H. Sugama

Collisionless damping of zonal flows in helical systems

Collisionless time evolution of zonal flows in helical systems is investigated. An analytical expression describing the collisionless response of the zonal-flow potential to the initial potential and a given turbulence source is derived from the gyrokinetic equations combined with the quasineutrality condition. The dispersion relation for the geodesic acoustic mode (GAM) in helical systems is derived from the short-time response kernel for the zonal-flow potential. It is found that helical ripples in the magnetic-field strength as well as finite orbit widths of passing ions enhance the GAM damping. The radial drift motions of particles trapped in helical ripples cause the residual zonal-flow level in the collisionless long-time limit to be lower for longer radial wavelengths and deeper helical ripples. On the other hand, a high-level zonal-flow response, which is not affected by helical-ripple-trapped particles, can be maintained for a longer time by reducing their radial drift velocity. This implies a possibility that helical configurations optimized for reducing neoclassical ripple transport can simultaneously enhance zonal flows which lower anomalous transport. The validity of our analytical results is verified by gyrokinetic Vlasov simulation.

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

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.

How to calculate the neoclassical viscosity, diffusion, and current coefficients in general toroidal plasmas

A novel method to obtain the full neoclassical transport matrix for general toroidal plasmas by using the solution of the linearized drift kinetic equation with the pitch-angle-scattering collision operator is shown. In this method, the neoclassical coefficients for both poloidal and toroidal viscosities in toroidal helical systems can be obtained, and the neoclassical transport coefficients for the radial particle and heat fluxes and the bootstrap current with the nondiagonal coupling between unlike-species particles are derived from combining the viscosity-flow relations, the friction-flow relations, and the parallel momentum balance equations. Since the collisional momentum conservation is properly retained, the well-known intrinsic ambipolar condition of the neoclassical particle fluxes in symmetric systems is recovered. Thus, these resultant neoclassical diffusion and viscosity coefficients are applicable to evaluating accurately how the neoclassical transport in quasi-symmetric toroidal systems devi...

Collisionless damping of geodesic acoustic modes

Collisionless time evolutions of geodesic acoustic modes (GAMs) in tokamaks arc Investigated by the gyrokinetic theory and simulation. It is shown that the collisionless damping of the GAM oscillations is enhanced when the ratio of the typical drift orbit width of passing ions to the radial wavelength of the zonal flow inereases.

Kinetic simulation of steady states of ion temperature gradient driven turbulence with weak collisionality

Statistically steady states of the ion temperature gradient driven turbulence with weak collisionality, where the collision frequency is much lower than characteristic ones of the turbulence, are investigated by means of a Eulerian kinetic simulation with high resolution. In the saturated state of the entropy variable, the ion heat transport balances with the collisional dissipation that is indispensable to realizing a steady-turbulence state of perturbed distribution function δf. The kinetic simulation definitely confirms the conventional hypothesis that, in a low-collisionality limit, the low-order velocity-space moments of δf as well as the ion heat transport flux agree with those in the quasisteady state of the collisionless turbulence with the constant entropy production. A spectral analysis of δf in the velocity-space clarifies the transfer and dissipation processes of the entropy variable associated with fluctuations, where the phase mixing, the E×B nonlinearity, and the finite collisionality are t...

Collisionless kinetic-fluid closure and its application to the three-mode ion temperature gradient driven system

A novel closure model is presented to give a set of fluid equations which describe a collisionless kinetic system. In order to take account of the time reversal symmetry of the collisionless kinetic equation, the new closure model relates the parallel heat flux to the temperature and the parallel flow in terms of the real-valued coefficients in the unstable wave number space. Effects of the closure model on turbulence saturation and anomalous transport are investigated based on kinetic and fluid entropy balances. When the closure model is applied to the three-mode ion temperature gradient (ITG) driven system, the fluid system of equations reproduces the exact nonlinear kinetic solution found by Watanabe, Sugama, and Sato [Phys. Plasmas 7, 984 (2000)]. Oscillatory behaviors and initial amplitude dependence of other numerical kinetic solutions of the three-mode ITG problem can also be accurately described by the fluid system.

Kinetic simulation of a quasisteady state in collisionless ion temperature gradient driven turbulence

Existence of a quasisteady state with a mean transport flux in the collisionless ion temperature gradient driven turbulence has been confirmed by means of a direct numerical simulation of a basic kinetic equation for the perturbed ion velocity distribution function δf. The phase mixing generates fine-scale fluctuations of δf and leads to continuous growth of high-order moments which balances the transport flux. The phase relation between the temperature and the parallel heat flux is also examined and compared with a fluid closure model.

Gyrokinetic simulation of zonal flows and ion temperature gradient turbulence in helical systems

The gyrokinetic-Vlasov simulation code (GKV code) is applied to zonal flows and the ion temperature gradient (ITG) turbulence in helical systems with L = 2 and M = 10 like the Large Helical Device (where L and M denote poloidal and toroidal periodicities of the main helical component of the confinement field, respectively) for the standard and inward-shifted model configurations. Because of the slower radial drift motion of helical-ripple-trapped particles, the inward-shifted case provides a higher zonal-flow response than that in the standard model with smaller side-band helical field components. The nonlinear GKV simulations show that the ITG turbulent transport in the inward-shifted model, which has larger growth rates of the ITG stability, is regulated by the zonal flows to a level comparable to the standard case.

Moment-equation methods for calculating neoclassical transport coefficients in general toroidal plasmas

A detailed comparison is made between moment-equation methods presented by H. Sugama and S. Nishimura [Phys. Plasmas 9, 4637 (2002)] and by M. Taguchi [Phys. Fluids B 4, 3638 (1992)] for calculating neoclassical transport coefficients in general toroidal plasmas including nonsymmetric systems. It is shown that these methods can be derived from the drift kinetic equation with the same collision model used for correctly taking account of collisional momentum conservation. In both methods, the Laguerre polynomials of the energy variable are employed to expand the guiding-center distribution function and to obtain the moment equations, by which the radial neoclassical transport fluxes and the parallel flows are related to the thermodynamic forces. The methods are given here in the forms applicable for an arbitrary truncation number of the Laguerre-polynomial expansion so that their accuracies can be improved by increasing the truncation number. Differences between results from the two methods appear when the ...

Non-local neoclassical transport simulation of geodesic acoustic mode

Neoclassical transport simulation code (FORTEC-3D) applicable to both axisymmetric and non-axisymmetric configurations is developed to investigate non-local effects on neoclassical transport phenomena. The time evolution of the radial electric field is simulated in the full volume of the confinement region of tokamak and helical model plasmas. It is found that the damping rate of the geodesic-acoustic-mode (GAM) oscillation becomes faster than that predicted from a single-surface transport analysis. The time evolution of the radial electric field towards the ambipolar state shows a non-local behaviour, which indicates a coupling of GAM oscillation between the neighbouring two flux surfaces because of the finite-orbit-width effect.