to the poloidal flux. diff --git a/torax/physics.py b/torax/physics.py index 78862751..a465eefe 100644 --- a/torax/physics.py +++ b/torax/physics.py @@ -471,19 +471,7 @@ def calculate_plh_scaling_factor( density corresponding to the P_LH minimum. """ - # Line-averaged electron density is poorly defined. In general, the definition - # is machine-dependent and even shot-dependent since it depends on the usage - # of a specific interferometry chord. Furthermore, even if we knew the - # specific chord used, its calculation would depend on magnetic geometry - # information beyond what is available in StandardGeometry. - # In lieu of a better solution, we use line-averaged electron density defined - # on the outer midplane. - Rmin_out = geo.Rout_face[-1] - geo.Rout_face[0] - line_avg_ne = ( - core_profiles.nref - * _trapz(core_profiles.ne.face_value(), geo.Rout_face) - / Rmin_out - ) + line_avg_ne = _calculate_line_avg_density(geo, core_profiles) # LH transition power for deuterium, in W. Eq 3 from Martin 2008. P_LH_hi_dens_D = ( 2.15 @@ -518,4 +506,130 @@ def calculate_plh_scaling_factor( return P_LH_hi_dens, P_LH_low_dens, ne_min_P_LH +def calculate_scaling_law_confinement_time( + geo: Geometry, + core_profiles: state.CoreProfiles, + Ploss: jax.Array, + scaling_law: str, +) -> jax.Array: + """Calculates the thermal energy confinement time for a given empirical scaling law. + + Args: + geo: Torus geometry. + core_profiles: Core plasma profiles. + Ploss: Plasma power loss in MW. + scaling_law: Scaling law to use. + + Returns: + Thermal energy confinement time in s. + """ + scaling_params = { + 'H98': { + # H98 empirical confinement scaling law: + # ITER Physics Expert Groups on Confinement and Transport and + # Confinement Modelling and Database, Nucl. Fusion 39 2175, 1999 + # Doyle et al, Nucl. Fusion 47 (2007) S18–S127, Eq 30 + 'prefactor': 0.0562, + 'Ip_exponent': 0.93, + 'B_exponent': 0.15, + 'line_avg_ne_exponent': 0.41, + 'Ploss_exponent': -0.69, + 'R_exponent': 1.97, + 'inverse_aspect_ratio_exponent': 0.58, + 'elongation_exponent': 0.78, + 'effective_mass_exponent': 0.19, + 'triangularity_exponent': 0.0, + }, + 'H97L': { + # From the ITER L-mode confinement database. + # S.M. Kaye et al 1997 Nucl. Fusion 37 1303, Eq 7 + 'prefactor': 0.023, + 'Ip_exponent': 0.96, + 'B_exponent': 0.03, + 'line_avg_ne_exponent': 0.4, + 'Ploss_exponent': -0.73, + 'R_exponent': 1.83, + 'inverse_aspect_ratio_exponent': -0.06, + 'elongation_exponent': 0.64, + 'effective_mass_exponent': 0.20, + 'triangularity_exponent': 0.0, + }, + 'H20': { + # Updated ITER H-mode confinement database, using full dataset. + # G. Verdoolaege et al 2021 Nucl. Fusion 61 076006, Eq 7 + 'prefactor': 0.053, + 'Ip_exponent': 0.98, + 'B_exponent': 0.22, + 'line_avg_ne_exponent': 0.24, + 'Ploss_exponent': -0.669, + 'R_exponent': 1.71, + 'inverse_aspect_ratio_exponent': 0.35, + 'elongation_exponent': 0.80, + 'effective_mass_exponent': 0.20, + 'triangularity_exponent': 0.36, # (1+delta)^exponent + }, + } + + if scaling_law not in scaling_params: + raise ValueError(f'Unknown scaling law: {scaling_law}') + + params = scaling_params[scaling_law] + + Ip = core_profiles.currents.Ip_profile_face[-1] / 1e6 # in MA + B = geo.B0 + line_avg_ne = _calculate_line_avg_density(geo, core_profiles) / 1e19 + R = geo.Rmaj + inverse_aspect_ratio = geo.Rmin / geo.Rmaj + + # Effective elongation definition. This is a different definition than + # the standard definition used in geo.elongation. + elongation = geo.area_face[-1] / (jnp.pi * geo.Rmin**2) + # TODO(b/317360834): extend when multiple ions are supported. + effective_mass = core_profiles.Ai + triangularity = geo.delta_face[-1] + + tau_scaling = ( + params['prefactor'] + * Ip**params['Ip_exponent'] + * B**params['B_exponent'] + * line_avg_ne**params['line_avg_ne_exponent'] + * Ploss**params['Ploss_exponent'] + * R**params['R_exponent'] + * inverse_aspect_ratio**params['inverse_aspect_ratio_exponent'] + * elongation**params['elongation_exponent'] + * effective_mass**params['effective_mass_exponent'] + * (1 + triangularity)**params['triangularity_exponent'] + ) + return tau_scaling + + +def _calculate_line_avg_density( + geo: Geometry, + core_profiles: state.CoreProfiles, +) -> jax.Array: + """Calculates line-averaged electron density. + + Line-averaged electron density is poorly defined. In general, the definition + is machine-dependent and even shot-dependent since it depends on the usage of + a specific interferometry chord. Furthermore, even if we knew the specific + chord used, its calculation would depend on magnetic geometry information + beyond what is available in StandardGeometry. In lieu of a better solution, we + use line-averaged electron density defined on the outer midplane. + + Args: + geo: Torus geometry. + core_profiles: Core plasma profiles. + + Returns: + Line-averaged electron density. + """ + Rmin_out = geo.Rout_face[-1] - geo.Rout_face[0] + line_avg_ne = ( + core_profiles.nref + * _trapz(core_profiles.ne.face_value(), geo.Rout_face) + / Rmin_out + ) + return line_avg_ne + + # pylint: enable=invalid-name diff --git a/torax/post_processing.py b/torax/post_processing.py index 0885eafe..681e2fc8 100644 --- a/torax/post_processing.py +++ b/torax/post_processing.py @@ -366,6 +366,33 @@ def make_outputs( physics.calculate_plh_scaling_factor(geo, sim_state.core_profiles) ) + # Thermal energy confinement time is the stored energy divided by the total + # input power into the plasma. + + # Ploss term here does not include the reduction of radiated power. Most + # analysis of confinement times from databases have not included this term. + # Therefore highly radiative scenarios can lead to skewed results. + + Ploss = ( + integrated_sources['P_alpha_tot'] + integrated_sources['P_external_tot'] + ) + # TODO(b/380848256): include dW/dt term + tauE = W_thermal_tot / Ploss + + tauH98 = physics.calculate_scaling_law_confinement_time( + geo, sim_state.core_profiles, Ploss/1e6, 'H98' + ) + tauH97L = physics.calculate_scaling_law_confinement_time( + geo, sim_state.core_profiles, Ploss/1e6, 'H97L' + ) + tauH20 = physics.calculate_scaling_law_confinement_time( + geo, sim_state.core_profiles, Ploss/1e6, 'H20' + ) + + H98 = tauE / tauH98 + H97L = tauE / tauH97L + H20 = tauE / tauH20 + # Calculate total external (injected) and fusion (generated) energies based on # interval average. if previous_sim_state is not None: @@ -408,6 +435,10 @@ def make_outputs( W_thermal_ion=W_thermal_ion, W_thermal_el=W_thermal_el, W_thermal_tot=W_thermal_tot, + tauE=tauE, + H98=H98, + H97L=H97L, + H20=H20, FFprime_face=FFprime_face, psi_norm_face=psi_norm_face, psi_face=sim_state.core_profiles.psi.face_value(), diff --git a/torax/state.py b/torax/state.py index 32af3e5a..e518e57b 100644 --- a/torax/state.py +++ b/torax/state.py @@ -283,6 +283,13 @@ class PostProcessedOutputs: W_thermal_ion: Ion thermal stored energy [J] W_thermal_el: Electron thermal stored energy [J] W_thermal_tot: Total thermal stored energy [J] + tauE: Thermal energy confinement time [s] + H98: H-mode confinement quality factor with respect to the ITER98y2 scaling + law derived from the ITER H-mode confinement database + H97L: L-mode confinement quality factor with respect to the ITER97L scaling + law derived from the ITER H-mode confinement database + H20: H-mode confinement quality factor with respect to the ITER20 scaling + law derived from the updated (2020) ITER H-mode confinement database FFprime_face: FF' on the face grid, where F is the toroidal flux function psi_norm_face: Normalized poloidal flux on the face grid [Wb] psi_face: Poloidal flux on the face grid [Wb] @@ -330,6 +337,10 @@ class PostProcessedOutputs: W_thermal_ion: array_typing.ScalarFloat W_thermal_el: array_typing.ScalarFloat W_thermal_tot: array_typing.ScalarFloat + tauE: array_typing.ScalarFloat + H98: array_typing.ScalarFloat + H97L: array_typing.ScalarFloat + H20: array_typing.ScalarFloat FFprime_face: array_typing.ArrayFloat psi_norm_face: array_typing.ArrayFloat # psi_face included in post_processed output for convenience, since the @@ -377,6 +388,10 @@ def zeros(cls, geo: geometry.Geometry) -> PostProcessedOutputs: W_thermal_ion=jnp.array(0.0), W_thermal_el=jnp.array(0.0), W_thermal_tot=jnp.array(0.0), + tauE=jnp.array(0.0), + H98=jnp.array(0.0), + H97L=jnp.array(0.0), + H20=jnp.array(0.0), FFprime_face=jnp.zeros(geo.rho_face.shape), psi_norm_face=jnp.zeros(geo.rho_face.shape), psi_face=jnp.zeros(geo.rho_face.shape), diff --git a/torax/tests/physics.py b/torax/tests/physics.py index d78827b1..9b8a82b0 100644 --- a/torax/tests/physics.py +++ b/torax/tests/physics.py @@ -366,12 +366,143 @@ def test_calculate_plh_scaling_factor(self): ) expected_PLH_low_dens = 0.36 * 10**0.27 * 5**1.25 * 6**1.23 * 3**0.08 expected_ne_min_P_LH = 0.7 * 10**0.34 * 5**0.62 * 2.0**-0.95 * 3**0.4 / 10 - # pylint: enable=invalid-name np.testing.assert_allclose(P_LH_hi_dens / 1e6, expected_PLH_hi_dens) np.testing.assert_allclose(P_LH_low_dens / 1e6, expected_PLH_low_dens) np.testing.assert_allclose(ne_min_P_LH, expected_ne_min_P_LH) + @parameterized.parameters([ + dict(elongation_LCFS=1.0), + dict(elongation_LCFS=1.5), + ]) + # pylint: disable=invalid-name + def test_calculate_scaling_law_confinement_time(self, elongation_LCFS): + """Compare `calculate_scaling_law_confinement_time` to reference values.""" + geo = geometry.build_circular_geometry( + n_rho=25, + elongation_LCFS=elongation_LCFS, + hires_fac=4, + Rmaj=6.0, + Rmin=2.0, + B0=5.0, + ) + core_profiles = state.CoreProfiles( + ne=cell_variable.CellVariable( + value=jnp.ones_like(geo.rho_norm) * 2, + left_face_grad_constraint=jnp.zeros(()), + right_face_grad_constraint=None, + right_face_constraint=jnp.array(2.0), + dr=geo.drho_norm, + ), + ni=cell_variable.CellVariable( + value=jnp.ones_like(geo.rho_norm) * 2, + left_face_grad_constraint=jnp.zeros(()), + right_face_grad_constraint=None, + right_face_constraint=jnp.array(1.0), + dr=geo.drho_norm, + ), + nimp=cell_variable.CellVariable( + value=jnp.ones_like(geo.rho_norm) * 0, + left_face_grad_constraint=jnp.zeros(()), + right_face_grad_constraint=None, + right_face_constraint=jnp.array(0.0), + dr=geo.drho_norm, + ), + temp_ion=cell_variable.CellVariable( + value=jnp.ones_like(geo.rho_norm) * 0, + left_face_grad_constraint=jnp.zeros(()), + right_face_grad_constraint=None, + right_face_constraint=jnp.array(0.0), + dr=geo.drho_norm, + ), + temp_el=cell_variable.CellVariable( + value=jnp.ones_like(geo.rho_norm) * 0, + left_face_grad_constraint=jnp.zeros(()), + right_face_grad_constraint=None, + right_face_constraint=jnp.array(0.0), + dr=geo.drho_norm, + ), + psi=cell_variable.CellVariable( + value=jnp.ones_like(geo.rho_norm) * 0, + left_face_grad_constraint=jnp.zeros(()), + right_face_grad_constraint=None, + right_face_constraint=jnp.array(0.0), + dr=geo.drho_norm, + ), + psidot=cell_variable.CellVariable( + value=jnp.ones_like(geo.rho_norm) * 0, + left_face_grad_constraint=jnp.zeros(()), + right_face_grad_constraint=None, + right_face_constraint=jnp.array(0.0), + dr=geo.drho_norm, + ), + currents=state.Currents.zeros(geo), + q_face=jnp.array(0.0), + s_face=jnp.array(0.0), + Zi=1.0, + Ai=3.0, + Zimp=20.0, + Aimp=40.0, + nref=1e20, + ) + core_profiles = dataclasses.replace( + core_profiles, + currents=dataclasses.replace( + core_profiles.currents, + Ip_profile_face=jnp.ones_like(geo.rho_face_norm) * 10e6, + ), + ) + Ploss = jnp.array(50.0) + + H98 = physics.calculate_scaling_law_confinement_time( + geo, core_profiles, Ploss, 'H98' + ) + H97L = physics.calculate_scaling_law_confinement_time( + geo, core_profiles, Ploss, 'H97L' + ) + H20 = physics.calculate_scaling_law_confinement_time( + geo, core_profiles, Ploss, 'H20' + ) + expected_H98 = ( + 0.0562 + * 10**0.93 + * 5**0.15 + * 20**0.41 + * 50**-0.69 + * 6**1.97 + * (1/3)**0.58 + * 3**0.19 + * elongation_LCFS**0.78 + ) + + expected_H97L = ( + 0.023 + * 10**0.96 + * 5**0.03 + * 20**0.4 + * 50**-0.73 + * 6**1.83 + * (1/3)**-0.06 + * 3**0.20 + * elongation_LCFS**0.64 + ) + + expected_H20 = ( + 0.053 + * 10**0.98 + * 5**0.22 + * 20**0.24 + * 50**-0.669 + * 6**1.71 + * (1/3)**0.35 + * 3**0.20 + * elongation_LCFS**0.80 + ) + # pylint: enable=invalid-name + np.testing.assert_allclose(H98, expected_H98) + np.testing.assert_allclose(H97L, expected_H97L) + np.testing.assert_allclose(H20, expected_H20) + if __name__ == '__main__': absltest.main() diff --git a/torax/tests/test_data/test_all_transport_crank_nicolson.nc b/torax/tests/test_data/test_all_transport_crank_nicolson.nc index 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