{
  "scope": "Website presentation derived from saved v26 fields; no solver or optimizer rerun.",
  "quantity": "Mounted-centerline second-order shim efficiency",
  "units": "mT/(m²·A)",
  "strength_units": "mT/m²",
  "coordinate_units": "m",
  "polynomial_basis": [
    "x²−y²",
    "z²−(x²+y²)/2",
    "xy",
    "xz",
    "yz"
  ],
  "fit_model": "Bz = offset + Gx*x + Gy*y + Gz*z + c0*(x²−y²) + c1*(z²−(x²+y²)/2) + c2*xy + c3*xz + c4*yz",
  "fit_method": "Unweighted least squares with an intercept, three linear terms and all five second-order harmonic polynomials; coordinates scaled by ROI radius before fitting and coefficients returned in physical SI units.",
  "efficiency_definition": "Intended polynomial coefficient in mT/m² divided by the saved per-part current in A. Polynomial and winding orientation define the sign.",
  "coefficient_convention": "These are coefficients multiplying the stated metre-based polynomial, not spatial second derivatives. In particular, the axial second derivative of c*(z²−(x²+y²)/2) is 2*c.",
  "error_policy": "Original relative RMS Bz error uses the original fixed-current Bz and target without a gain or offset fit; the descriptive polynomial fit does not change this error.",
  "cases": [
    {
      "case": "shim",
      "label": "Cylindrical X²−Y² shim",
      "polynomial": "x²−y²",
      "polynomial_basis_index": 0,
      "ROI_radius_m": 0.02,
      "target_coefficient_mT_per_m2": 25.0,
      "common_per_part_current_A": 1.92105341949404,
      "primary": {
        "sample_count": 2048,
        "rank": 9,
        "offset_T": -2.7640018370666566e-09,
        "gradient_xyz_T_per_m": [
          1.4894938150481454e-08,
          -5.6341706972580046e-08,
          3.8120876865216655e-07
        ],
        "quadratic_coefficients_T_per_m2": [
          0.024272216160891022,
          2.108314754171834e-06,
          -6.076354732968372e-06,
          -4.012878157382763e-06,
          4.820033311759608e-07
        ],
        "fit_residual_rms_T": 1.1907638083607021e-07,
        "scaled_design_matrix_condition_number": 5.92110939061025,
        "coefficient_mT_per_m2": 24.272216160891023,
        "shim_efficiency_mT_per_m2_per_A": 12.634847065983074,
        "target_coefficient_recovered_mT_per_m2": 25.00000000000002,
        "original_relative_RMS_Bz_error_percent": 4.57152847356923
      },
      "sensitivity": {
        "sample_count": 4096,
        "rank": 9,
        "offset_T": -2.7617302621943043e-09,
        "gradient_xyz_T_per_m": [
          -7.261882805476582e-08,
          -6.152591509174706e-08,
          4.316943256751604e-07
        ],
        "quadratic_coefficients_T_per_m2": [
          0.024272211756523894,
          2.109329470301688e-06,
          -5.95271200110935e-06,
          -2.8752735728110485e-06,
          3.010917661582511e-07
        ],
        "fit_residual_rms_T": 1.1907446814077585e-07,
        "scaled_design_matrix_condition_number": 5.91888376219825,
        "coefficient_mT_per_m2": 24.272211756523895,
        "shim_efficiency_mT_per_m2_per_A": 12.634844773299756,
        "target_coefficient_recovered_mT_per_m2": 25.000000000000043,
        "original_relative_RMS_Bz_error_percent": 4.571878652421981
      },
      "sources": [
        {
          "path": "v26/numerical/stages/shim/results.json",
          "sha256": "c8dfa6c8165ee219eb046056b40f43540afb2a2bdd15afa583de5ef4bb47dca3"
        },
        {
          "path": "v26/numerical/stages/shim/fields.npz",
          "sha256": "db70432df874c3e2d7de493ad00634b6a5058fd77967cb800a3c28fc5f43887d"
        }
      ]
    },
    {
      "case": "conic",
      "label": "Conical Z2 shim",
      "polynomial": "z²−(x²+y²)/2",
      "polynomial_basis_index": 1,
      "ROI_radius_m": 0.05,
      "target_coefficient_mT_per_m2": 4.0,
      "common_per_part_current_A": 1.6010144933322359,
      "primary": {
        "sample_count": 2048,
        "rank": 9,
        "offset_T": 2.796195335741869e-07,
        "gradient_xyz_T_per_m": [
          6.803828841313355e-08,
          -1.5735859828419895e-08,
          2.9738860436221115e-07
        ],
        "quadratic_coefficients_T_per_m2": [
          2.4840784711245184e-07,
          0.003909323986951689,
          -3.945102772701861e-07,
          9.892707455675211e-06,
          2.1953787728880456e-07
        ],
        "fit_residual_rms_T": 1.1525592725772205e-07,
        "scaled_design_matrix_condition_number": 5.921109390610249,
        "coefficient_mT_per_m2": 3.909323986951689,
        "shim_efficiency_mT_per_m2_per_A": 2.441779261357656,
        "target_coefficient_recovered_mT_per_m2": 4.000000000000001,
        "original_relative_RMS_Bz_error_percent": 10.57689831656658
      },
      "sensitivity": {
        "sample_count": 4096,
        "rank": 9,
        "offset_T": 2.7961952614415515e-07,
        "gradient_xyz_T_per_m": [
          8.080709570294348e-08,
          -1.574516806904765e-08,
          2.9712143492692347e-07
        ],
        "quadratic_coefficients_T_per_m2": [
          1.76184249447136e-07,
          0.003909321911702519,
          -6.266337349482262e-07,
          1.0299939905604682e-05,
          -3.902761445877281e-07
        ],
        "fit_residual_rms_T": 1.1525345656588097e-07,
        "scaled_design_matrix_condition_number": 5.918883762198256,
        "coefficient_mT_per_m2": 3.9093219117025195,
        "shim_efficiency_mT_per_m2_per_A": 2.4417779651487974,
        "target_coefficient_recovered_mT_per_m2": 3.9999999999999933,
        "original_relative_RMS_Bz_error_percent": 10.57700942426303
      },
      "sources": [
        {
          "path": "v26/numerical/stages/conic/results.json",
          "sha256": "591185389dba9807a2edde671ccea06cdf626462d8f9469b9f34265427582259"
        },
        {
          "path": "v26/numerical/stages/conic/fields.npz",
          "sha256": "9aaa76f91fb0ad9b8a23dba42efed7444e3e50ddc800c20a4071e350896937a4"
        }
      ]
    }
  ]
}