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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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
Issue number6
Early online date10 Apr 2015
Publication statusPublished - Jun 2015


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

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