Ryutaro Kanno

Ideal-Magnetohydrodynamic-Stable Tilting in Field-Reversed Configurations

The tilting mode in field-reversed configurations (FRC) is examined using ideal-magnetohydrodynamic stability theory. Tilting, a global mode, is the greatest threat for disruption of FRC confinement. Previous studies uniformly found tilting to be unstable in ideal theory: the objective here is to ascertain if stable equilibria were overlooked in past work. Solving the variational problem with the Rayleigh-Ritz technique, tilting-stable equilibria are found for sufficiently hollow current profile and sufficient racetrackness of the separatrix shape. Although these equilibria were not examined previously, the present conclusion is quite surprising. Consequently checks of the method are offered. Even so it cannot yet be claimed with complete certainty that stability has been proved: absolute confirmation of ideal-stable tilting awaits the application of more complete methods.

Ion Temperature Gradient Modes in Toroidal Helical Systems

Linear properties of ion temperature gradient (ITG) modes in toroidal helical systems are studied. The real frequencies, growth rates, and eigenfunctions are obtained for both stable and unstable c...

Calculation of neoclassical toroidal viscosity in tokamaks with broken toroidal symmetry

A new numerical simulation to evaluate neoclassical toroidal viscosity (NTV) in tokamak configurations with a small perturbation field is developed using the ?f Monte Carlo method. The numerical scheme solves the guiding-centre distribution function in non-axisymmetric plasmas according to the drift-kinetic equation, and evaluates the NTV directly from the pressure anisotropy by utilizing the Fourier spectrum expression of the magnetic field in Boozer coordinates. As a first benchmark, the accuracy of the viscosity calculation is demonstrated in a helical configuration of LHD. The convergence of the calculation and dependence of the viscosity on perturbation field amplitude are also tested in a simple tokamak configuration with model perturbation field, which proves the reliability of the simulation. Next, the basic properties of NTV as dependence of the viscosity on collision frequency and magnetic shear are investigated in a multi-helicity perturbation model field and compared with a bounce-averaged analytic formula. It is found that the clear 1/? and superbanana-plateau dependences cannot be seen in the FORTEC-3D simulation, and the toroidicity of the magnetic field makes a toroidal coupling effect, which enhances NTV if the perturbation has (m, n) and (m ? 1, n) Fourier components simultaneously, where m and n are the poloidal and toroidal numbers of the perturbation field. Local magnetic shear is also found to affect the amplitude of the viscosity.

Effects of magnetic drift tangential to magnetic surfaces on neoclassical transport in non-axisymmetric plasmas

In evaluating neoclassical transport by radially local simulations, the magnetic drift tangential to a flux surface is usually ignored in order to keep the phase-space volume conservation. In this paper, effect of the tangential magnetic drift on the local neoclassical transport is investigated. To retain the effect of the tangential magnetic drift in the local treatment of neoclassical transport, a new local formulation for the drift kinetic simulation is developed. The compressibility of the phase-space volume caused by the tangential magnetic drift is regarded as a source term for the drift kinetic equation, which is solved by using a two-weight δf Monte Carlo method for non-Hamiltonian system [G. Hu and J. A. Krommes, Phys. Plasmas 1, 863 (1994)]. It is demonstrated that the effect of the drift is negligible for the neoclassical transport in tokamaks. In non-axisymmetric systems, however, the tangential magnetic drift substantially changes the dependence of the neoclassical transport on the radial ele...

Formation and healing of n = 1 magnetic islands in LHD equilibrium

Magnetic islands with the toroidal mode number n = 1, e.g. m/n = 1/1 and 2/1 islands, in a Large Helical Device (LHD) equilibrium are studied using the three-dimensional MHD equilibrium code, HINT. In order to accomplish this purpose, the HINT code has been improved. The equilibrium analysis, in particular an analysis of the LHD equilibrium with an m/n = 1/1 island, is required for the local island divertor experiment, in order to understand the magnetic structures of field lines, i.e. flux surfaces, islands and ergodic field lines. We find that the m/n = 2/1 island can be healed for a finite equilibrium beta, while the m/n = 1/1 island is not healed and is surrounded with ergodic field lines for finite-β. From the latter result, we can conjecture that the island divertor concept is effective even for finite equilibrium beta-values, but the performance of the island divertor is deteriorated for finite-β because of the existence of the ergodic zone between the closed surfaces (i.e. the core region) and the m/n = 1/1 island. We also find that the width of the m/n = 1/1 island depends on the equilibrium beta value and that the island located at the inside of the torus has the advantage of retaining its width.

Statistical properties of the radial transport in the magnetic field with radially bounded stochastic region

Statistical properties of the radial heat transport of electrons are clarified in the various types of the radially bounded irregular magnetic field inside an axisymmetric torus plasma, where the collisional stochasticity due to the Coulomb collision and the magnetic stochasticity due to a radially bounded perturbed field coexist. Extensive Monte Carlo numerical analysis are performed in the two dimensional parameter space (sb/sbc,ν/νt) with a delta function initial distribution in the radial direction. The parameters sb and ν are the strength of a magnetic field perturbation and the collision frequency, respectively. The normalization parameter sbc corresponds to the islands overlapping criterion, and νt is the characteristic frequency of the passing particle orbits in the corresponding regular magnetic field. It is shown that the type of the transport process is closely connected with the locality of the particle radial displacements. As sb/sbc(⩾1) increases and ν/νt decreases, the particle distribution spreads out in a whole stochastic region after the short time ballistic (dynamical) phase reflecting the non-locality of radial displacements. As a consequence the subdiffusive process (sb/sbc⩾1,ν/νt⩾0) or the uniform mixing process (sb/sbc⪢1,ν/νt=0) are observed in the long time limit. The standard diffusion approach is applicable only in the limited parameter region when the fairly frequent collisions inside the radially bounded stochastic region with the mixture of regular and irregular domains can recover the locality of particle displacements.

Computational study of three-dimensional equilibria with the bootstrap current

The three-dimensional currentless equilibrium code, HINT is revised so that it can handle equilibria with a net toroidal current, for example the bootstrap current. The revised HINT code is applied to Large Helical Device-like equilibria with good nested flux surfaces.

Initial value problem of the toroidal ion temperature gradient mode

The initial value problem of the toroidal ion temperature gradient mode is studied based on the Laplace transform of the ion gyrokinetic equation and the electron Boltzmann relation with the charge neutrality condition. Due to the toroidal magnetic drift, the Laplace-transformed density and potential perturbations have a branch cut as well as poles on the complex-frequency plane. The inverse Laplace transform shows that the temporal evolution of the density and potential perturbations consists of the normal modes and the continuum mode, which correspond to contributions from the poles and the branch cut, respectively. The normal modes have exponential time dependence with the eigenfrequencies determined by the dispersion relation while the continuum mode shows power-law decay oscillation. For the stable case, the long-time asymptotic behavior of the potential and density perturbations is dominated by the continuum mode which decays slower than the normal modes.

Effects of finite beta and radial electric fields on neoclassical transport in the Large Helical Device

The effects of finite beta and radial electric fields on neoclassical transport in LHD are investigated with the Drift Kinetic Equation Solver (DKES) code. In the finite- beta configuration, even orbits of deeply trapped particles deviate significantly from magnetic flux surfaces. Thus, neoclassical ripple transport coefficients in the finite- beta configuration are several times larger than those in the vacuum configuration under the same conditions of temperatures and radial electric fields. When the plasma temperature is several kiloelectronvolts, a bifurcation of the electric fields appears under the ambipolarity condition. The E*B drift due to the resultant sufficiently large radial electric fields causes the orbits to curve so that they more closely follow the pressure surfaces and improves significantly the transport coefficients in the finite- beta configuration

Simulation studies of the effect of E × B rotation on neoclassical toroidal viscosity in tokamaks with small magnetic perturbations

The effect of non-axisymmetric magnetic perturbations and E???B rotation on neoclassical toroidal viscosity (NTV) is investigated using a drift-kinetic ?f Monte-Carlo simulation code, FORTEC-3D, and the simulation is benchmarked with an analytic formula which uses bounce-average approximation. Although the ?f code agrees with the analytic formula if the E???B velocity is low or the radial position is away from the resonant rational flux surface, a clear difference appears in the radial profile of NTV when the E???B velocity becomes large. A double-peak profile of NTV appears around the resonant rational flux surface only in the ?f simulation. The double peak is created as a result of the resonance of E???B drift and passing particle motion. The benchmark result suggests that the precise drift-kinetic simulation, which treats both trapped and passing particle contributions to neoclassical viscosity, is essential for quantitative evaluation of the rotation damping rate by NTV when the E???B rotation is not slow.