Using a local gyrokinetic code to study global ion temperature gradient modes in tokamaks

P. A. Abdoul, D. Dickinson, C. M. Roach, H. R. Wilson

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Abstract

In this paper the global eigenmode structures of linear ion temperature gradient (ITG) modes in tokamak plasmas are obtained using a novel technique which combines results from the local gyrokinetic code GS2 with analytical theory to reconstruct global properties. Local gyrokinetic calculations are performed for a range of radial flux surfaces, x, and ballooning phase angles, p, to map out the local complex mode frequency, Ω<inf>0</inf>(x, p) = ω<inf>0</inf>(x, p) + iγ<inf>0</inf>(x, p) for a single toroidal mode number, n. Taylor expanding Ω<inf>0</inf> about a reference surface at x = 0, and employing the Fourier-ballooning representation leads to a second order ODE for the amplitude envelope, A(p), which describes how the local results are combined to form the global mode. The equilibrium profiles impact on the variation of Ω<inf>0</inf>(x, p) and hence influence the global mode structure. The simulations presented here are based upon a global extension to the CYCLONE base case and employ the circular Miller equilibrium model. In an equilibrium with radially varying profiles of a/L<inf>T</inf> and a/L<inf>n</inf>, peaked at x = 0, and with all other equilibrium profiles held constant, including η<inf>i</inf> = L<inf>n</inf>/L<inf>T</inf>, Ω<inf>0</inf>(x, p) is found to have a stationary point. The reconstructed global mode sits at the outboard mid-plane of the tokamak, with global growth rate, γ ∼ Max[γ<inf>0</inf>]. Including the radial variation of other equilibrium profiles like safety factor and magnetic shear, leads to a mode that peaks away from the outboard mid-plane, with a reduced global growth rate. Finally, the influence of toroidal flow shear has also been investigated through the introduction of a Doppler shift, ω<inf>0</inf> → ω<inf>0</inf> - nΩ′<inf>φ</inf> x, where Ω<inf>φ</inf> is the equilibrium toroidal flow, and a prime denotes the radial derivative. The equilibrium profile variations introduce an asymmetry into the global growth rate spectrum with respect to the sign of Ω′<inf>φ</inf>, such that the maximum growth rate is achieved with non-zero shearing, consistent with recent global gyrokinetic calculations.

Original languageEnglish
Article number065004
Number of pages10
JournalPlasma Physics and Controlled Fusion
Volume57
Issue number6
Early online date10 Apr 2015
DOIs
Publication statusPublished - Jun 2015

Keywords

  • flow shear
  • global gyrokinetics
  • local gyrokinetics
  • profile shearing

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