# Physics-regularized neural network of the ideal-MHD solution operator in Wendelstein 7-X configurations

@inproceedings{Merlo2022PhysicsregularizedNN, title={Physics-regularized neural network of the ideal-MHD solution operator in Wendelstein 7-X configurations}, author={Andrea Merlo and Daniel Bockenhoff and Jonathan Schilling and Samuel Aaron Lazerson and Thomas Sunn Pedersen and The W7-X Team}, year={2022} }

The stellarator is a promising concept to produce energy from nuclear fusion by magnetically conﬁning a high-pressure plasma. Magnetohydrodynamics (MHD) describes how plasma pressure, current density and magnetic ﬁeld interact. In a stellarator, the conﬁning ﬁeld is three-dimensional, and the computational cost of solving the 3D MHD equations currently limits stellarator comprehension, exploration and optimization. Although data-driven approaches have been proposed to provide fast 3D MHD…

## References

SHOWING 1-10 OF 94 REFERENCES

### Proof of concept of a fast surrogate model of the VMEC code via neural networks in Wendelstein 7-X scenarios

- Computer ScienceNuclear Fusion
- 2021

Artificial neural network models able to quickly compute the equilibrium magnetic field of Wendelstein 7-X are presented, and the feasibility of a fast NN drop-in surrogate model for VMEC is shown, which opens up new operational scenarios where target applications could make use of magnetic equilibria at unprecedented scales.

### Fast recovery of vacuum magnetic configuration of the W7-X stellarator using function parametrization and artificial neural networks

- Physics
- 2004

W7-X, a five-period, fully optimized stellarator, currently under construction at IPP-Greifswald, Germany, is built with superconducting coils to show the steady state capability of stellarators.…

### Solving Equilibria with a Neural Network

- Physics
- 1995

A general method to solve differential equations that was introduced recently, based on the use of MLP-1 type neural networks, is applied to the fast solution of ideal magnetohydrodynamic (MHD)…

### Gradient-based optimization of 3D MHD equilibria

- PhysicsJournal of Plasma Physics
- 2021

Using recently developed adjoint methods for computing the shape derivatives of functions that depend on magnetohydrodynamic (MHD) equilibria (Antonsen et al., J. Plasma Phys., vol. 85, issue 2,…

### Physics and Engineering Design for Wendelstein VII-X

- Physics
- 1990

AbstractThe future experiment Wendelstein VII-X (W VII-X) is being developed at the Max-Planck-Institut fur Plasmaphysik. A Helical Advanced Stellarator (Helias) configuration has been chosen because…

### Verification of the ideal magnetohydrodynamic response at rational surfaces in the VMEC code

- Physics
- 2016

The VMEC nonlinear ideal MHD equilibrium code [S. P. Hirshman and J. C. Whitson, Phys. Fluids 26, 3553 (1983)] is compared against analytic linear ideal MHD theory in a screw-pinch-like…

### Steepest‐descent moment method for three‐dimensional magnetohydrodynamic equilibria

- Physics
- 1983

An energy principle is used to obtain the solution of the magnetohydrodynamic (MHD) equilibrium equation J×B−∇p=0 for nested magnetic flux surfaces that are expressed in the inverse coordinate…

### Full linearized Fokker–Planck collisions in neoclassical transport simulations

- Physics
- 2011

The complete linearized Fokker–Planck collision operator has been implemented in the drift-kinetic code NEO (Belli and Candy 2008 Plasma Phys. Control. Fusion 50 095010) for the calculation of…

### Preconditioned descent algorithm for rapid calculations of magnetohydrodynamic equilibria

- Computer Science
- 1991

### Neural network differential equation and plasma equilibrium solver.

- PhysicsPhysical review letters
- 1995

A new generally applicable method to solve differential equations, based on neural networks, is proposed, which is especially promising for the three-dimensional plasma equilibrium problem.