Ideal MHD Stability Codes
Ideal magnetohydrodynamic stability codes test whether a plasma equilibrium is stable to large-scale distortions by evaluating a potential-energy functional.
The energy principle
Ideal-MHD stability rests on the energy principle: an equilibrium is stable if every allowed displacement of the plasma raises the system's potential energy. Stability codes evaluate this potential-energy functional, delta-W, over trial displacements; if any displacement makes delta-W negative, the equilibrium is unstable and will distort exponentially.
What is being tested
- Kink modes driven by plasma current
- Ballooning modes driven by pressure gradient in bad-curvature regions
- Pressure-driven interchange and internal modes
- The pressure limit (beta limit) and current limit for stable operation
Numerical methods
The plasma is represented in flux coordinates from an equilibrium solver, and the displacement is expanded in Fourier harmonics over the poloidal and toroidal angles. The energy functional becomes a matrix eigenvalue problem; the sign of the lowest eigenvalue determines stability, and its eigenvector gives the mode structure. Codes differ in how they treat the plasma-vacuum boundary and the surrounding wall.
Ideal vs resistive
Ideal MHD assumes perfect conductivity, so magnetic field lines cannot break. This gives the fastest, most violent instabilities and the hard operating limits. Modes that require field lines to reconnect, such as tearing modes, are outside ideal theory and need resistive codes.
Design use
Stability codes define the safe operating space of a design. For the Hyperion breeder, they check that the intended pressure and current, with its negative-triangularity shape, sit inside the ideal-stable region with adequate margin, including the stabilizing effect of a nearby conducting wall.
Results are reported as stability boundaries and margins, not single points, because real operation must keep a buffer from every limit.