Maximilian Ruth - A Statistical Magnetohydrodynamic Equilibrium Model - IPAM at UCLA
Recorded 25 March 2026. Maximilian Ruth of the University of Texas at Austin presents "A Statistical Magnetohydrodynamic Equilibrium Model" at IPAM's Multi-Fidelity Methods for Fusion Plasma Physics Workshop.Abstract: The baseline model for computing stellarator equilibria is the static magnetohydrodynamic (MHD) equations with zero flow. The input to the model is two profile functions (pressure and rotational transform) and a boundary condition. The output is a magnetic field with nested surfaces. Because MHD equilibria are simple to specify and fast to compute, they are used for most stellarator tasks, such as optimization, equilibrium reconstruction, and as a background for neoclassical and gyrokinetic transport.
However, there is a known flaw. In non-axisymmetric 3D toroidal domains, the MHD equilibrium model does not generally support smooth solutions. This leads to both unphysical singular plasma currents on resonant flux surfaces and non- or slow convergence of numerical approximations under refinement. In this work, we present an improved equilibrium principle derived from a statistical model for plasma fluctuations. Instead of being static, we assume that the plasma magnetic field is ergodically and rapidly fluctuating relative to the MHD time scale. By averaging the resulting force, we derive a variational equilibrium problem for the statistical mean magnetic field which depends on fluctuation variance. Then, through asymptotics, numerical simulations, and a Grad-Shafranov type argument, we show that the variational principle supports smooth solutions for specific fluctuation statistics chosen to minimally modify the standard equilibrium modeling paradigm. Physically, this model smooths singular current sheets with a length scale determined by the magnetic field fluctuations.
Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-i-multi-fidelity-methods-for-fusion-plasma-physics/?tab=overview Receive SMS online on sms24.me
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