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Varennes R, Garbet X, Vermare L, Sarazin Y, Dif-Pradalier G, Grandgirard V, Ghendrih P, Donnel P, Peret M, Obrejan K, Bourne E. Synergy of Turbulent Momentum Drive and Magnetic Braking. Phys Rev Lett 2022; 128:255002. [PMID: 35802431 DOI: 10.1103/physrevlett.128.255002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2021] [Revised: 02/17/2022] [Accepted: 06/10/2022] [Indexed: 06/15/2023]
Abstract
In absence of external torque, plasma rotation in tokamaks results from a balance between collisional magnetic braking and turbulent drive. The outcome of this competition and cooperation is essential to determine the plasma flow. A reduced model, supported by gyrokinetic simulations, is first used to explain and quantify the competition only. The ripple amplitude above which magnetic drag overcomes turbulent viscosity is obtained. The synergetic impact of ripple on the turbulent toroidal Reynolds stress is explored. Simulations show that the main effect comes from an enhancement of the radial electric field shear by the ripple, which in turn impacts the residual stress.
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Affiliation(s)
- R Varennes
- CEA, IRFM, F-13108 Saint-Paul-Lez-Durance, France
| | - X Garbet
- CEA, IRFM, F-13108 Saint-Paul-Lez-Durance, France
| | - L Vermare
- LPP, CNRS, Ecole polytechnique, 91128 Palaiseau, France
| | - Y Sarazin
- CEA, IRFM, F-13108 Saint-Paul-Lez-Durance, France
| | | | | | - P Ghendrih
- CEA, IRFM, F-13108 Saint-Paul-Lez-Durance, France
| | - P Donnel
- CEA, IRFM, F-13108 Saint-Paul-Lez-Durance, France
| | - M Peret
- CEA, IRFM, F-13108 Saint-Paul-Lez-Durance, France
| | - K Obrejan
- CEA, IRFM, F-13108 Saint-Paul-Lez-Durance, France
| | - E Bourne
- CEA, IRFM, F-13108 Saint-Paul-Lez-Durance, France
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2
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Dif-Pradalier G, Hornung G, Ghendrih P, Sarazin Y, Clairet F, Vermare L, Diamond PH, Abiteboul J, Cartier-Michaud T, Ehrlacher C, Estève D, Garbet X, Grandgirard V, Gürcan ÖD, Hennequin P, Kosuga Y, Latu G, Maget P, Morel P, Norscini C, Sabot R, Storelli A. Finding the elusive E×B staircase in magnetized plasmas. Phys Rev Lett 2015; 114:085004. [PMID: 25768769 DOI: 10.1103/physrevlett.114.085004] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2014] [Indexed: 06/04/2023]
Abstract
Turbulence in hot magnetized plasmas is shown to generate permeable localized transport barriers that globally organize into the so-called "ExB staircase" [G. Dif-Pradalier et al., Phys. Rev. E, 82, 025401(R) (2010)]. Its domain of existence and dependence with key plasma parameters is discussed theoretically. Based on these predictions, staircases are observed experimentally in the Tore Supra tokamak by means of high-resolution fast-sweeping X-mode reflectometry. This observation strongly emphasizes the critical role of mesoscale self-organization in plasma turbulence and may have far-reaching consequences for turbulent transport models and their validation.
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Affiliation(s)
| | - G Hornung
- Department of Applied Physics, Ghent University, 9000 Gent, Belgium
| | - Ph Ghendrih
- CEA, IRFM, F-13108 St. Paul-lez-Durance cedex, France
| | - Y Sarazin
- CEA, IRFM, F-13108 St. Paul-lez-Durance cedex, France
| | - F Clairet
- CEA, IRFM, F-13108 St. Paul-lez-Durance cedex, France
| | - L Vermare
- Laboratoire de Physique des Plasmas, Ecole Polytechnique, 91128 Palaiseau, France
| | - P H Diamond
- CASS and CMTFO, University of California at San Diego, San Diego, California 92093, USA
- WCI Center for Fusion Theory, NFRI, Daejeon 305-333, Korea
| | - J Abiteboul
- Max-Planck-Institut für Plasmaphysik, 85748 Garching, Germany
| | | | - C Ehrlacher
- CEA, IRFM, F-13108 St. Paul-lez-Durance cedex, France
| | - D Estève
- CEA, IRFM, F-13108 St. Paul-lez-Durance cedex, France
| | - X Garbet
- CEA, IRFM, F-13108 St. Paul-lez-Durance cedex, France
| | - V Grandgirard
- CEA, IRFM, F-13108 St. Paul-lez-Durance cedex, France
| | - Ö D Gürcan
- Laboratoire de Physique des Plasmas, Ecole Polytechnique, 91128 Palaiseau, France
| | - P Hennequin
- Laboratoire de Physique des Plasmas, Ecole Polytechnique, 91128 Palaiseau, France
| | - Y Kosuga
- Institute for Advanced Study, Kyushu University, Fukuoka 816-8580, Japan
| | - G Latu
- CEA, IRFM, F-13108 St. Paul-lez-Durance cedex, France
| | - P Maget
- CEA, IRFM, F-13108 St. Paul-lez-Durance cedex, France
| | - P Morel
- Laboratoire de Physique des Plasmas, Ecole Polytechnique, 91128 Palaiseau, France
| | - C Norscini
- CEA, IRFM, F-13108 St. Paul-lez-Durance cedex, France
| | - R Sabot
- CEA, IRFM, F-13108 St. Paul-lez-Durance cedex, France
| | - A Storelli
- Laboratoire de Physique des Plasmas, Ecole Polytechnique, 91128 Palaiseau, France
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Bécoulet M, Orain F, Huijsmans GTA, Pamela S, Cahyna P, Hoelzl M, Garbet X, Franck E, Sonnendrücker E, Dif-Pradalier G, Passeron C, Latu G, Morales J, Nardon E, Fil A, Nkonga B, Ratnani A, Grandgirard V. Mechanism of edge localized mode mitigation by resonant magnetic perturbations. Phys Rev Lett 2014; 113:115001. [PMID: 25259985 DOI: 10.1103/physrevlett.113.115001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2014] [Indexed: 06/03/2023]
Abstract
A possible mechanism of edge localized modes (ELMs) mitigation by resonant magnetic perturbations (RMPs) is proposed based on the results of nonlinear resistive magnetohydrodynamic modeling using the jorek code, realistic JET-like plasma parameters and an RMP spectrum of JET error-field correction coils (EFCC) with a main toroidal number n=2 were used in the simulations. Without RMPs, a large ELM relaxation is obtained mainly due to the most unstable medium-n ballooning mode. The externally imposed RMP drives nonlinearly the modes coupled to n=2 RMP which produce small multimode relaxations, mitigated ELMs. The modes driven by RMPs exhibit a tearinglike structure and produce additional islands. Mitigated ELMs deposit energy into the divertor mainly in the structures ("footprints") created by n=2 RMPs, however, slightly modulated by other nonlinearly driven even harmonics. The divertor power flux during a ELM phase mitigated by RMPs is reduced almost by a factor of 10. The mechanism of ELM mitigation by RMPs proposed here reproduces generic features of high collisionality RMP experiments, where large ELMs are replaced by small, much more frequent ELMs or magnetic turbulence. Total ELM suppression was also demonstrated in modeling at higher RMP amplitude.
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Affiliation(s)
- M Bécoulet
- CEA, IRFM, 13108 Saint-Paul-Lez-Durance, France
| | - F Orain
- CEA, IRFM, 13108 Saint-Paul-Lez-Durance, France
| | - G T A Huijsmans
- ITER Organization, Route de Vinon-sur-Verdon, 13067 Saint-Paul-Lez-Durance, France
| | - S Pamela
- CCFE, Culham Science Centre, Oxon OX14 3DB, United Kingdom
| | - P Cahyna
- Institute of Plasma Physics ASCR, 182 00 Prague 8, Czech Republic
| | - M Hoelzl
- Max-Planck-Institut, 85748 Garching, Germany
| | - X Garbet
- CEA, IRFM, 13108 Saint-Paul-Lez-Durance, France
| | - E Franck
- Max-Planck-Institut, 85748 Garching, Germany
| | | | | | - C Passeron
- CEA, IRFM, 13108 Saint-Paul-Lez-Durance, France
| | - G Latu
- CEA, IRFM, 13108 Saint-Paul-Lez-Durance, France
| | - J Morales
- CEA, IRFM, 13108 Saint-Paul-Lez-Durance, France
| | - E Nardon
- CEA, IRFM, 13108 Saint-Paul-Lez-Durance, France
| | - A Fil
- CEA, IRFM, 13108 Saint-Paul-Lez-Durance, France
| | - B Nkonga
- Laboratoire de Mathématiques J.A. Dieudonné, UMR 7351, CNRS UNS, Université de Nice-Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 02, France
| | - A Ratnani
- Laboratoire de Mathématiques J.A. Dieudonné, UMR 7351, CNRS UNS, Université de Nice-Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 02, France
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Strugarek A, Sarazin Y, Zarzoso D, Abiteboul J, Brun AS, Cartier-Michaud T, Dif-Pradalier G, Garbet X, Ghendrih P, Grandgirard V, Latu G, Passeron C, Thomine O. Unraveling quasiperiodic relaxations of transport barriers with gyrokinetic simulations of tokamak plasmas. Phys Rev Lett 2013; 111:145001. [PMID: 24138245 DOI: 10.1103/physrevlett.111.145001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2012] [Indexed: 06/02/2023]
Abstract
The generation and dynamics of transport barriers governed by sheared poloidal flows are analyzed in flux-driven 5D gyrokinetic simulations of ion temperature gradient driven turbulence in tokamak plasmas. The transport barrier is triggered by a vorticity source that polarizes the system. The chosen source captures characteristic features of some experimental scenarios, namely, the generation of a sheared electric field coupled to anisotropic heating. For sufficiently large shearing rates, turbulent transport is suppressed and a transport barrier builds up, in agreement with the common understanding of transport barriers. The vorticity source also governs a secondary instability--driven by the temperature anisotropy (T(∥)≠T(⊥)). Turbulence and its associated zonal flows are generated in the vicinity of the barrier, destroying the latter due to the screening of the polarization source by the zonal flows. These barrier relaxations occur quasiperiodically, and generically result from the decoupling between the dynamics of the barrier generation, triggered by the source driven sheared flow, and that of the crash, triggered by the secondary instability. This result underlines that barriers triggered by sheared flows are prone to relaxations whenever secondary instabilities come into play.
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Affiliation(s)
- A Strugarek
- CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France and Laboratoire AIM Paris-Saclay, CEA/Irfu Université Paris-Diderot CNRS/INSU, F-91191 Gif-sur-Yvette, France
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5
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Zarzoso D, Sarazin Y, Garbet X, Dumont R, Strugarek A, Abiteboul J, Cartier-Michaud T, Dif-Pradalier G, Ghendrih P, Grandgirard V, Latu G, Passeron C, Thomine O. Impact of energetic-particle-driven geodesic acoustic modes on turbulence. Phys Rev Lett 2013; 110:125002. [PMID: 25166813 DOI: 10.1103/physrevlett.110.125002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2012] [Indexed: 06/03/2023]
Abstract
The impact on turbulent transport of geodesic acoustic modes excited by energetic particles is evidenced for the first time in flux-driven 5D gyrokinetic simulations using the Gysela code. Energetic geodesic acoustic modes (EGAMs) are excited in a regime with a transport barrier in the outer radial region. The interaction between EGAMs and turbulence is such that turbulent transport can be enhanced in the presence of EGAMs, with the subsequent destruction of the transport barrier. This scenario could be particularly critical in those plasmas, such as burning plasmas, exhibiting a rich population of suprathermal particles capable of exciting energetic modes.
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Affiliation(s)
- D Zarzoso
- CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France
| | - Y Sarazin
- CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France
| | - X Garbet
- CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France
| | - R Dumont
- CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France
| | - A Strugarek
- CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France and Laboratoire AIM Paris-Saclay, CEA/Irfu Université Paris-Diderot CNRS/INSU, 91191 Gif-sur-Yvette, France
| | - J Abiteboul
- CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France
| | | | | | - Ph Ghendrih
- CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France
| | | | - G Latu
- CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France
| | - C Passeron
- CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France
| | - O Thomine
- CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France
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6
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Hertout P, Boulbe C, Nardon E, Blum J, Brémond S, Bucalossi J, Faugeras B, Grandgirard V, Moreau P. The CEDRES++ equilibrium code and its application to ITER, JT-60SA and Tore Supra. Fusion Engineering and Design 2011. [DOI: 10.1016/j.fusengdes.2011.03.092] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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7
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Nguyen C, Lütjens H, Garbet X, Grandgirard V, Lesur M. Existence of metastable kinetic modes. Phys Rev Lett 2010; 105:205002. [PMID: 21231240 DOI: 10.1103/physrevlett.105.205002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2010] [Indexed: 05/30/2023]
Abstract
The nonlinear evolution of resonantly driven systems, such as suprathermal particle driven modes in magnetically confined plasmas, is shown to strongly depend on the existence and nature of an underlying damping mechanism. When background resonant damping is present, subcritical states can take place. In particular, purely nonlinear steady-state regimes are found, whose destabilization threshold and saturation levels are calculated and validated using numerical simulations. This nonlinear behavior can be of relevance for acoustic modes in magnetically confined plasmas.
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Affiliation(s)
- C Nguyen
- Centre de Physique Théorique, CNRS-Ecole Polytechnique, Palaiseau, France.
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8
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Dif-Pradalier G, Diamond PH, Grandgirard V, Sarazin Y, Abiteboul J, Garbet X, Ghendrih P, Strugarek A, Ku S, Chang CS. On the validity of the local diffusive paradigm in turbulent plasma transport. Phys Rev E Stat Nonlin Soft Matter Phys 2010; 82:025401. [PMID: 20866867 DOI: 10.1103/physreve.82.025401] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2009] [Indexed: 05/29/2023]
Abstract
A systematic, constructive and self-consistent procedure to quantify nonlocal, nondiffusive action at a distance in plasma turbulence is exposed and applied to turbulent heat fluxes computed from the state-of-the-art full- f, flux-driven gyrokinetic GYSELA and XGC1 codes. A striking commonality is found: heat transport below a dynamically selected mesoscale has the structure of a Lévy distribution, is strongly nonlocal, nondiffusive, scale-free, and avalanche mediated; at larger scales, we report the observation of a self-organized flow structure which we call the " E × B staircase" after its planetary analog.
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Affiliation(s)
- G Dif-Pradalier
- Center for Astrophysics and Space Sciences, UCSD, La Jolla, CA 92093, USA.
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Dif-Pradalier G, Grandgirard V, Sarazin Y, Garbet X, Ghendrih P. Interplay between gyrokinetic turbulence, flows, and collisions: perspectives on transport and poloidal rotation. Phys Rev Lett 2009; 103:065002. [PMID: 19792575 DOI: 10.1103/physrevlett.103.065002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2009] [Revised: 04/15/2009] [Indexed: 05/28/2023]
Abstract
The impact of ion-ion collisions on confinement is investigated with the full-f and global gyrokinetic Gysela code through a series of nonlinear turbulence simulations for tokamak parameters. A twofold scan in the turbulence drive and in collisionality is performed, highlighting (i) a heat transport expressed in terms of critical quantities-threshold and exponent, (ii) a first evidence of turbulent generation of poloidal momentum, and (iii) the dominance of mean flow shear, mediated through the turbulent corrugation of the mean profiles, with regard to the oft-invoked zonal flow shear.
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Affiliation(s)
- G Dif-Pradalier
- Association Euratom-CEA, CEA/IRFM, F-13108 St. Paul-lez-Durance cedex, France
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10
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Angelino P, Garbet X, Villard L, Bottino A, Jolliet S, Ghendrih P, Grandgirard V, McMillan BF, Sarazin Y, Dif-Pradalier G, Tran TM. Role of plasma elongation on turbulent transport in magnetically confined plasmas. Phys Rev Lett 2009; 102:195002. [PMID: 19518964 DOI: 10.1103/physrevlett.102.195002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2008] [Indexed: 05/27/2023]
Abstract
The theoretical study of plasma turbulence is of central importance to fusion research. Experimental evidence indicates that the confinement time results mainly from the turbulent transport of energy, the magnitude of which depends on the turbulent state resulting from nonlinear saturation mechanisms, in particular, the self-generation of coherent macroscopic structures and large scale flows. Plasma geometry has a strong impact on the structure and magnitude of these flows and also modifies the mode linear growth rates. Nonlinear global gyrokinetic simulations in realistic tokamak magnetohydrodynamic equilibria show how plasma shape can control the turbulent transport. Results are best described in terms of an effective temperature gradient. With increasing plasma elongation, the nonlinear critical effective gradient is not modified while the stiffness of transport is decreasing.
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Affiliation(s)
- P Angelino
- Association Euratom-CEA, CEA/DSM/IRFM, Cadarache, France
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Casati A, Gerbaud T, Hennequin P, Bourdelle C, Candy J, Clairet F, Garbet X, Grandgirard V, Gürcan OD, Heuraux S, Hoang GT, Honoré C, Imbeaux F, Sabot R, Sarazin Y, Vermare L, Waltz RE. Turbulence in the TORE SUPRA tokamak: measurements and validation of nonlinear simulations. Phys Rev Lett 2009; 102:165005. [PMID: 19518721 DOI: 10.1103/physrevlett.102.165005] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2009] [Indexed: 05/27/2023]
Abstract
Turbulence measurements in TORE SUPRA tokamak plasmas have been quantitatively compared to predictions by nonlinear gyrokinetic simulations. For the first time, numerical results simultaneously match within experimental uncertainty (a) the magnitude of effective heat diffusivity, (b) rms values of density fluctuations, and (c) wave-number spectra in both the directions perpendicular to the magnetic field. Moreover, the nonlinear simulations help to revise as an instrumental effect the apparent experimental evidence of strong turbulence anisotropy at spatial scales of the order of ion-sound Larmor radius.
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Affiliation(s)
- A Casati
- CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France.
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