Tokamak L/H mode transition

Tsui, K. H.; Navia, C. E.

doi:10.1063/1.3671975

Cited by 4 publications

(6 citation statements)

References 27 publications

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“…For this reason among others, stationary equilibria with plasma flow have been extensively studied on the basis of generalized GSEs (e.g. Mashke and Perrin 1984;Clemente and Farengo 1984;Greene 1988;Throumoulopoulos and Pantis 1996;Throumoulopoulos and Tasso 1997, 2010Goedbloed and Lifschitz 1997;Tasso and Throumoulopoulos 1998;Betti and Freidberg 2000;Simintzis et al 2001;Krasheninnikov et al 2002;Poulipoulis et al 2005;Throumoulopoulos et al 2006Throumoulopoulos et al , 2008Throumoulopoulos et al , 2009Apostolaki et al 2008;Khater and Moawad 2009;Kuiroukidis 2010; Kuiroukidis andThroumoulopoulos 2011, 2012;Tsui et al 2011;Shi 2011). In particular, although complex numerical codes are extensively used to attempt simulations of the L-H transition, certain equilibrium considerations in connection with this transition are helpful (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, although complex numerical codes are extensively used to attempt simulations of the L-H transition, certain equilibrium considerations in connection with this transition are helpful (e.g. Ilgisonis and Pozdnyakov 2004;Solano 2004;Garcia and Giruzzi 2010;Tsui and Navia 2012).…”

Section: Introductionmentioning

confidence: 99%

“…Most of the solutions are associated with pressure and current profiles, including up to quadratic terms in the flux function ψ to linearize the resulting equation (Solovév 1968;Herrnegger 1972;Maschke 1972;Berk et al 1981;Mc Carthy 1999;Weening 2000;Yavorskij et al 2001;Atanasiu et al 2004;Cerfon and Freidberg 2010;Srinivasan et al 2010). Linear equilibria with flow were constructed in (Clemente and Farengo 1984;Mashke and Perrin 1984;Greene 1988;Throumoulopoulos and Pantis 1996;Goedbloed and Lifschitz 1997;Tasso 1997, 2012;Tasso and Throumoulopoulos 1998;Betti and Freidberg 2000;Simintzis et al 2001;Krasheninnikov et al 2002;Poulipoulis et al 2005;Throumoulopoulos et al 2006Throumoulopoulos et al , 2008Apostolaki et al 2008;Khater and Moawad 2009;Kuiroukidis 2010; Kuiroukidis andThroumoulopoulos 2011, 2012;Tsui et al 2011;Shi 2011,and references cited therein). Also, the nonlinear translational symmetric equilibria of 'cat eyes' and counter-rotating vortices with flow parallel to the magnetic field were studied in Throumoulopoulos et al (2009) and Throumoulopoulos and Tasso (2010).…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear translational symmetric equilibria relevant to the L–H transition

Kuiroukidis

Throumoulopoulos²

2012

J. Plasma Phys.

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Nonlinear z-independent solutions to a generalized Grad-Shafranov equation (GSE) with up to quartic flux terms in the free functions and incompressible plasma flow non parallel to the magnetic field are constructed quasi-analytically. Through an ansatz the GSE is transformed to a set of three ordinary differential equations and a constraint for three functions of the coordinate x, in cartesian coordinates (x, y), which then are solved numerically. Equilibrium configurations for certain values of the integration constants are displayed. Examination of their characteristics in connection with the impact of nonlinearity and sheared flow indicates that these equilibria are consistent with the L-H transition phenomenology. For flows parallel to the magnetic field one equilibrium corresponding to the H-state is potentially stable in the sense that a sufficient condition for linear stability is satisfied in an appreciable part of the plasma while another solution corresponding to the L-state does not satisfy the condition. The results indicate that the sheared flow in conjunction with the equilibrium nonlinearity play a stabilizing role.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear translational symmetric equilibria relevant to the L–H transition

Kuiroukidis

Throumoulopoulos²

2012

J. Plasma Phys.

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“…To describe plasma equilibrium with poloidal and toroidal flows, this set of equations is quite inconvenient. We will use the MHD equations for divergence-free plasma flows, where the plasma velocity is density weighed so that the plasma density appears only through the density weighed velocity w * = (µρ) 1/2 v, except in the gravity term (Tsui et al 2011;Tsui & Navia 2012).…”

Section: Divergence-free Rotational Mhdmentioning

confidence: 99%

Plasma Pressure Driven Asymmetric Supernovae and Highly Collimated Gamma-Ray Bursts

Tsui,

Navia

2012

Preprint

Self Cite

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During the process of collapse of a massive star, a cavity is generated between the central iron core and an outer stellar envelope. The dynamics of this cavity, filled with plasma and magnetic field of the rapidly rotating proto-magnetar's magnetosphere, is believed to be very relevant in understanding supernovae and gamma-ray bursts. The interactions of the pressurized conducting plasma and the magnetic fields are described by a set of magnetohydrodynamic (MHD) equations with poloidal and toroidal plasma flows not aligned with magnetic fields. A sequence of MHD equilibria in response to the increasing plasma pressure in the cavity, by continuous filling from the rotating magnetosphere, is solved to account for asymmetric supernovae, highly collimated gamma-ray burst jets, and also active galactic nucleus plasma torus. It is shown that the magnetosphere of the central compact star is likely the central engine of supernova and gamma-ray burst by feeding them plasma, magnetic energy, and rotational energy.

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“…Appendix: Quantities appearing in the ODEs and algebraic constraints (11)(12)(13)(14)(15) The functions G 1 , G 4 , G 5 appearing into Eqs. (11), (12), (13) are given by…”

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confidence: 99%

Two-dimensional nonlinear cylindrical equilibria with reversed magnetic shear and sheared flow

Kuiroukidis

Throumoulopoulos

2013

J. Plasma Phys.

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Nonlinear translational symmetric equilibria with up to quartic flux terms in free functions, reversed magnetic shear, and sheared flow are constructed in two ways: (i) quasi-analytically by an ansatz, which reduces the pertinent generalized GradShafranov equation to a set of ordinary differential equations and algebraic constraints which is then solved numerically, and (ii) completely numerically by prescribing analytically a boundary having an X-point. This latter case presented in Sec. 4 is relevant to the International Thermonuclear Experimental Reactor project. The equilibrium characteristics are then examined by means of pressure, safety factor, current density, and electric field. For flows parallel to the magnetic field, the stability of the equilibria constructed is also examined by applying a sufficient condition. It turns out that the equilibrium nonlinearity has a stabilizing impact, which is slightly enhanced by the sheared flow. In addition, the results indicate that the stability is affected by the up-down asymmetry.

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Tokamak L/H mode transition

Cited by 4 publications

References 27 publications

Nonlinear translational symmetric equilibria relevant to the L–H transition

Nonlinear translational symmetric equilibria relevant to the L–H transition

Plasma Pressure Driven Asymmetric Supernovae and Highly Collimated Gamma-Ray Bursts

Two-dimensional nonlinear cylindrical equilibria with reversed magnetic shear and sheared flow

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