Atsushi Fukuyama

Self-consistent simulation of torque generation by radial current due to fast particles

The generation of toroidal rotation due to the radial current torque induced by the charge separation is studied by using the one-dimensional multi-fluid transport code TASK/TX. Owing to the effect of the drift motion, the charge separation occurs as long as fast neutrals, typically from near-perpendicular NBI, are ionized. Coupling the TASK/TX code with the orbit-following Monte Carlo code (OFMC), we have shown that the toroidal rotation is driven due to the generation of the radial current jbulk flowing in the bulk plasma with the near-perpendicular NBI. The simulations have clarified that the NB on the equatorial plane drives the toroidal rotation most efficiently from the aspects of the collisional and jbulk × B torques. The jbulk × B torque becomes a major driver of the rotation in a high density plasma, replacing the collisional torque. In a steady state, the toroidal rotation driven by the jbulk × B torque is determined by the balance among the torque, the viscosity, the convection, the friction with neutrals and the loss of momentum due to charge exchange.

Numerical analysis of the effect of fast-ion losses on plasma rotation in a tokamak with toroidal field ripple

The effect of fast-ion losses due to the toroidal field ripple on the toroidal rotation is studied through numerical simulations. The simulations are carried out by utilizing a multi-fluid one-dimensional transport code, TASK/TX, with a ripple transport model suitable for implementing one-dimensional transport codes. Simulation results are qualitatively consistent with the experiments in JT-60U. It is shown that the return current associated with the outward radial fast-ion current due to the ripple loss flows inwards in the bulk plasma and the resultant torque drives the plasma toroidally in the counter direction of the plasma current. The equilibrium value of the toroidal rotation velocity is determined by the balance between the perpendicular viscosity and the total torque.

On the Neoclassical Relationship between the Radial Electric Field and Radial Current in Tokamak Plasmas

The fluid equation is analytically derived in a rigorous manner, stipulating the relationship between the radial electric field and radial current in tokamak plasmas, especially when heated by neutral beam injection. On a very short time scale compared to the decay in poloidal rotation, the polarization current compensates for the non-ambipolar fast-ion radial current, producing a concomitant time change in the radial electric field. This polarization current predominates among the constituents of the radial current that produces the j × B torque. For times comparable to or longer than the decay time, the polarization current is no longer sufficient to compensate for the fast-ion radial current. In a steady state where the radial electric field is constant over time, the polarization current vanishes and the orthogonal conduction current becomes a sole component of the radial current that continues to flow as long as the charge separation occurs due to the neutral beam injection. Analytical work demonstra...

Numerical calculation of equilibria with poloidal-sonic flow and finite Larmor radius effects in large aspect-ratio tokamaks

A code has been developed for calculating magnetohydrodynamic equilibria with poloidal-sonic flow and finite Larmor radius effects in high-beta tokamaks using an inverse aspect-ratio expansion and a reduced two-fluid model. The Grad–Shafranov equations governing the first- and second-order poloidal fluxes can be expressed in terms of five free profiles of the first-order poloidal flux. Sample equilibria, illustrating behaviors such as the deviation of pressure contours from the flux surfaces, and the criteria for the presence of the “poloidal-sonic singularity” are presented.

Modelling of anomalous particle transport for dynamic transport simulations

A force model leading to the usual quasilinear particle flux is developed for the equations of motion used in the transport equations of the multi-fluid transport code TASK/TX. The model precisely corresponds to a quasilinear flux consisting of diagonal, thermodiffusive and pure convective contributions, where the turbulent coefficients of the force model are externally provided by a model of the turbulent process. Our approach is consistent in that particle transport can be described through a change in radial particle flux by solving the continuity equation and the equations of motion self-consistently. Time-dependent simulations that vary the ratio of particle diffusivity to thermal diffusivity show that thermal neutrals as a particle source in the core region affect the formation of density profile in the limit of the smallness of the ratio, while an increase in the ratio rapidly decreases the effectiveness of the source effect.

Integrated Transport Simulation of Burning Plasmas

In order to predict the behavior of burning plasmas and develop optimized operation scenarios of ITER, integrated modeling and simulation of fusion plasmas is indispensable. Transport process is one of the main issues in integrated modeling of burning plasmas. In this lecture, first, aim of the integrated simulation, research activities of integrated modeling, desired features of integrated simulation codes, and the integrated tokamak simulation code, TASK, are briefly described. Then the present role of transport modeling in the integrated modeling is discussed based on the time scale separation. Basic equations of the transport simulation coupled with the equilibrium analysis are explained. Modeling of transport phenomena, comparison of transport models, simulation of internal transport barrier formation are described. After brief discussion of source modeling, an example of burning plasma simulation. Finally remaining issues are discussed and summaries are given.

Kinetic Integrated Modeling of Heating and Current Drive In Tokamak Plasmas

Abstract. In order to self-consistently describe heating and current drive and various influences of energetic particles in tokamak plasmas, we have been developing a kinetic integrated modeling code TASK3G. This modeling is based on the behavior of the momentum distribution function of each particle species. The time evolution of the momentum distribution function is described by a newly-extended Fokker-Planck component TASK/FP and the influence of energetic particles on global stability is studied by a full wave component TASK/WM. Self-consistent analysis of multi-scheme heating in a ITER plasma is demonstrated for the first time including radial transport and fusion reaction rate calculated from the momentum distribution function. The linear stability of global eigen modes in the presence of energetic particles is also discussed.

Simulation Study of Toroidal Shear Flow Generation by a Local ICRF Heating

The toroidal shear flow generation by a local ICRF heating is studied using GNET code, in which the drift kinetic equation is solved in 5D phase‐space. Verification of the Ohkawa model [T. Ohkawa and Miller, Phys. Plasmas 12 (2005) 094506.] predicting the toroidal shear flow generation is done including the finite orbit effect of energetic ions in a tokamak configuration. The Alcator C‐mod plasma is assumed as a first step. A co‐directional toroidal flow outside of the power absorption region (resonance position) is observed. The dominant part of toroidal flow dose not depend on the sign k// and this fact indicates that the driving mechanism of the dominant part is different from that proposed by the Ohkawa model.

Modeling of Two-Dimensional Transport in Tokamak Plasmas

For integrated modeling of core and peripheral plasmas and analysis of transient transport phenomena where poloidal dependence of quantity is important, describing transport phenomena in the entire tokamak plasma as two-dimensional problems is desirable and becoming feasible owing to recent remarkable progress in computational resources. The set of two-dimensional transport equations with poloidal angle dependence is formulated from Braginskii’s equations and the neoclassical theory in order to develop an integrated two-dimensional transport simulation code.

Toroidal Flow Generation by the ICRF Minority Heating and RF Wave Field Profile Dependence

The toroidal flow generation by the ICRF minority heating is investigated in the Alcator C‐Mod like tokamak plasma applying GNET code, in which the drift kinetic equation is solved in 5D phase‐space. An asymmetry of velocity distribution function in the parallel direction is found and two kinds of toroidal flows are observed. One is the sheared flow near the RF power absorption region depending on the sign of k∥ and the other is the toroidal flow, which is larger than the previous one, independent of the sign of k∥. It is found that the k∥ sign dependent flow would be related to the mechanism proposed by Ohkawa et al. [Phys. Plasmas 12 (2005) 094506.] and that the k∥ sign independent toroidal flow is generated by the net toroidal motion of energetic tail ions. We also investigate the effect of RF wave field profile on the toroidal flow generation comparing the local and broad heating cases. A broader toroidal flow is obtained and about 5 times of ICRF heating power is necessary for generating the similar ...