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Field AR, Chapman-Oplopoiou B, Connor JW, Frassinetti L, Hatch DR, Roach CM, Saarelma S. Comparing pedestal structure in JET-ILW H-mode plasmas with a model for stiff ETG turbulent heat transport. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20210228. [PMID: 36587822 PMCID: PMC9805819 DOI: 10.1098/rsta.2021.0228] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/08/2022] [Accepted: 05/20/2022] [Indexed: 06/17/2023]
Abstract
A predictive model for the electron temperature profile of the H-mode pedestal is described, and its results are compared with the pedestal structure of JET-ILW plasmas. The model is based on a scaling for the gyro-Bohm normalized, turbulent electron heat flux [Formula: see text] resulting from electron temperature gradient (ETG) turbulence, derived from results of nonlinear gyrokinetic (GK) calculations for the steep gradient region. By using the local temperature gradient scale length [Formula: see text] in the normalization, the dependence of [Formula: see text] on the normalized gradients [Formula: see text] and [Formula: see text] can be represented by a unified scaling with the parameter [Formula: see text], to which the linear stability of ETG turbulence is sensitive when the density gradient is sufficiently steep. For a prescribed density profile, the value of [Formula: see text] determined from this scaling, required to maintain a constant electron heat flux [Formula: see text] across the pedestal, is used to calculate the temperature profile. Reasonable agreement with measurements is found for different cases, the model providing an explanation of the relative widths and shifts of the [Formula: see text] and [Formula: see text] profiles, as well as highlighting the importance of the separatrix boundary conditions. Other cases showing disagreement indicate conditions where other branches of turbulence might dominate. This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'.
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Affiliation(s)
- A. R. Field
- United Kingdom Atomic Energy Authority, Culham Centre for Fusion Energy, Culham Science Centre, Abingdon, Oxon OX14 3DB, UK
| | - B. Chapman-Oplopoiou
- United Kingdom Atomic Energy Authority, Culham Centre for Fusion Energy, Culham Science Centre, Abingdon, Oxon OX14 3DB, UK
| | - J. W. Connor
- United Kingdom Atomic Energy Authority, Culham Centre for Fusion Energy, Culham Science Centre, Abingdon, Oxon OX14 3DB, UK
| | - L. Frassinetti
- Division of Fusion Plasma Physics, KTH Royal Institute of Technology SE-100 44 Stockholm, Sweden
| | - D. R. Hatch
- Institute for Fusion Studies, University of Texas at Austin, Austin, TX 78712, USA
| | - C. M. Roach
- United Kingdom Atomic Energy Authority, Culham Centre for Fusion Energy, Culham Science Centre, Abingdon, Oxon OX14 3DB, UK
| | - S. Saarelma
- United Kingdom Atomic Energy Authority, Culham Centre for Fusion Energy, Culham Science Centre, Abingdon, Oxon OX14 3DB, UK
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Zocco A, Podavini L, Garcìa-Regaña JM, Barnes M, Parra FI, Mishchenko A, Helander P. Gyrokinetic electrostatic turbulence close to marginality in the Wendelstein 7-X stellarator. Phys Rev E 2022; 106:L013202. [PMID: 35974606 DOI: 10.1103/physreve.106.l013202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2022] [Accepted: 07/07/2022] [Indexed: 06/15/2023]
Abstract
The transition from strong (fluidlike) to nearly marginal (Floquet-type) regimes of ion-temperature-gradient (ITG) driven turbulence is studied in the stellarator Wendelstein 7-X by means of numerical simulations. Close to marginality, extended (along magnetic field lines) linearly unstable modes are dominant, even in the presence of kinetic electrons, and provide a drive that results in finite turbulent transport. A total suppression of turbulence above the linear stability threshold of the ITG modes, commonly present in tokamaks and known as the "Dimits shift," is not observed. We show that this is mostly due to the peculiar radial structure of marginal turbulence, which is more localized than in the fluid case and therefore less likely to be stabilized by shearing flows.
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Affiliation(s)
- Alessandro Zocco
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, D-17491 Greifswald, Germany
| | - Linda Podavini
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, D-17491 Greifswald, Germany
- Università Milano Bicocca, Dipartimento di Fisica Giuseppe Occhialini, Piazza della Scienza, 3 20126 Milano, Italy
- Institut für Physik, Universität Greifswald, 17489 Greifswald, Germany
| | | | - Michael Barnes
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom
| | - Felix I Parra
- Princeton Plasma Physics Laboratory, 100 Stellarator Road, Princeton, New Jersey 08540, USA
| | - A Mishchenko
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, D-17491 Greifswald, Germany
| | - Per Helander
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, D-17491 Greifswald, Germany
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Carralero D, Happel T, Estrada T, Tokuzawa T, Martínez J, de la Luna E, Cappa A, García J. A feasibility study for a Doppler reflectometer system in the JT-60SA tokamak. FUSION ENGINEERING AND DESIGN 2021. [DOI: 10.1016/j.fusengdes.2021.112803] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Plunk GG, Xanthopoulos P, Weir GM, Bozhenkov SA, Dinklage A, Fuchert G, Geiger J, Hirsch M, Hoefel U, Jakubowski M, Langenberg A, Pablant N, Pasch E, Stange T, Zhang D, W-X Team T. Stellarators Resist Turbulent Transport on the Electron Larmor Scale. PHYSICAL REVIEW LETTERS 2019; 122:035002. [PMID: 30735428 DOI: 10.1103/physrevlett.122.035002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2018] [Revised: 11/07/2018] [Indexed: 06/09/2023]
Abstract
Electron temperature gradient (ETG)-driven turbulence, despite its ultrafine scale, is thought to drive significant thermal losses in magnetic fusion devices-but what role does it play in stellarators? The first numerical simulations of ETG turbulence for the Wendelstein 7-X stellarator, together with power balance analysis from its initial experimental operation phase, suggest that the associated transport should be negligible compared to other channels. The effect, we argue, originates essentially from the geometric constraint of multiple field periods, a generic feature of stellarators.
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Affiliation(s)
- G G Plunk
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, 17491 Greifswald, Germany
| | - P Xanthopoulos
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, 17491 Greifswald, Germany
| | - G M Weir
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, 17491 Greifswald, Germany
| | - S A Bozhenkov
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, 17491 Greifswald, Germany
| | - A Dinklage
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, 17491 Greifswald, Germany
| | - G Fuchert
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, 17491 Greifswald, Germany
| | - J Geiger
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, 17491 Greifswald, Germany
| | - M Hirsch
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, 17491 Greifswald, Germany
| | - U Hoefel
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, 17491 Greifswald, Germany
| | - M Jakubowski
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, 17491 Greifswald, Germany
| | - A Langenberg
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, 17491 Greifswald, Germany
| | - N Pablant
- Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA
| | - E Pasch
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, 17491 Greifswald, Germany
| | - T Stange
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, 17491 Greifswald, Germany
| | - D Zhang
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, 17491 Greifswald, Germany
| | - The W-X Team
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, 17491 Greifswald, Germany
- Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA
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Plunk GG, Xanthopoulos P, Helander P. Distinct Turbulence Saturation Regimes in Stellarators. PHYSICAL REVIEW LETTERS 2017; 118:105002. [PMID: 28339251 DOI: 10.1103/physrevlett.118.105002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2016] [Indexed: 06/06/2023]
Abstract
In the complex 3D magnetic fields of stellarators, ion-temperature-gradient turbulence is shown to have two distinct saturation regimes, as revealed by petascale numerical simulations and explained by a simple turbulence theory. The first regime is marked by strong zonal flows and matches previous observations in tokamaks. The newly observed second regime, in contrast, exhibits small-scale quasi-two-dimensional turbulence, negligible zonal flows, and, surprisingly, a weaker heat flux scaling. Our findings suggest that key details of the magnetic geometry control turbulence in stellarators.
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Affiliation(s)
- G G Plunk
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstrasse 1, 17491 Greifswald, Germany
| | - P Xanthopoulos
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstrasse 1, 17491 Greifswald, Germany
| | - P Helander
- Max-Planck-Institut für Plasmaphysik, Wendelsteinstrasse 1, 17491 Greifswald, Germany
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Friedman B, Carter TA. Linear technique to understand non-normal turbulence applied to a magnetized plasma. PHYSICAL REVIEW LETTERS 2014; 113:025003. [PMID: 25062197 DOI: 10.1103/physrevlett.113.025003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2013] [Indexed: 06/03/2023]
Abstract
In nonlinear dynamical systems with highly nonorthogonal linear eigenvectors, linear nonmodal analysis is more useful than normal mode analysis in predicting turbulent properties. However, the nontrivial time evolution of nonmodal structures makes quantitative understanding and prediction difficult. We present a technique to overcome this difficulty by modeling the effect that the advective nonlinearities have on spatial turbulent structures. The nonlinearities are taken as a periodic randomizing force with time scale consistent with critical balance arguments. We apply this technique to a model of drift wave turbulence in the Large Plasma Device [W. Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)], where nonmodal effects dominate the turbulence. We compare the resulting growth rate spectra to the spectra obtained from a nonlinear simulation, showing good qualitative agreement, especially in comparison to the eigenmode growth rate spectra.
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Affiliation(s)
- B Friedman
- Department of Physics and Astronomy, University of California, Los Angeles, California 90095-1547, USA
| | - T A Carter
- Department of Physics and Astronomy, University of California, Los Angeles, California 90095-1547, USA
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Hatch DR, Jenko F, Bañón Navarro A, Bratanov V. Transition between saturation regimes of gyrokinetic turbulence. PHYSICAL REVIEW LETTERS 2013; 111:175001. [PMID: 24206497 DOI: 10.1103/physrevlett.111.175001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2013] [Indexed: 06/02/2023]
Abstract
A gyrokinetic model of ion temperature gradient driven turbulence in magnetized plasmas is used to study the injection, nonlinear redistribution, and collisional dissipation of free energy in the saturated turbulent state over a broad range of driving gradients and collision frequencies. The dimensionless parameter L(T)/L(C), where L(T) is the ion temperature gradient scale length and L(C) is the collisional mean free path, is shown to parametrize a transition between a saturation regime dominated by nonlinear transfer of free energy to small perpendicular (to the magnetic field) scales and a regime dominated by dissipation at large scales in all phase space dimensions.
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Affiliation(s)
- D R Hatch
- Institute for Fusion Studies, University of Texas at Austin, Austin, Texas 78712, USA and Max Planck Institute for Plasma Physics, EURATOM Association, 85748 Garching, Germany
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Ghim YC, Schekochihin AA, Field AR, Abel IG, Barnes M, Colyer G, Cowley SC, Parra FI, Dunai D, Zoletnik S. Experimental signatures of critically balanced turbulence in MAST. PHYSICAL REVIEW LETTERS 2013; 110:145002. [PMID: 25166998 DOI: 10.1103/physrevlett.110.145002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2012] [Indexed: 06/03/2023]
Abstract
Beam emission spectroscopy (BES) measurements of ion-scale density fluctuations in the MAST tokamak are used to show that the turbulence correlation time, the drift time associated with ion temperature or density gradients, the particle (ion) streaming time along the magnetic field, and the magnetic drift time are consistently comparable, suggesting a "critically balanced" turbulence determined by the local equilibrium. The resulting scalings of the poloidal and radial correlation lengths are derived and tested. The nonlinear time inferred from the density fluctuations is longer than the other times; its ratio to the correlation time scales as ν(*i)(-0.8 ± 0.1), where ν(*i) = ion collision rate/streaming rate. This is consistent with turbulent decorrelation being controlled by a zonal component, invisible to the BES, with an amplitude exceeding those of the drift waves by ∼ ν(*i)(-0.8).
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Affiliation(s)
- Y-C Ghim
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom and EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon OX14 3DB, United Kingdom and Department of Nuclear and Quantum Engineering, KAIST, Daejeon 305-701, Republic of Korea
| | - A A Schekochihin
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom and Merton College, Oxford OX1 4JD, United Kingdom
| | - A R Field
- EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon OX14 3DB, United Kingdom
| | - I G Abel
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom and Merton College, Oxford OX1 4JD, United Kingdom
| | - M Barnes
- Plasma Science and Fusion Center, MIT, Cambridge, Massachusetts 02139, USA and Oak Ridge Institute for Science and Education, Oak Ridge, Tennessee 37831, USA
| | - G Colyer
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom and EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon OX14 3DB, United Kingdom
| | - S C Cowley
- EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon OX14 3DB, United Kingdom and Blackett Laboratory, Imperial College, London SW7 2AZ, United Kingdom
| | - F I Parra
- Plasma Science and Fusion Center, MIT, Cambridge, Massachusetts 02139, USA
| | - D Dunai
- Wigner Research Centre for Physics, Association EURATOM/HAS, P.O. Box 49, H-1525 Budapest, Hungary
| | - S Zoletnik
- Wigner Research Centre for Physics, Association EURATOM/HAS, P.O. Box 49, H-1525 Budapest, Hungary
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9
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Highcock EG, Schekochihin AA, Cowley SC, Barnes M, Parra FI, Roach CM, Dorland W. Zero-turbulence manifold in a toroidal plasma. PHYSICAL REVIEW LETTERS 2012; 109:265001. [PMID: 23368571 DOI: 10.1103/physrevlett.109.265001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2012] [Revised: 11/30/2012] [Indexed: 06/01/2023]
Abstract
Sheared toroidal flows can cause bifurcations to zero-turbulent-transport states in tokamak plasmas. The maximum temperature gradients that can be reached are limited by subcritical turbulence driven by the parallel velocity gradient. Here it is shown that q/ϵ (magnetic field pitch/inverse aspect ratio) is a critical control parameter for sheared tokamak turbulence. By reducing q/ϵ, far higher temperature gradients can be achieved without triggering turbulence, in some instances comparable to those found experimentally in transport barriers. The zero-turbulence manifold is mapped out, in the zero-magnetic-shear limit, over the parameter space (γ(E), q/ϵ, R/L(T)), where γ(E) is the perpendicular flow shear and R/L(T) is the normalized inverse temperature gradient scale. The extent to which it can be constructed from linear theory is discussed.
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Affiliation(s)
- E G Highcock
- Magdalen College, Oxford OX1 4AU, United Kingdom.
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10
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Teaca B, Navarro AB, Jenko F, Brunner S, Villard L. Locality and universality in gyrokinetic turbulence. PHYSICAL REVIEW LETTERS 2012; 109:235003. [PMID: 23368214 DOI: 10.1103/physrevlett.109.235003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2012] [Indexed: 06/01/2023]
Abstract
The nature of nonlinear interactions in gyrokinetic turbulence, driven by the ion-temperature gradient instability, is investigated using direct numerical simulations in toroidal flux tube geometry. To account for the level of separation existing between scales involved in an energetic interaction, the degree of locality of the free energy scale flux is analyzed employing Kraichnan's infrared (IR) and ultraviolet locality functions. Because of the nontrivial dissipative nature of gyrokinetic turbulence, an asymptotic level for the locality exponents, indicative of a universal dynamical regime for gyrokinetics, is not recovered and an accentuated nonlocal behavior of the IR interactions is found instead, in spite of the local energy cascade observed.
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Affiliation(s)
- Bogdan Teaca
- Ecole Polytechnique Fédérale de Lausanne (EPFL), Centre de Recherches en Physique des Plasmas, Association Euratom-Confédération Suisse, CH-1015 Lausanne, Switzerland.
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11
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Barnes M, Parra FI, Dorland W. Turbulent transport and heating of trace heavy ions in hot magnetized plasmas. PHYSICAL REVIEW LETTERS 2012; 109:185003. [PMID: 23215287 DOI: 10.1103/physrevlett.109.185003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2012] [Indexed: 06/01/2023]
Abstract
Scaling laws for the transport and heating of trace heavy ions in low-frequency magnetized plasma turbulence are derived and compared with direct numerical simulations. The predicted dependences of turbulent fluxes and heating on ion charge and mass number are found to agree with numerical results for both stationary and differentially rotating plasmas. Heavy ion momentum transport is found to increase with mass, and heavy ions are found to be preferentially heated, implying a mass-dependent ion temperature for very weakly collisional plasmas and for partially ionized heavy ions in strongly rotating plasmas.
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Affiliation(s)
- M Barnes
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02138, USA.
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12
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Parra FI, Nave MFF, Schekochihin AA, Giroud C, de Grassie JS, Severo JHF, de Vries P, Zastrow KD. Scaling of spontaneous rotation with temperature and plasma current in tokamaks. PHYSICAL REVIEW LETTERS 2012; 108:095001. [PMID: 22463645 DOI: 10.1103/physrevlett.108.095001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2011] [Indexed: 05/31/2023]
Abstract
Using theoretical arguments, a simple scaling law for the size of the intrinsic rotation observed in tokamaks in the absence of a momentum injection is found: The velocity generated in the core of a tokamak must be proportional to the ion temperature difference in the core divided by the plasma current, independent of the size of the device. The constant of proportionality is of the order of 10 km·s(-1)·MA·keV(-1). When the intrinsic rotation profile is hollow, i.e., it is countercurrent in the core of the tokamak and cocurrent in the edge, the scaling law presented in this Letter fits the data remarkably well for several tokamaks of vastly different size and heated by different mechanisms.
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Affiliation(s)
- F I Parra
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, UK.
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