Magnetic analysis of non-circular cross-section tokamaks

Luxon, J.L.; Brown, Ben

doi:10.1088/0029-5515/22/6/009

Cited by 137 publications

(122 citation statements)

References 19 publications

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“…This general technique is in principle similar to that used before to establish the MHD equilibrium in noncircular-cross-section tokamaks [see, e.g., Luxon and Brown, 9 and references therein]. Application of the technique to the CTX spheromak benefits from increased sensitivity to equilibrium changes since the spheromak is a small-aspect-ratio system; changes in the equilibrium affect the position of the magnetic axis and have a large effect on toroidal MFC image currents near the symmetry axis.…”

Section: Observations Of Spheromak Equilibria Which Differ From the Mmentioning

confidence: 99%

Observations of spheromak equilibria which differ from the minimum-energy state and have internal kink distortions

et al. 1986

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Experimental spheromak magnetic equilibria are measured which differ significantly from the minimum-energy state, and are well described by a numerical model where jw/Bhas a linear dependence on the poloidal flux function. Equilibria are determined in a nonperturbing manner by the combination of measurements of flux-conserver image currents with calculations from this model. These equilibria are corroborated by the observation of nondisruptive rotating internal kink distortions (with toroidal mode numbers n = 1, 2, and 3), coupled with theoretical MHD thresholds for the onset of these modes. PACS numbers: 52.55.Hc, 52.35.Py, 52.70.Ds In a spheromak, the magnetic fields are generated primarily by internal currents rather than by external coils. Once established, these fields are conjectured 1 to relax towards a state of minimum energy subject to the constraint that the magnetic helicity 2 is conserved. In a closed system the minimum-energy equilibrium satisfies VxB = XB with X^/xoJ 11/5 = const. Since competing effects are certainly present in any experiment, small deviations from a uniform, constant X can be expected. However, these departures from the minimum-energy or "Taylor" state are expected 1 to relax towards this lowest-energy configuration on a time scale shorter than the resistive diffusion time.We report results from the compact toroid experiment 3 ' 4 (CTX) which give spheromak equilibria (determined in a nonperturbing manner) not with X = const, but with X = X(iJ/), where t// is the normalized poloidal flux function [t|/ = (poloidal flux value)/ (total poloidal flux)]. The departures in magnetic energy of these equilibria with respect to the minimumenergy state is small. Coherent oscillations are seen, generated by rotating kink modes within the equilibria. The onset of the modes is shown to be consistent with the slope of X(i|/) from the equilibrium measurement.Other spheromak experiments 5,6 have measured the magnetic fields with internal probes, and have found experimental agreement with a zero-pressure, constants model. Hart et al? obtained for their data better agreement by including a finite-plasma-pressure correction to a constant-X model,In CTX, the X(i/i) profile is inferred from external measurements of induced image currents flowing in a mesh flux conserver 8 (MFC) surrounding the plasma, combined with results from numerical calculations of the equilibrium. This general technique is in principle similar to that used before to establish the MHD equilibrium in noncircular-cross-section tokamaks [see, e.g., Luxon and Brown, 9 and references therein]. Application of the technique to the CTX spheromak benefits from increased sensitivity to equilibrium changes since the spheromak is a small-aspect-ratio system; changes in the equilibrium affect the position of the magnetic axis and have a large effect on toroidal MFC image currents near the symmetry axis. Arrays of small Rogowski loops (5% relative calibration) measure the MFC currents, with the ratios of the currents (filtered to remove osci...

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Section: Observations Of Spheromak Equilibria Which Differ From the Mmentioning

confidence: 99%

Observations of spheromak equilibria which differ from the minimum-energy state and have internal kink distortions

et al. 1986

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“…The variable λ is determined by imposing that the total plasma current equals a predetermined value I P . We refer to [21] for a physical interpretation of these parameters.…”

Section: Free Boundary Equilibrium Computationmentioning

confidence: 99%

Towards Automated Magnetic Divertor Design for Optimal Heat Exhaust

et al. 2016

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Abstract. Avoiding excessive structure heat loads in future fusion tokamaks is regarded as one of the greatest design challenges. In this paper, we aim at developing a tool to study how the severe divertor heat loads can be mitigated by reconfiguring the magnetic confinement. For this purpose, a free boundary equilibrium code is integrated with a plasma edge transport code to work in an automated fashion. Next, a practical and efficient adjoint based sensitivity calculation is proposed to evaluate the sensitivities of the integrated code. The sensitivity calculation is finally applied to a realistic test case and compared with finite difference sensitivity calculations.

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“…0018-9464/00$10.00 © 2000 IEEE The time evolution of the poloidal flux per radian is determined by: (4) In the plasma region, the Grad-Shafranov equation provides the following expression for the plasma current density: (5) where is the pressure and is the vacuum magnetic permeability.…”

Section: A Plasmamentioning

confidence: 99%

“…Following [5], we assume the plasma current density profile to be a function of , , and a set of three parameters associated with the physical quantities of , , and . The time evolution of , and is assumed to be prescribed.…”

Section: A Plasmamentioning

confidence: 99%

Time evolution of tokamak plasmas in the presence of 3D conducting structures

et al. 2000

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This paper presents a method for the simulation of the time evolution of fusion plasmas in the presence of eddy currents induced in nonmagnetic 3D structures. The plasma is assumed to be 2D axisymmetric. The interaction between the plasma and the external currents is assumed to occur via the magnetic field averaged through the toroidal angle. The average poloidal field is computed by means of a 2D axisymmetric differential FEM formulation in terms of the poloidal magnetic flux. The 3D induced currents are calculated via an integral edge-element formulation in terms of a two-component current density vector potential. The method is also applied to derive a linearized plasma response model for the control of the plasma current position and shape in the presence of 3D conducting structures.

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Magnetic analysis of non-circular cross-section tokamaks

Cited by 137 publications

References 19 publications

Observations of spheromak equilibria which differ from the minimum-energy state and have internal kink distortions

Observations of spheromak equilibria which differ from the minimum-energy state and have internal kink distortions

Towards Automated Magnetic Divertor Design for Optimal Heat Exhaust

Time evolution of tokamak plasmas in the presence of 3D conducting structures

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