T.-H. Watanabe

Gyrokinetic simulations of turbulent transport

This overview is an assessment of the gyrokinetic framework and simulations to compute turbulent transport in fusion plasmas. It covers an introduction to the gyrokinetic theory, the principal numerical techniques which are being used to solve the gyrokinetic equations, fundamentals in gyrokinetic turbulence and the main results which have been brought by simulations with regard to transport in fusion devices and fluctuation measurements.

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.

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...

Comprehensive simulation study on local and global development of auroral arcs and field‐aligned potentials

Extensive three-dimensional computer simulations of the magnetosphere-ionosphere (M-I) coupling are performed to study self-excitation of an auroral arclike structure with special emphasis on (1) nonlinear evolution of the feedback instability in the M-I coupling system, (2) controlling mechanisms of the arc structure, (3) formation of a field-aligned electric potential structure in association with the development of the feedback instability, and (4) effects of the parallel potential generation on the development of the arclike structure. The present study takes the first step toward the theoretical understanding of the M-I coupling system with parallel potentials. As was already shown by Sato [1978] and Watanabe and Sato [1988], it is reconfirmed that the feedback instability produces a longitudinally elongated, latitudinally striated structure where the upward field-aligned current and the ionospheric density are locally enhanced. On top of this the present extended study reveals the following important new features: The global distribution of the striation structure is primarily governed by the magnetospheric convection pattern and the ionospheric density distribution. There appears a significant dawn-dusk asymmetry in the arc formation, even though the apparent geometrical relationship is symmetric. This dawn-dusk asymmetry reflects the geometrical fact that the ionospheric Pedersen current closing the magnetospheric current is antisymmetric with respect to the noon-midnight plane, while the self-closed Hall current is symmetric. The recombination effect plays a significant role in the global, as well as local, development of the arc structure. The nonlinearity of recombination, in conjunction with the closure of an arc-associated local field-aligned current system, acts to destroy an old arc and creates a new arc in a different but adjacent position. This results in a peculiar dynamic evolution of the arclike structure. A V-shaped field-aligned potential structure is created in association with an arc structure, when we introduce the parallel anomalous resistivity. The nonlinear phase mismatching due to the parallel resistivity reduces the growth rate of the feedback instability, and suppresses the growth of the arc structure. When the effect of precipitating hot electrons is taken into account, the ionospheric density is considerably enhanced locally at the foot of the field lines where the field-aligned potential is generated. An oscillatory behavior is observed in the development of the ionospheric density, field-aligned current and potential. The period seems to be governed by the Alfven bounce time and the ionospheric density.

Magnetohydrodynamic Vlasov simulation of the toroidal Alfvén eigenmode

A new simulation method has been developed to investigate the excitation and saturation processes of toroidal Alfven eigenmodes (TAE modes). The background plasma is described by a magnetohydrodynamic (MHD) fluid model, while the kinetic evolution of energetic alpha particles is followed by the drift kinetic equation. The magnetic fluctuation of n=2 mode develops and saturates at the level of 1.8×10−3 of the equilibrium field when the initial beta of alpha particles is 2% at the magnetic axis. After saturation, the TAE mode amplitude shows an oscillatory behavior with a frequency corresponding to the bounce frequency of the alpha particles trapped by the TAE mode. The decrease of the power transfer rate from the alpha particles to the TAE mode, which is due to the trapped particle effect of a finite‐amplitude wave, causes the saturation. From the linear growth rate the saturation level can be estimated.

Momentum balance and radial electric fields in axisymmetric and nonaxisymmetric toroidal plasmas

We have investigated the influence of symmetry properties of toroidal magnetic configurations on the mechanisms used for determining the radial electric field such as the momentum balance and the ambipolar particle transport. Both neoclassical and anomalous transport of particles, heat and momentum in axisymmetric and nonaxisymmetric toroidal systems are taken into account. Generally, in nonaxisymmetric systems, the radial electric field is determined by the neoclassical ambipolarity condition. For axisymmetric systems with up–down symmetry and quasisymmetric systems with stellarator symmetry, it is shown using a novel parity transformation that the particle fluxes are automatically ambipolar up to and the determination of the radial electric field Es requires solving the momentum balance equations, where δ denotes the ratio of the thermal gyroradius to the characteristic equilibrium scale length. In axisymmetric systems with large E × B flows on the order of the ion thermal velocity vTi, the radial fluxes of particles, heat and toroidal momentum are dependent on Es and its radial derivative while the time evolution of the Es profile is governed by the toroidal momentum balance equation. In nonaxisymmetric systems, E × B flows of are not generally allowed even in the presence of quasisymmetry because the nonzero radial current is produced by the large flow term in the equilibrium force balance for which the Boozer and Hamada coordinates cannot be constructed.

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.