Numerical calculation of free boundary equilibrium via meshfree method and its application in Alborz tokamak

The problem of bifurcation of a free boundary equilibrium is reconsidered in a simple model. We find which combinations of specified parameters result in a non-unique solution and find the resulting bifurcation point. By including reversed current solutions, the model sheds some light on the equilibrium βp limit obtained in previous analytic and numerical models.

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Novel free-boundary equilibrium and transport solver with theory-based models and its validation against ASDEX Upgrade current ramp scenarios

Plasma Physics and Controlled Fusion ◽

10.1088/0741-3335/55/12/124028 ◽

2013 ◽

Vol 55 (12) ◽

pp. 124028 ◽

Cited By ~ 12

Author(s):

E Fable ◽

C Angioni ◽

F J Casson ◽

D Told ◽

A A Ivanov ◽

...

Keyword(s):

Free Boundary ◽

Current Ramp ◽

Boundary Equilibrium

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Combined plasma–coil optimization algorithms

Journal of Plasma Physics ◽

10.1017/s0022377821000271 ◽

2021 ◽

Vol 87 (2) ◽

Author(s):

S. A. Henneberg ◽

S. R. Hudson ◽

D. Pfefferlé ◽

P. Helander

Keyword(s):

Free Boundary ◽

Optimization Algorithms ◽

Energy Functional ◽

Equilibrium Calculation ◽

Weak Formulation ◽

Fixed Boundary ◽

Minimization Principle ◽

Boundary Equilibrium ◽

Boundary Optimization ◽

Coil Optimization

Combined plasma–coil optimization approaches for designing stellarators are discussed and a new method for calculating free-boundary equilibria for multiregion relaxed magnetohydrodynmics (MRxMHD) is proposed. Four distinct categories of stellarator optimization, two of which are novel approaches, are the fixed-boundary optimization, the generalized fixed-boundary optimization, the quasi-free-boundary optimization, and the free-boundary (coil) optimization. These are described using the MRxMHD energy functional, the Biot–Savart integral, the coil-penalty functional and the virtual casing integral and their derivatives. The proposed free-boundary equilibrium calculation differs from existing methods in how the boundary-value problem is posed, and for the new approach it seems that there is not an associated energy minimization principle because a non-symmetric functional arises. We propose to solve the weak formulation of this problem using a spectral-Galerkin method, and this will reduce the free-boundary equilibrium calculation to something comparable to a fixed-boundary calculation. In our discussion of combined plasma–coil optimization algorithms, we emphasize the importance of the stability matrix.

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