An efficient method is given to reconstruct the current profile parameters, the plasma shape, and a current profile consistent with the magnetohydrodynamic equilibrium constraint from external magnetic measurements, based on a Picard iteration approach which approximately conserves the measurements. Computational efforts are reduced by parametrizing the current profile linearly in terms of a number of physical parameters. Results of detailed comparative calculations and a sensitivity study are described. Illustrative calculations to reconstruct the current profiles and plasma shapes in ohmically and auxiliarily heated Doublet III plasmas are given which show many interesting features of the current profiles.

https://iopscience.iop.org/article/10.1088/0029-5515/25/11/007/pdf

Reconstruction of current profile parameters and plasma shapes in tokamaks

An efficient method is given for self-consistent reconstruction of the tokamak current profiles and their associated magnetic topology using the magnetohydrodynamic (MHD) equilibrium constraint from external magnetic measurements, kinetic profile measurements, internal poloidal magnetic field measurements, and topological information from soft X-ray (SXR) measurements. Illustrative examples for beam heated H-mode divertor discharges in the DIII-D tokamak are presented, using the experimentally measured kinetic profile information and external magnetic data from the existing diagnostics. Comparative reconstructions of the current profile using various combinations of diagnostics are given. Also presented is an alternative magnetic analysis method in which the MHD equilibrium is reconstructed using external magnetic data and a constraint on the edge pressure gradient. The results of a sensitivity study are given which show that the axial safety factor q(0) can be more accurately determined when additional information from internal poloidal magnetic measurements is used in conjunction with the external magnetic, kinetic and SXR topological data.

https://iopscience.iop.org/article/10.1088/0029-5515/30/6/006/pdf

Equilibrium analysis of current profiles in tokamaks

Recent results from confinement scaling experiments on tokamaks with ohmic and strong auxiliary heating are reviewed. An attempt is made to draw these results together into a low-density ohmic confinement scaling law, and a scaling law for confinement with auxiliary heating. The auxiliary heating confinement law may also serve to explain the saturation in tau/sub E/ vs anti n/sub e/ observed in some ohmic heating density scaling experiments.

/pdf/energy-confinement-scaling-in-tokamaks-some-implications-of-3p6ex87vfz.pdf

Energy confinement scaling in tokamaks: Some implications of recent experiments with ohmic and strong auxiliary heating

Physics elements and advances crucial for the development of axisymmetric magnetohydrodynamic equilibrium reconstruction to support plasma operation and data analysis in the DIII-D tokamak are revi...

https://web.gat.com/pubs-ext/FusionSciTechnol/A24687abs.pdf

MHD Equilibrium Reconstruction in the DIII-D Tokamak

Integral relations for the average poloidal beta p and the plasma internal inductance li are derived from the magnetohydrodynamic (MHD) equilibrium equation for an axisymmetric torus. The volume-dependent parameters that appear depend only weakly on the actual current density distribution inside the plasma and can be evaluated approximately, given the plasma shape and boundary poloidal magnetic field. In practice, these can be accurately and efficiently obtained for both diverted and limited plasmas from measured external poloidal magnetic field and flux values by approximating the plasma current distribution using a few filaments or distributed sources. For a tokamak plasma with a non-circular cross-section of sufficient elongation, p and li can then be approximately determined separately. This is demonstrated for analytic equilibria of known shape as well as for actual Doublet III (D-III) plasmas for which p and li have been determined by using other methods. Results of a sensitivity study are described.

https://iopscience.iop.org/article/10.1088/0029-5515/25/10/004/pdf

Separation of β̄p and ℓi in tokamaks of non-circular cross-section

A method for determining plasma shape and global properties of high-beta non-circular tokamak equilibria (βp, β, q and li) from magnetic sensor data is described. The technique uses a least-squares fitting procedure to find the plasma boundary and a global force balance analysis (as opposed to a complete solution of the MHD equilibrium equation) to determine plasma pressure. Estimates of the uncertainties in the computed quantities are also obtained, and the method is fast enough that it can be used to provide a complete time history (up to 100 time points) of ISX-B high-beta discharges within two to three minutes of each shot. Values obtained using this method are in excellent agreement with more detailed measurements and with free-boundary MHD equilibrium computations.

D.W. Swain

Papers

An efficient technique for magnetic analysis of non-circular, high-beta tokamak equilibria