[jmlmir369]

Ports the local ballooning-stability solver from Julia GPEC into Fortran DCON, RDCON, and STRIDE, consolidating the local stability evaluations into a unified bal_scan routine.

Control Flags

• mer_flag = t: Evaluates the Mercier and resistive interchange indices ($D_I, D_R, H$).
• bal_flag = t: Additionally solves the high-$n$ ballooning ODE and searches the marginal pressure-gradient boundary:
  • ballooning_Delta_prime: High-$n$ ballooning matching index ($\Delta' > 0$ is unstable).
  • alpha and alpha_critical: Equilibrium pressure-gradient parameter and the first infinite-$n$ ballooning stability boundary ($\alpha > \alpha_{\mathrm{critical}}$ is unstable).

Validation

1. Legacy Fortran Consistency (mercier.f vs bal.f):
   • Compared on the DIII-D-like ideal equilibrium (33 radial surfaces).
   • $D_I, D_R, H$ signs agree 100% across all surfaces.
   • Median relative differences: $1.77 \times 10^{-5}$ ($D_I$), $7.78 \times 10^{-5}$ ($D_R$); $H$ is identical ($\Delta H \equiv 0$).
   • Core behavior remains physically consistent ($D_I, D_R < 0$, stable).

2. Julia JPEC Cross-Check (Ballooning Solver):
   • Ballooning $\Delta'$: 100% sign agreement across all 33 surfaces; median relative difference is $1.24 \times 10^{-5}$.
   • Boundary $\alpha_{\mathrm{critical}}$: Evaluated on the same 13 surfaces ($0.22 \le \psi_N \le 0.77$) with 100% sign agreement; median relative difference is $1.20 \times 10^{-4}$ (max absolute error $0.041$).
   • Equilibrium $\alpha$: Median relative difference $7.15 \times 10^{-7}$ across common finite surfaces.