References

Background and canonical references for VMEC and related equilibrium methods:

  1. S. P. Hirshman and J. C. Whitson, “Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria,” Physics of Fluids 26 (1983).

  2. S. P. Hirshman, W. I. van Rij, and P. Merkel, “Three-dimensional free boundary calculations using a spectral Green’s function method,” Computer Physics Communications 43 (1986).

  3. P. Merkel, “Solution of stellarator boundary value problems with external currents,” Nuclear Fusion 27 (1987).

  4. VMEC2000 reference documentation and wout file format notes (VMEC/LIBSTELL distribution and Princeton VMEC resources).

  5. VMEC++ numerics notes (local copy): vmecpp/docs/the_numerics_of_vmecpp.pdf.

  6. VMEC++ Fourier basis implementation note (local copy): vmecpp/docs/fourier_basis_implementation.md.

  7. VMEC2000 solver core (residuals, bcovar, preconditioner): STELLOPT/VMEC2000/Sources/General/funct3d.f and STELLOPT/VMEC2000/Sources/General/bcovar.f.

  8. VMEC2000 time-step control and restart logic: STELLOPT/VMEC2000/Sources/TimeStep/evolve.f and STELLOPT/VMEC2000/Sources/TimeStep/restart.f.

  9. VMEC2000 diagnostic scalars and Mercier stability: STELLOPT/VMEC2000/Sources/Input_Output/eqfor.f and STELLOPT/VMEC2000/Sources/Input_Output/mercier.f.

  10. A. H. Glasser, J. M. Greene, and J. L. Johnson, “Resistive instabilities in general toroidal plasma configurations,” Physics of Fluids 18(7), 875-888 (1975).

  11. M. Landreman and R. Jorge, “Magnetic well and Mercier stability of stellarators near the magnetic axis,” Journal of Plasma Physics 86(5), 905860510 (2020), arXiv:2006.14881.

  12. VMEC++ solver/restart structure and parity-relevant control flow: vmecpp/src/vmecpp/cpp/vmecpp/vmec/vmec/vmec.cc.

  13. VMEC++ output-quantity and near-axis extrapolation notes: vmecpp/src/vmecpp/cpp/vmecpp/vmec/output_quantities/output_quantities.cc.

  14. P. Kim, R. Jorge, and W. Dorland, “The On-Axis Magnetic Well and Mercier’s Criterion for Arbitrary Stellarator Geometries,” Journal of Plasma Physics 87(4), 905870409 (2021), arXiv:2011.07416.

  15. J. Schilling et al., “Magnetohydrodynamic equilibrium and stability properties of the Infinity Two fusion pilot plant,” Journal of Plasma Physics 90(6), 905900615 (2024), Appendix B.