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

Early operation of the Alcator‐C‐MOD tokamak [I.H. Hutchinson, Proceedings of IEEE 13th Symposium on Fusion Engineering, Knoxville, TN, edited by M. Lubell, M. Nestor, and S. Vaughan (Institute of Electrical and Electronic Engineers, New York, 1990), Vol. 1, p. 13] is surveyed. Reliable operation, with plasma current up to 1 MA, has been obtained, despite the massive conducting superstructure and the associated error fields. However, vertical disruptions are not slowed by the long vessel time constant. With pellet fueling, peak densities up to 9×1020 m−3 have been attained and ‘‘snakes’’ are often seen. Initial characterization of divertor and scrape‐off layer is presented and indicates approximately Bohm diffusion. The edge plasma shows a wealth of marfe‐like phenomena, including a transition to detachment from the divertor plates with accompanying radiative divertor regions. Energy confinement generally appears to exceed the expectations of neo‐Alcator scaling. A transition to Ohmic H mode has been observed. Ion cyclotron heating experiments have demonstrated good power coupling, in agreement with theory.

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First results from Alcator‐C‐MOD*

A new computational tool, edge localized instabilities in tokamaks equilibria (ELITE), has been developed to help our understanding of short wavelength instabilities close to the edge of tokamak plasmas. Such instabilities may be responsible for the edge localized modes observed in high confinement H-mode regimes, which are a serious concern for next step tokamaks because of the high transient power loads which they can impose on divertor target plates. ELITE uses physical insight gained from analytic studies of peeling and ballooning modes to provide an efficient way of calculating the edge ideal magnetohydrodynamic stability properties of tokamaks. This paper describes the theoretical formalism which forms the basis for the code.

/pdf/numerical-studies-of-edge-localized-instabilities-in-gbssnt7bf0.pdf

Numerical studies of edge localized instabilities in tokamaks

Intermittent plasma objects (IPOs) featuring higher pressure than the surrounding plasma, and responsible for ∼50% of the E×BT radial transport, are observed in the scrape off layer (SOL) and edge of the DIII-D tokamak [J. Watkins et al., Rev. Sci. Instrum. 63, 4728 (1992)]. Conditional averaging reveals that the IPOs, produced at a rate of ∼3×103 s−1, are positively charged and also polarized, featuring poloidal electric fields of up to 4000 V/m. The IPOs move poloidally at speeds of up to 5000 m/s and radially with E×BT/B2 velocities of ∼2600 m/s near the last closed flux surface (LCFS), and ∼330 m/s near the wall. The IPOs slow down as they shrink in radial size from 4 cm at the LCFS to 0.5 cm near the wall. The IPOs appear in the SOL of both L and H mode discharges and are responsible for nearly 50% of the SOL radial E×B transport at all radii; however, they are highly reduced in absolute amplitude in H-mode conditions.

/pdf/transport-by-intermittent-convection-in-the-boundary-of-the-jlmzni2mac.pdf

Transport by intermittent convection in the boundary of the DIII-D tokamak

A practical method for performing a tokamak equilibrium reconstruction in real time for arbitrary time varying discharge shapes and current profiles is described. An approximate solution to the Grad-Shafranov equilibrium relation is found which best fits the diagnostic measurements. Thus, a solution for the spatial distribution of poloidal flux and toroidal current density is available in real time that is consistent with plasma force balance, allowing accurate evaluation of parameters such as discharge shape and safety factor profile. The equilibrium solutions are produced at a rate sufficient for discharge control. This equilibrium reconstruction algorithm has been implemented on the digital plasma control system for the DIII-D tokamak. The first application of real time equilibrium reconstruction to discharge shape control is described.

https://iopscience.iop.org/article/10.1088/0029-5515/38/7/308/pdf

Real time equilibrium reconstruction for tokamak discharge control

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

A.G. Kellman

Papers

Reconstruction of current profile parameters and plasma shapes in tokamaks