{
  "experiment": "Experiment 13: Self-Consistent Equilibria and the Troyon Limit",
  "method": "FreeGS Grad-Shafranov solver + shaped CHT ballooning",
  "machine": {
    "R0": 6.2,
    "a": 2.0,
    "B0": 5.3,
    "kappa": 1.7,
    "delta": 0.33
  },
  "key_finding": "Self-consistent equilibria remain ballooning-stable past Troyon.",
  "troyon_limit": 2.8,
  "interpretation": "Troyon limit is external kink (n=1), not ballooning.",
  "results": {
    "5MA": [
      {
        "Ip_MA": 5,
        "p0_kPa": 50,
        "beta_N": 0.3161351097951994,
        "beta_pct": 0.14912033480905632,
        "spectral_gap": -0.996786450997381,
        "n_stable": 0,
        "n_total": 28,
        "converged": true,
        "worst_s": 1.1976020290523401,
        "worst_alpha": 1.1104811713517848,
        "time_s": 0.5715696811676025
      },
      {
        "Ip_MA": 5,
        "p0_kPa": 100,
        "beta_N": 0.6322702195903988,
        "beta_pct": 0.29824066961811263,
        "spectral_gap": -1.5266092314987019,
        "n_stable": 0,
        "n_total": 28,
        "converged": true,
        "worst_s": 1.2811402602768025,
        "worst_alpha": 1.9820824004747997,
        "time_s": 0.718958854675293
      },
      {
        "Ip_MA": 5,
        "p0_kPa": 200,
        "beta_N": 1.2645404391807975,
        "beta_pct": 0.5964813392362253,
        "spectral_gap": -1.5671605779554332,
        "n_stable": 0,
        "n_total": 28,
        "converged": true,
        "worst_s": 1.3489242282507017,
        "worst_alpha": 2.472131085801447,
        "time_s": 0.7864975929260254
      },
      {
        "Ip_MA": 5,
        "p0_kPa": 500,
        "beta_N": 3.1613510979519934,
        "beta_pct": 1.4912033480905629,
        "spectral_gap": -0.5806931527229665,
        "n_stable": 23,
        "n_total": 28,
        "converged": true,
        "worst_s": 0.20895522388059698,
        "worst_alpha": 1.6428401685206941,
        "time_s": 0.6610977649688721
      },
      {
        "Ip_MA": 5,
        "p0_kPa": 1000,
        "beta_N": 6.322702195903987,
        "beta_pct": 2.9824066961811257,
        "spectral_gap": 0.4812053104339085,
        "n_stable": 28,
        "n_total": 28,
        "converged": true,
        "worst_s": 0.20895522388059698,
        "worst_alpha": 3.2856803370413883,
        "time_s": 0.5882019996643066
      },
      {
        "Ip_MA": 5,
        "p0_kPa": 2000,
        "beta_N": 12.645404391807974,
        "beta_pct": 5.9648133923622515,
        "spectral_gap": 9.036812353023151,
        "n_stable": 28,
        "n_total": 28,
        "converged": true,
        "worst_s": 0.20895522388059698,
        "worst_alpha": 6.571360674082777,
        "time_s": 0.5385074615478516
      },
      {
        "Ip_MA": 5,
        "p0_kPa": 3000,
        "beta_N": 18.968106587711958,
        "beta_pct": 8.947220088543377,
        "spectral_gap": 25.328276312243098,
        "n_stable": 28,
        "n_total": 28,
        "converged": true,
        "worst_s": 0.20895522388059698,
        "worst_alpha": 9.857041011124165,
        "time_s": 0.5553874969482422
      },
      {
        "Ip_MA": 5,
        "p0_kPa": 5000,
        "beta_N": 31.61351097951993,
        "beta_pct": 14.912033480905627,
        "spectral_gap": 78.85148293993448,
        "n_stable": 28,
        "n_total": 28,
        "converged": true,
        "worst_s": 0.20895522388059698,
        "worst_alpha": 16.42840168520694,
        "time_s": 1.1433320045471191
      }
    ],
    "10MA": [
      {
        "Ip_MA": 10,
        "p0_kPa": 50,
        "beta_N": 0.1580675548975997,
        "beta_pct": 0.14912033480905632,
        "spectral_gap": 0.01972600314434666,
        "n_stable": 28,
        "n_total": 28,
        "converged": true,
        "worst_s": 0.20895522388059698,
        "worst_alpha": 0.04107100421301736,
        "time_s": 1.5294077396392822
      },
      {
        "Ip_MA": 10,
        "p0_kPa": 100,
        "beta_N": 0.3161351097951994,
        "beta_pct": 0.29824066961811263,
        "spectral_gap": -0.3299388349798067,
        "n_stable": 5,
        "n_total": 28,
        "converged": true,
        "worst_s": 1.173592970790786,
        "worst_alpha": 0.5545654526423435,
        "time_s": 1.4288909435272217
      },
      {
        "Ip_MA": 10,
        "p0_kPa": 200,
        "beta_N": 0.6322702195903988,
        "beta_pct": 0.5964813392362253,
        "spectral_gap": -0.996786450997381,
        "n_stable": 0,
        "n_total": 28,
        "converged": true,
        "worst_s": 1.1976020290523401,
        "worst_alpha": 1.1104811713517848,
        "time_s": 1.354276180267334
      },
      {
        "Ip_MA": 10,
        "p0_kPa": 500,
        "beta_N": 1.5806755489759967,
        "beta_pct": 1.4912033480905629,
        "spectral_gap": -1.5701090084816656,
        "n_stable": 0,
        "n_total": 28,
        "converged": true,
        "worst_s": 1.3167092087178478,
        "worst_alpha": 2.1022076182680514,
        "time_s": 0.9414448738098145
      },
      {
        "Ip_MA": 10,
        "p0_kPa": 1000,
        "beta_N": 3.1613510979519934,
        "beta_pct": 2.9824066961811257,
        "spectral_gap": -1.2502992428642015,
        "n_stable": 6,
        "n_total": 28,
        "converged": true,
        "worst_s": 1.3489242282507017,
        "worst_alpha": 3.0901638572518078,
        "time_s": 0.789189338684082
      },
      {
        "Ip_MA": 10,
        "p0_kPa": 2000,
        "beta_N": 6.322702195903987,
        "beta_pct": 5.9648133923622515,
        "spectral_gap": -0.5806931527229665,
        "n_stable": 23,
        "n_total": 28,
        "converged": true,
        "worst_s": 0.20895522388059698,
        "worst_alpha": 1.6428401685206941,
        "time_s": 0.6712620258331299
      },
      {
        "Ip_MA": 10,
        "p0_kPa": 3000,
        "beta_N": 9.484053293855979,
        "beta_pct": 8.947220088543377,
        "spectral_gap": -0.299719730795368,
        "n_stable": 27,
        "n_total": 28,
        "converged": true,
        "worst_s": 0.20895522388059698,
        "worst_alpha": 2.4642602527810413,
        "time_s": 0.7099142074584961
      },
      {
        "Ip_MA": 10,
        "p0_kPa": 5000,
        "beta_N": 15.806755489759965,
        "beta_pct": 14.912033480905627,
        "spectral_gap": 1.8330503610271498,
        "n_stable": 28,
        "n_total": 28,
        "converged": true,
        "worst_s": 0.20895522388059698,
        "worst_alpha": 4.107100421301735,
        "time_s": 0.6641004085540771
      }
    ],
    "15MA": [
      {
        "Ip_MA": 15,
        "p0_kPa": 50,
        "beta_N": 0.10537836993173313,
        "beta_pct": 0.14912033480905632,
        "spectral_gap": 0.021304486245484783,
        "n_stable": 28,
        "n_total": 28,
        "converged": true,
        "worst_s": 0.208955223880597,
        "worst_alpha": 0.01825377965022994,
        "time_s": 0.7181036472320557
      },
      {
        "Ip_MA": 15,
        "p0_kPa": 100,
        "beta_N": 0.21075673986346627,
        "beta_pct": 0.29824066961811263,
        "spectral_gap": 0.02013757432237078,
        "n_stable": 28,
        "n_total": 28,
        "converged": true,
        "worst_s": 0.208955223880597,
        "worst_alpha": 0.03650755930045988,
        "time_s": 0.9208838939666748
      },
      {
        "Ip_MA": 15,
        "p0_kPa": 200,
        "beta_N": 0.42151347972693254,
        "beta_pct": 0.5964813392362253,
        "spectral_gap": -0.2459836237038125,
        "n_stable": 7,
        "n_total": 28,
        "converged": true,
        "worst_s": 1.173592970790786,
        "worst_alpha": 0.4929470690154168,
        "time_s": 0.8357219696044922
      },
      {
        "Ip_MA": 15,
        "p0_kPa": 500,
        "beta_N": 1.053783699317331,
        "beta_pct": 1.4912033480905629,
        "spectral_gap": -1.108111995291984,
        "n_stable": 0,
        "n_total": 28,
        "converged": true,
        "worst_s": 1.1976020290523404,
        "worst_alpha": 1.2338679681686504,
        "time_s": 0.676522970199585
      },
      {
        "Ip_MA": 15,
        "p0_kPa": 1000,
        "beta_N": 2.107567398634662,
        "beta_pct": 2.9824066961811257,
        "spectral_gap": -1.5511214919744882,
        "n_stable": 0,
        "n_total": 28,
        "converged": true,
        "worst_s": 1.2993758808133682,
        "worst_alpha": 2.0543401042031766,
        "time_s": 0.6242413520812988
      },
      {
        "Ip_MA": 15,
        "p0_kPa": 2000,
        "beta_N": 4.215134797269324,
        "beta_pct": 5.9648133923622515,
        "spectral_gap": -1.466255704671918,
        "n_stable": 0,
        "n_total": 28,
        "converged": true,
        "worst_s": 1.348924228250702,
        "worst_alpha": 2.7468123175571644,
        "time_s": 0.6420791149139404
      },
      {
        "Ip_MA": 15,
        "p0_kPa": 3000,
        "beta_N": 6.322702195903986,
        "beta_pct": 8.947220088543377,
        "spectral_gap": -0.7155843770497702,
        "n_stable": 18,
        "n_total": 28,
        "converged": true,
        "worst_s": 0.41457858769931666,
        "worst_alpha": 1.95587372092963,
        "time_s": 0.5889630317687988
      },
      {
        "Ip_MA": 15,
        "p0_kPa": 5000,
        "beta_N": 10.53783699317331,
        "beta_pct": 14.912033480905627,
        "spectral_gap": -0.544529667894061,
        "n_stable": 24,
        "n_total": 28,
        "converged": true,
        "worst_s": 0.208955223880597,
        "worst_alpha": 1.825377965022994,
        "time_s": 0.695197582244873
      }
    ]
  }
}