M. Okamoto

EFFECTS OF NET TOROIDAL CURRENT ON THE MERCIER CRITERION IN THE LARGE HELICAL DEVICE

The effects of the net toroidal current on the local ideal MHD stability or the Mercier criterion are investigated for a plasma in the heliotron/torsatron configuration by taking the Large Helical Device as an example. The three dimensional equilibrium code VMEC is used to study the local stability of equilibria with given net toroidal currents. It is found that a subtractive current that decreases the rotational transform improves the stability, while an additive current that increases the rotational transform reduces the stability. The change of the rotational transform at the magnetic axis due to the net toroidal current is the essential mechanism for the change of stability. Mercier stability diagrams are given for the configurations of the Large Helical Device in which the plasma position is shifted inward or outward

Effect of collisionality and radial electric field on bootstrap current in the large helical device

The bootstrap current decreases in a more highly collisional regime, and in stellarator/heliotron it is predicted that a neoclassical current component proportional to the radial electric field exists when electrons and ions belong to different regimes of collisionality. To evaluate the bootstrap current in stellarator/heliotron in the whole range of collisionality from the collisionless 1/ν to the Pfirsch-Schluter regime, a new connection formula has been proposed. This connection formula has been applied to Large Helical Device (LHD) plasmas in which ions and electrons belong to different collisionality regimes, and finite beta MHD equilibria including the bootstrap current have been obtained. For LHD plasmas such as ECRH (T1 << Te) in electron root, the bootstrap current with an electric potential twice as high as the electron temperature reduces to about 1/5 to 2/3 of that with zero electric potential. Then, the MHD equilibrium configuration changes significantly, depending on collisionality and radial electric field, even for the same beta value of the LHD plasmas

Flexibility of LHD configuration with multilayer helical coils

The Large Helical Device (LHD) is a heliotron device with two helical coils, each of which has a structure of three current layers. It is designed so that the current in each layer can be controlled independently by changing the combination of the coil current in the layers, it is possible to vary the effective minor radius of the helical coils, which enlarges the flexibility of the configuration. The properties of the plasmas for several combinations of the layers are investigated numerically. In the vacuum configuration, it is found that the combination of layers corresponding to a large effective coil radius has a large outermost surface. In this case, the rotational transform decreases and the magnetic hill is reduced compared with the configuration with all three layers. The large Shafranov shift, which is due to the small rotational transform, enhances the magnetic well and the magnetic shear to stabilize the Mercier mode; however, it degrades the equilibrium beta limit. In the case of the combination of layers for a small effective coil radius, the Mercier mode is destabilized, because the magnetic hill is enhanced. The effect on the bootstrap current is also studied

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

A method to solve the impurity diffusion equation with ionization and recombination source terms

Abstract Diffusion equations of impurities with ionization and recombination source terms are solved numerically by the splitting and fractional-step method for noncommutative operators. Diffusion equations without source terms and rate equations are solved successively and the very small time step for calculation determined by fast ionization processes can be avoided by solving the rate equation as an eigenvalue problem. The time step is determined by the diffusion process and it is possible to follow the time evolution of impurities for a long time. The present method is second-order accurate in Δ t .

Equilibrium and localized flute instability of a tokamak with non-circular cross-section

The equilibrium equations are solved for tokamaks with non-circular cross-sections, by the method of the expansion in powers of the inverse aspect ratio. The analysis is extended to a more general class of equilibria, especially to study the effect of non-uniformity of plasma current distribution.For tokamaks with non-circular cross-sections, a simplified condition of stability against localized flute disturbances is obtained, which is a direct extension of Shafranov and Yurchenkos result. The kinds of variation of the cross-sections of the magnetic surfaces which improve the stability criterion are considered.

Realization and classification of symmetric stellarator configurations through plasma boundary modulations

The basic roles of several of the principal modulations of plasma boundary shape on MHD equilibria are investigated. The appropriate combination of the principal helical modulations for elimination of the bumpy field component in the realization of the quasi-axisymmetric (QAS) and quasi-helically symmetric (QHS) configurations is explained by considering the variation of the areas of the magnetic surface cross-sections. A triangular modulation is utilized effectively to form a magnetic well by shifting the magnetic axis outward compared with the centre of mass of the magnetic surface cross-section. The spatialization of the magnetic axis or the bumpy modulations of the plasma boundary are rather important for reducing the toroidicity in the magnetic field, which can lead to QHS configurations. Some stellarator magnetic configurations at present in the design stage or in existing experimental devices are discussed from the point of view of plasma boundary modulations. On the basis of these main findings about plasma boundary modulations, examples of the essential approach to QAS and QHS configurations are demonstrated step by step. The possibility of a quasi-bumpy (or poloidally) symmetric (QBS) configuration is also mentioned.

Theoretical prediction of bootstrap current in the Large Helical Device with unbalanced helical coil currents

The Large Helical Device (LHD), which is a heliotron/torsatron device with two helical coils, is designed so that the current in each helical coil can be controlled independently. Unbalancing these currents leads to spatial axis configurations. The bootstrap current is found to be strongly affected by any imbalance between these currents. When the ratio of the currents in the two helical coils is small enough, a bootstrap current flows in a direction so as to decrease the rotational transform because of the enhancement of the bumpiness component of the magnetic field as well as of the spatial axis component. This leads to improved stability

Equilibrium and Stability of a Tokamak with Non-Circular Cross Section

Under the condition which the shell has a shape of a non-circular cross section, the equilibrium equation, ∇p=j×B, is analysed by means of the expansion in the inverse of the aspect ratio, e, and the equilibrium of a Tokamak with a non-circular cross section is considered. The plasma with βp∇√e are treated. For such plasmas, the criterion for the stability against local disturbances is obtained for arbitrary current distributions and compared with one in the case of round toroidal plasmas. As a result, it is shown that suitable variations of the cross section improve the stability condition.