Resistive MHD and Nonlinear Codes
Resistive MHD codes allow magnetic field lines to reconnect, capturing tearing modes and the slower, nonlinear instabilities that ideal theory cannot describe.
Beyond ideal MHD
Ideal MHD forbids field lines from breaking, so it misses a whole family of instabilities that depend on finite resistivity. Resistive MHD codes reinstate the resistive term in Ohm's law, permitting reconnection and the formation of magnetic islands. These modes grow more slowly than ideal ones but are pervasive in real operation.
Tearing and neoclassical tearing modes
Tearing modes reconnect field lines at rational surfaces to form islands that degrade confinement. Neoclassical tearing modes are sustained by the loss of bootstrap current inside the island, making them a leading concern at high pressure. Resistive codes, sometimes with added neoclassical physics, predict their onset and growth.
Linear and nonlinear operation
- Linear resistive codes give growth rates and the mode structure near onset
- Nonlinear extended-MHD codes follow islands as they grow, saturate, and interact
- Some codes add two-fluid and finite-Larmor-radius effects for realism
Extended MHD
The most capable codes solve extended-MHD equations that go beyond single-fluid resistive MHD, including separate ion and electron dynamics, Hall terms, and pressure anisotropy. These three-dimensional, time-dependent simulations are computationally heavy but capture the nonlinear evolution of major events.
What they inform
Resistive and extended-MHD modeling underpins the design of feedback and control systems that suppress islands, and helps set operating margins that avoid the most damaging nonlinear events. They also feed disruption studies, since many disruptions begin as a growing resistive mode.
Such analyses are part of assessing the robustness of any design, including how a machine like the Hyperion breeder would respond to the slow instabilities that ideal analysis cannot see.