Analytical description of poloidally diverted tokamak equilibrium with linear stream functions

Several classes of analytic solutions to a generalized Grad-Shafranov equation with incompressible plasma flow non-parallel to the magnetic field are constructed. The solutions include higher transcendental functions such as the Meijer G-function and describe D-shaped and diverted configurations with either a single or double X-points. Their characteristics are examined in particular with respect to the flow parameters associated with the electric field. It turns out that the electric field makes the safety factor flatter and increases the magnitude and shear of the toroidal velocity in qualitative agreement with experimental evidence on the formation of internal transport barriers in tokamaks, thus indicating a potential stabilizing effect of the electric field.

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“…This limitation of j guarantees regularity of the flow velocity v in view of Eqs. (9) and (35) below. Also, integration of Eq.…”

Section: Equilibrium Characteristicsmentioning

confidence: 99%

Symmetric and asymmetric equilibria with non-parallel flows

Kuiroukidis

Throumoulopoulos

2012

Physics of Plasmas

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“…Analytical solutions to the GSE are obtained by specifying the plasma pressure and poloidal current functions of ψ, usually in such a way as to linearize the resulting partial differential equation, e.g. [3]- [12]. Analytical solutions to the GSE are very useful for theoretical studies of plasma equilibrium, transport and stability as well as benchmarks for numerical codes [13].…”

Section: Introductionmentioning

confidence: 99%

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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“…(4) with arbitrary number of free parameters. Unlike previous papers, [2][3][4] in which such solutions were produced by using an iterative algorithm, here a homogeneous separable solution is expressed in terms of Bessel functions restricting the separation constant to integer values by exploiting the orthogonality of these functions. The homogeneous solution is…”

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confidence: 99%

Generalized Solovev equilibrium with sheared flow of arbitrary direction and stability consideration

Kaltsas

Throumoulopoulos

2014

Physics of Plasmas

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A Solovev-like solution describing equilibria with field aligned incompressible flows [G. N. Throumoulopoulos and H. Tasso, Phys. Plasmas 19, 014504 (2012)] is extended to non parallel flows. The solution expressed as a superposition of Bessel functions contains an arbitrary number of free parameters which are exploited to construct a variety of configurations including ITER shaped ones. For parallel flows, application of a sufficient condition for linear stability shows that this condition is satisfied in an appreciable part of the plasma region on the high-field side mostly due to the variation of the magnetic field perpendicular to the magnetic surfaces. Also, the results indicate that depending on the shape of the Mach-function profile and the values of the free parameters the flow and flow shear may have either stabilizing or destabilizing effects.

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Analytical description of poloidally diverted tokamak equilibrium with linear stream functions

Cited by 20 publications

References 18 publications

Symmetric and asymmetric equilibria with non-parallel flows

Symmetric and asymmetric equilibria with non-parallel flows

Nonlinear translational symmetric equilibria relevant to the L–H transition

Generalized Solovev equilibrium with sheared flow of arbitrary direction and stability consideration

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