Resistive MHD Stability Codes
Resistive stability codes admit finite resistivity, allowing reconnection and slow-growing tearing and resistive-wall modes that ideal analysis misses.
When resistivity matters
Ideal MHD forbids field lines from breaking. Real plasmas have small but finite resistivity, which allows magnetic reconnection at rational surfaces and permits slower instabilities that ideal analysis declares stable. Resistive MHD stability codes retain resistivity and solve for these modes, most importantly tearing modes and the resistive wall mode.
Because resistivity is small, resistive layers are thin and the growth rates are slow, scaling with fractional powers of the resistivity. This creates a boundary-layer structure that codes must resolve with fine radial meshing near rational surfaces.
Tearing modes and Delta-prime
The classical tearing-mode drive is captured by the stability index Delta-prime, the jump in the logarithmic derivative of the perturbed flux across the resistive layer. A positive Delta-prime drives an island to grow. Resistive codes compute Delta-prime from the outer ideal region and match it to inner-layer physics.
Resistive wall modes
An external kind stabilized by a perfect wall becomes unstable on the wall's resistive timescale if the wall conducts imperfectly. Resistive codes model the wall as a resistive shell and predict the resistive-wall-mode growth rate, which sets requirements for feedback stabilization.
Design relevance
For the Hyperion breeder, resistive stability analysis identifies which rational surfaces are prone to tearing and what wall and feedback are needed to hold the target pressure. Neoclassical tearing physics, addressed by dedicated modules, extends this to bootstrap-current-driven islands. All results are simulation-stage.
- Finite resistivity enables reconnection
- Predicts tearing modes via Delta-prime
- Models resistive wall modes and feedback needs
- Requires fine resolution of thin resistive layers