Reconstruction of current profile parameters and plasma shapes in tokamaks
TL;DR: In this paper, 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.
Abstract: 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.
Citations
More filters
TL;DR: In this paper, 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.
Abstract: 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.
584 citations
TL;DR: Early operation of the Alcator C-MOD tokamak [I.H. Hutchinson et al., 1990] is surveyed and the edge plasma shows a wealth of marfe-like phenomena, including a transition to detachment from the divertor plates with accompanying radiative divertor regions.
Abstract: 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.
391 citations
TL;DR: In this paper, 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 tokak plasmas.
Abstract: 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.
355 citations
TL;DR: 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.
Abstract: 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.
328 citations
TL;DR: In this article, a real-time solution for the spatial distribution of poloidal flux and toroidal current density is presented, which is consistent with plasma force balance, allowing accurate evaluation of parameters such as discharge shape and safety factor profile.
Abstract: 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.
292 citations
References
More filters
TL;DR: In this paper, 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.
Abstract: 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.
214 citations
TL;DR: In this paper, a review of two-and three-dimensional ideal MHD equilibrium codes, with particular emphasis on axisymmetric toroidal calculations, is presented. But this paper is restricted to the case of Tokyoamak geometry.
186 citations
TL;DR: In this paper, 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.
Abstract: 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.
155 citations
TL;DR: In this paper, the MHD equilibrium configuration for circular and non-circular plasmas from measurements of the magnetic field and flux made outside the discharge was determined using least squares minimization techniques.
Abstract: Techniques are presented for determining the MHD equilibrium configuration for circular and non-circular plasmas from measurements of the magnetic field and flux made outside the discharge. Least-squares minimization techniques are introduced to provide an objective means for comparing the experimental data with the corresponding calculated equilibrium and for error estimation. Free-boundary equilibria using a simple model for the plasma-current profile with three free parameters – total current, poloidal beta, and a single parameter describing the peakedness of the current profile – are found to be statistically adequate and sufficient to describe the magnetic configuration of the discharge. In plasmas with significant non-circularity, the Shafranov dimensionless inductance, li, can be determined independent of βp. Examples of the application of the technique to discharges in the Doublet-Ill tokamak are presented.
128 citations