Analytical tokamak equilibrium for shaped plasmas

Zonal ‡ow helps reduce the turbulent transport level in tokamaks. Rosenbluth and Hinton have shown that zonal ‡ow damps to to a non-vanishing residual level in collisionless and collisional banana regime plasmas Recent zonal ‡ow advances are summarized including the evaluation of the e¤ects on this zonal ‡ow residual of plasma cross section shaping, shorter wavelengths including those less than an electron gyroradius, and aritrary collisionality relative to the zonal low frequency.In addition to giving a brief summary of these new developments, the analytic results are compared with GS2 numerical simulations to demonstarte their value as benchmarks for turbulence codes.

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“…The analytical approach applies a global equilibrium [19], whose ‡ux surface in the large aspect ratio limit can be simpli…ed as [8] …”

Section: Plasma Shaping Effects On Zonal Flow Residualmentioning

confidence: 99%

Effects of finite poloidal gyroradius, shaping, and collisions on the zonal flow residual

2007

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“…We note that for M = 0 the zero-frequency continuum modes x À = 0 can be thought of as equilibrium flows described by Eq. (16). These flows are the linear counterpart of zonal flows.…”

Section: A Torusmentioning

confidence: 99%

“…Convenient homogeneous solutions are provided in Refs. [16,17]. In the presence of toroidal rotation, one additionally has to specify how the angular rotation frequency depends on w.…”

Section: Introductionmentioning

confidence: 99%

The Brunt–Väisälä frequency of rotating tokamak plasmas

Haverkort

Blank

Koren

2012

Journal of Computational Physics

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a b s t r a c tThe continuous spectrum of analytical toroidally rotating magnetically confined plasma equilibria is investigated analytically and numerically. In the presence of purely toroidal flow, the ideal magnetohydrodynamic equations leave the freedom to specify which thermodynamic quantity is constant on the magnetic surfaces. Introducing a general parametrization of this quantity, analytical equilibrium solutions are derived that still posses this freedom. These equilibria and their spectral properties are shown to be ideally suited for testing numerical equilibrium and stability codes including toroidal rotation. Analytical expressions are derived for the low-frequency continuous Alfvén spectrum. These expressions still allow one to choose which quantity is constant on the magnetic surfaces of the equilibrium, thereby generalizing previous results. The centrifugal convective effect is shown to modify the lowest Alfvén continuum branch to a buoyancy frequency, or Brunt-Väisälä frequency. A comparison with numerical results for the case that the specific entropy, the temperature, or the density is constant on the magnetic surfaces yields excellent agreement, showing the usefulness of the derived expressions for the validation of numerical codes.

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“…Static equilibrium of axi-symmetric toroidal configurations such as tokamak, is mainly described by well known GradShafranov equation (GSE) which in cylindrical coordinate system can be written as [1,20,21] R o oR…”

Section: Physical Description Of Energy Confinement Time and Equilibrmentioning

confidence: 99%

Application of poloidal beta and plasma internal inductance in determination of input power time of Damavand tokamak

2016

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In this study, magnetic measurement of poloidal fields were used to determine poloidal beta and plasma internal inductance of Damavand tokamak combination of poloidal beta and plasma internal inductance (b p þ l i 2 ), known as Shafranov parameter, was obtained experimentally in terms of normal and tangential components of the magnetic field. Plasma internal inductance and poloidal beta were obtained using parametrization method based on analytical solution of Grad-Shafranov equation (GSE) and compared with parabolic-like profile of toroidal current density approach for determination of the plasma internal inductance. Finding evolution of b p þ l i 2 and plasma internal inductance. Finding poloidal beta (Shafranov parameter and internal inductance) and using energy balance equation, thermal energy and energy confinement were determined qualitatively in terms of poloidal beta during a regular discharge of Damavand tokamak.

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Analytical tokamak equilibrium for shaped plasmas

Cited by 100 publications

References 0 publications

Effects of finite poloidal gyroradius, shaping, and collisions on the zonal flow residual

Effects of finite poloidal gyroradius, shaping, and collisions on the zonal flow residual

The Brunt–Väisälä frequency of rotating tokamak plasmas

Application of poloidal beta and plasma internal inductance in determination of input power time of Damavand tokamak

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