Abstract
In the gyrokinetic model and simulations, when the double-gyroaverage term incorporates the combining effect contributed by the finite Larmor radius, short scales of the perturbation, and steep gradient of the equilibrium profile, the low-order approximation of this term could generate unignorable error. This paper implements an interpolation algorithm to compute the double-gyroaverage term without low-order approximation to avoid this error. For a steep equilibrium density, the obvious difference between the density on the gyrocenter coordinate frame and the one on the particle coordinate frame should be accounted for in the quasi-neutrality equation. A Euler–Maclaurin-based quadrature integrating algorithm is developed to compute the quadrature integral for the distribution of the magnetic moment. The application of the interpolation algorithm to computing the double-gyroaverage term and to solving the quasi-neutrality equation is benchmarked by comparing the numerical results with the known analytical solutions. Finally, to take advantage of the interpolation solver clearer, the numerical comparison between the interpolation solver and a classical second order solver is carried out in a constant theta-pinch magnetic field configuration using SELALIB code. When the equilibrium profile is not steep and the perturbation only has the non-zero mode number along the parallel spatial dimension, the results computed by the two solvers match each other well. When the gradient of the equilibrium profile is steep, the interpolation solver provides a bigger driving effect for the ion-temperature-gradient modes, which possess large polar mode numbers.
Highlights
Micro-scale turbulence plays a significant role in the confinement capability of magnetized fusion plasma through its interaction with low-frequency zonal flow [1,2,3,4,5,6,7], equilibrium profile at the pedestal region, and edge localized modes [8,9,10,11,12], etc
The gradient of the equilibrium temperature and density at the pedestal region could be very sharp; alternatively, the truncation of exp(ρ0 · ∇) acting over n0 or T0 at the first order, which is used by the standard gyrokinetic model [16,17,18], is not a good approximation, where ρ0 is the Larmor radius vector defined as r
The first gyroaverage term could incorporate the effect contributed by the finite Larmor radius and short scales of the perturbation at the core and edge tokamak plasma, while the double-gyroaverage term (DGT)
Summary
Micro-scale turbulence plays a significant role in the confinement capability of magnetized fusion plasma through its interaction with low-frequency zonal flow [1,2,3,4,5,6,7], equilibrium profile at the pedestal region, and edge localized modes [8,9,10,11,12], etc. To overcome the mentioned drawbacks of the low-order approximation of DGT, this paper develops an interpolation algorithm to compute DGT for the purpose of the resolving of the short-scale perturbation and the steep equilibrium profile together. As a comparison to the interpolation solver, a classical 2nd order truncation of DGT is carried out in this paper to obtain QNE with the 2nd-order accuracy It consists of the truncation of the exponential operator exp(ρ0 · ∇) over the potential up to the second order and the truncation of the operator exp(ρ0 · ∇) acting on the density up to the first order. Euler–Maclaurin-based quadrature integrating algorithm to the gyrokinetic simulations is provided by Section 7, where the parallel scheme of the whole simulations is presented
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