Velocity–space structures of distribution function in toroidal ion temperature gradient turbulence

Abstract

Velocity-space structures of ion distribution function associated with the ion temperature gradient (ITG) turbulence and the collisionless damping of the zonal flow are investigated by means of a newly developed toroidal gyrokinetic-Vlasov simulation code with high velocity-space resolution. The present simulation on the zonal flow and the geodesic acoustic mode (GAM) successfully reproduces the neoclassical polarization of trapped ions as well as ballistic mode structures produced by collisionless particle motions. During the collisionless damping of GAM, the finer-scale structures of the ion distribution function in the velocity-space continue to develop while preserving an invariant defined by a sum of an entropy variable and the potential energy. The simulation results of the toroidal ITG turbulent transport clearly show generation of the fine velocity-space structures of the distribution function and their collisional dissipation. Detailed calculation of the entropy balance confirms the statistically steady state of turbulence, where the anomalous transport balances with the dissipation are given by the weak collisionality. The above results obtained by simulations with high velocity-space resolution are also understood in terms of generation, transfer and dissipation processes of the entropy variable in the phase-space.

Collisionless damping of zonal flows in helical systems

“…In fact, it is observed in the large helical device 17 ͑LHD͒ that not only neoclassical but also anomalous transport is reduced by the inward shift of the magnetic axis which decreases the radial drift of helical-ripple-trapped particles but increases the unfavorable magnetic curvature to destabilize pressure-gradient-driven instabilities such as the ITG mode. [18][19][20] In this work, we also verify the validity of our theoretical predictions by a recently developed gyrokinetic Vlasov ͑GKV͒ simulation code 6 that can resolve detailed structures of the gyrocenter distribution function on the phase space. Here, we do not treat collisional decay of zonal flows, which occurs in the long course of time 21 although the residual zonal flows in a collisionless time scale are still regarded as critical factors to regulate the turbulent transport.…”

“…They showed that the initial zonal flow is not fully damped by collisionless processes but it approaches a finite value. It was verified by collisionless gyrokinetic simulations 5,6 that the zonal flow, which is added initially as an impulse, shows the convergence to the theoretically predicted value after oscillations of the geodesic acoustic mode 7 ͑GAM͒ are damped.…”

“…6 The perturbed electron density is simply calculated by using n ek Ќ = ͑n 0 e / T e ͒͑ k Ќ − ͗ k Ќ ͒͘ with T e = T i in the present simulations and accordingly the radial drift motions of nonadiabatic helical-ripple-trapped electrons are not treated here. Thus, the terms proportional to T i / T e in Eqs.…”

Suppression of phase mixing in drift-kinetic plasma turbulence

“…Including a constant flux of free energy into velocity space leads to non-universal spectra that tend to be steeper than those empirically observed [12][13][14][15][16][17]. Some simulations show a significant proportion of injected free energy cascading and dissipating in velocity space [18], albeit with a slower transfer rate than in the linear case, and with a dissipation rate that depends on collision frequency [19,20]. These observations suggest a complicated relationship between parallel phase mixing and the nonlinear cascade; there is as yet no complete picture of free-energy flow and dissipation in phase space.…”

Gyrokinetic turbulent transport simulation of a high ion temperature plasma in large helical device experiment

“…17, the GKV-X incorporates large number of Fourier components of the magnetic field as well as full geometrical information of the flux surfaces by using VMEC code 18 for the three-dimensional MHD equilibrium configuration corresponding to experimental profiles of the plasmas. The GKV-X solves the nonlinear gyrokinetic equation 19,20 for the ion perturbed gyrocenter distribution function df with the mass m i in the low-b electrostatic limit, a) Electronic mail: nunami.masanori@nifs.ac.jp. …”