{
    "metadata": {
        "calculation_date": "2025-09-26T06:00:51.455525",
        "author": "Yoshiyuki Matsuyama",
        "article": "#002 Magnetic Field Visualization",
        "version": "1.0 (accurate)"
    },
    "physical_constants": {
        "G": 6.6743e-11,
        "c": 299792458,
        "M_sun": 1.98847e+30
    },
    "torus_parameters": {
        "R_over_r": 1000,
        "R_meters": 19196705983434708,
        "r_meters": 19196705983434.707,
        "R_Rs_units": 1000,
        "r_Rs_units": 1
    },
    "schwarzschild_radius": {
        "value_meters": 19196705983434.707,
        "value_km": 19196705983.434708,
        "value_AU": 128.3202271619967
    },
    "results": {
        "jet_velocity": {
            "formula": "v\/c = sqrt(1 - (r\/R)^2)",
            "inputs": {
                "R\/r": 1000,
                "r\/R": 0.001
            },
            "steps": [
                "r\/R = 1\/1000 = 0.001000",
                "(r\/R)^2 = 0.000001000000",
                "1 - (r\/R)^2 = 0.999999000000",
                "v\/c = sqrt(0.999999000000) = 0.999999500"
            ],
            "result": {
                "v_over_c": 0.999999499999875,
                "gamma_factor": 1000.0000000411333
            }
        },
        "magnetic_field_structure": {
            "reference_field_strength": 100,
            "pitch_angle_rad": 0.0009999996666668668,
            "pitch_angle_deg": 0.057295760414500616,
            "helical_turns": 6283.185307179587,
            "characteristic_scale": 6.283185307179586,
            "magnetic_field_data": [
                {
                    "w_phase": 0,
                    "B_toroidal": 3.162277660168379,
                    "B_poloidal": 0,
                    "B_w_max": 5,
                    "B_total_mean": 4.669647209941432,
                    "B_total_max": 5.916079783099616,
                    "B_total_min": 3.1663358303598805
                },
                {
                    "w_phase": 0.8975979010256552,
                    "B_toroidal": 3.162277660168379,
                    "B_poloidal": 7.818314824680298,
                    "B_w_max": 5,
                    "B_total_mean": 9.129079741176671,
                    "B_total_max": 9.804389154751851,
                    "B_total_min": 8.435148444955578
                },
                {
                    "w_phase": 1.7951958020513104,
                    "B_toroidal": 3.162277660168379,
                    "B_poloidal": 9.749279121818237,
                    "B_w_max": 5,
                    "B_total_mean": 10.823797673114932,
                    "B_total_max": 11.403878436528554,
                    "B_total_min": 10.250567105567464
                },
                {
                    "w_phase": 2.6927937030769655,
                    "B_toroidal": 3.162277660168379,
                    "B_poloidal": 4.338837391175582,
                    "B_w_max": 5,
                    "B_total_mean": 6.403262625213864,
                    "B_total_max": 7.336587074864124,
                    "B_total_min": 5.371330607743684
                },
                {
                    "w_phase": 3.5903916041026207,
                    "B_toroidal": 3.162277660168379,
                    "B_poloidal": -4.33883739117558,
                    "B_w_max": 5,
                    "B_total_mean": 6.403262625213861,
                    "B_total_max": 7.336587074864123,
                    "B_total_min": 5.3713306077436815
                },
                {
                    "w_phase": 4.487989505128276,
                    "B_toroidal": 3.162277660168379,
                    "B_poloidal": -9.749279121818237,
                    "B_w_max": 5,
                    "B_total_mean": 10.82379767311493,
                    "B_total_max": 11.403878436528554,
                    "B_total_min": 10.250567105567464
                },
                {
                    "w_phase": 5.385587406153931,
                    "B_toroidal": 3.162277660168379,
                    "B_poloidal": -7.818314824680299,
                    "B_w_max": 5,
                    "B_total_mean": 9.129079741176671,
                    "B_total_max": 9.804389154751853,
                    "B_total_min": 8.43514844495558
                },
                {
                    "w_phase": 6.283185307179586,
                    "B_toroidal": 3.162277660168379,
                    "B_poloidal": -2.4492935982947065e-15,
                    "B_w_max": 5,
                    "B_total_mean": 4.669647209941432,
                    "B_total_max": 5.916079783099616,
                    "B_total_min": 3.16633583035988
                }
            ]
        },
        "energy_distribution": {
            "magnetic_energy_density": 39.78873577297384,
            "kinetic_energy_density": 4.093376368176375e-6,
            "total_energy_density": 39.788739866350205,
            "conversion_efficiency": 1.0287775842929346e-7,
            "plasma_beta": 2.0575574378199921e-7,
            "detailed_calculation": {
                "B_field_Tesla": 0.01,
                "electron_density_per_m3": 100000000,
                "jet_velocity_m_per_s": 299792308.10373354,
                "vacuum_permeability": 1.2566370614359173e-6
            }
        },
        "observational_predictions": {
            "W_axis_period": {
                "seconds": 402333.20673251693,
                "hours": 111.75922409236581,
                "days": 4.656634337181909
            },
            "characteristic_frequencies": {
                "major_radius_Hz": 2.4855020248548107e-9,
                "minor_radius_Hz": 2.4855020248548107e-6,
                "ratio": 1000
            },
            "expected_polarization": {
                "pattern": "Helical with pitch angle",
                "pitch_angle_rad": 0.0009999996666668668,
                "rotation_measure": "Variable with W-phase"
            }
        },
        "visualization": {
            "file": "magnetic_field_3d.html",
            "grid_points": 10000,
            "field_lines": 20,
            "coordinate_system": "Schwarzschild radius units"
        }
    }
}