Analysis of Pellet Ablation with Atomic Processes

A new type of a magnetohydrodynamics (MHD) code applicable to solid, liquid and gas states, “CAP” has been developed in order to investigate ablation process of a pellet with ato mic processes in hot plasmas. One of the most important features of the code is to be able to treat re cession of the pellet surface by ablation without any artificial boundary condition between the pellet an d ablation cloud. A region excluding a magnetic field is induced because the magnetic pressure is overcome by the ablation pressure. It is found that a stationary shock wave is driven by ionization

Ellipticity of axisymmetric equilibria with flow and pressure anisotropy in single-fluid and Hall magnetohydrodynamics

The ellipticity criteria for the partial differential equations of axisymmetric single-fluid and Hall magnetohydrodynamic (MHD) equilibria with flow and pressure anisotropy are investigated. The MHD systems are closed with cold ions and electron pressures derived from their parallel heat flux equations, a closure that reproduces the corresponding kinetic dispersion relation. In the single-fluid model, which differs from the double-adiabatic Chew?Goldberger?Low model, it is verified that the elliptic region boundaries occur at poloidal flow velocities equal to wave velocities from the kinetic dispersion relation. For Hall magnetohydrodynamics, a set of anisotropic-pressure equilibrium equations is derived and an ellipticity condition corresponding to a poloidal flow velocity slightly smaller than the ion sound velocity is obtained

Magnetic flux coordinates for analytic high-beta tokamak equilibria with flow

Magnetic flux coordinates are constructed from an analytic solution (Ito and Nakajima 2009 Plasma Phys. Control. Fusion 51 035007) for the reduced magnetohydrodynamics (MHD) equilibrium equations for high-beta tokamaks in the presence of poloidal and toroidal flows comparable to the poloidal sound velocity. The analytic solution indicates non-circular magnetic flux surfaces and transition between sub- and super-sonic poloidal flows. The magnetic flux coordinates for such non-circular magnetic flux surfaces are obtained for stability analysis. The flux coordinates are numerically obtained from the high order polynomial equations for the relation with the geometrical coordinates. As applications, pressure profiles in the poloidal direction on each flux surface, which become non-constant due to flow, and the flux average of the pressure are obtained. The transitions of the pressure profiles and the flux average of the pressure between sub- and super-sonic poloidal flows are discussed in relation with the radial force balance. The flux coordinates are also obtained analytically by expanding the coordinate relations with respect to the inverse aspect ratio

High-beta axisymmetric equilibria with flow in reduced single-fluid and two-fluid models

Reduced single-fluid and two-fluid equations for axisymmetric toroidal equilibria of high-beta plasmas with flow are derived by using asymptotic expansions in terms of the inverse aspect ratio. Two different orderings for the flow velocity, comparable to the poloidal Alfv?n velocity and comparable to the poloidal sound velocity, are considered. For a poloidal-Alfv?nic flow, the two-fluid equilibrium equations with hot ion effects are shown to have a singularity that is shifted by the gyroviscous cancellation from the Alfv?n singularity found in singlefluid magnetohydrodynamics (MHD) when the poloidal flow velocity equals the poloidal Alfv?n velocity. For a poloidal-sonic flow, a reduced single-fluid model is used to derive a set of equilibrium equations that includes higher-order terms. The singularity at a poloidal flow velocity equal to the poloidal sound velocity is recovered in the higher order equations

Two-fluid and finite Larmor radius effects on high-beta tokamak equilibria with flow in reduced magnetohydrodynamics

High-beta tokamak equilibria with flow comparable to the poloidal Alfvén velocity in the reduced magnetohydrodynamics (MHD) model with two-fluid and ion finite Larmor radius (FLR) effects are investigated. The reduced form of Grad-Shafranov equation for equilibrium with flow, two-fluid and FLR effects is analytically solved for simple profiles. The dependence of the Shafranov shift for the magnetic axis and the equilibrium limits on the poloidal beta and the poloidal Alfvén Mach number are modified by the two-fluid and FLR effects. In the presence of the diamagnetic drift due to the two-fluid effect, the equilibrium depends on the sign of the E × B drift velocity. The FLR effect suppresses the large modification due to the two-fluid effect. By constructing magnetic flux coordinates and a local equilibrium model from the analytic solution, the effects of the non-circular property of the magnetic flux surfaces in the poloidal cross-section on the components of the curvature vector is examined in detail. The analytic solution is also used for the benchmark of the numerical code. The numerical solutions with non-uniform pressure, density and temperature profiles show similar behavior to analytic solution

THE FRICTIONAL COEFFICIENTS IN TI-NB ALLOY

Objectives: To determine the frictional force (FF) of the novel, elastic, bendable titanium-niobium (Ti-Nb) alloy orthodontic wire in stainless steel (SS) brackets and to compare it with those of titanium-nickel (Ti-Ni) and titanium-molybdenum (Ti-Mo) alloy wires. Materials and Methods: Three sizes of Ti-Nb, Ti-Ni, and Ti-Mo alloy wires were ligated with elastic modules to 0.018-inch and 0.022-inch SS brackets. The dynamic FFs between the orthodontic wires and SS brackets were measured at three bracket-wire angles (0゜, 5゜, and 10゜) with an Instron 5567 loading apparatus (Canton, Mass). Results: FFs increased gradually with the angle and wire size. In the 0.018-inch-slot bracket, the dynamic FFs of Ti-Nb and Ti-Ni alloy wires were almost the same, and those of the Ti-Mo alloy wire were significantly greater (P<0.05). FF values were 1.5–2 times greater in the 0.022-inch-slot bracket than in the 0.018-inch-slot bracket, regardless of alloy wire type, and the Ti-Mo alloy wire showed the greatest FF. Scanning electric microscopic images showed that the surface of the Ti-Mo alloy wire was much rougher than that of the Ti-Ni and Ti-Nb alloy wires. Conclusion: These findings demonstrate that the Ti-Nb alloy wire has almost the same frictional resistance as the Ti-Ni alloy wire, although it has a higher elastic modulus

Simulation Study of Ballooning Modes in the Large Helical Device

The magnetohydrodynamic (MHD) simulation code MHD Infrastructure for Plasma Simulation (MIPS) was benchmarked on ballooning instability in the Large Helical Device (LHD) plasma. The results were compared to the results of linear analysis by using the CAS3D code. Both the linear growth rates and the spatial profiles were found to be in good agreement. An extended MHD model with finite ion Larmor radius effects was implemented into the MIPS code. Ballooning instabilities were investigated using the extended MHD model, and the results were compared with those using the MHD model. Ion diamagnetic drift was found to reduce the growth rate of the short-wavelength modes; hence, modes with a diamagnetic drift frequency comparable to the ideal MHD growth rate are the most unstable. The most unstable toroidal mode number of ballooning instability in the LHD is reduced to |n| ? 5 for hydrogen plasma with ion number density ni ? 1019 m?3

On the Characteristic Difference of Neoclassical Bootstrap Current and Its Effects on MHD Equilibria between CHS Heliotron/Torsatron and CHS-qa Quasi-Axisymmetric Stellarator

The characteristic difference of neoclassical bootstrap current and its effects on MHD equilibria are described for the CHS heliotron/torsatron and the CHS-qa quasi-axisymmetric stellarator. The direction of bootstrap current strongly depends on collisionality in CHS, whereas it does not in CHS-qa because of quasi-axisymmetry. In the CHS configuration, it appears that enhanced bumpy (Bs1) and sideband components of helical ripple (By1) play an important role in reducing the magnetic geometrical factor, which is a key factor in evaluating the value of bootstrap cuffent, and determining its polarity. The bootstrap current in CHS-qa is theoretically predicted to be larger than that in CHS and produces significant effects on the resulting rotational transform and magnetic shear. In the finite B plasmas, the magnetic well becomes deeper in both CHS and CHS-qa and its region is expanded in CHS. The existence of co-flowing bootstrap current makes the magnetic well shallow in comparison with that in currentless equilibrium

Orbit Topology and Confinement of Energetic Ions in the CHS-qa Quasi-Axisymmetric Stellarator

The orbit topology and confinement of neutral beam-injected energetic ions are investigated for the current target configuration of the CHS-qa quasi-axisymmetric stellarator. It was shown that tangentially co-injected neutral beam (NB) heating is efficient even at a low magnetic field strength Bt of 0.5 T, whereas the heating efficiency of the counter-injected NB becomes significantly lower as Bt decreases because of the increase of first orbit loss. The energy loss rate increases as the beam injection angle becomes perpendicular, suggesting that the residual non-axisymmetric ripple in the peripheral domain plays a role in enhancing the transport of trapped ions. An interesting observation involves the appearance of the island structure in both the gyro motion following orbit and the guiding center collisionless orbit of counter-moving transit beam ions. It appears under a particular, narrow range of parameters, i.e., energy, pitch angle v///v, normalized minor radius r/a at the launching point and Bt

Electromagnetic gyrokinetic simulation of turbulence in torus plasmas

Gyrokinetic simulations of electromagnetic turbulence in magnetically confined torus plasmas including tokamak and heliotron/stellarator are reviewed. Numerical simulation of turbulence in finite beta plasmas is an important task for predicting the performance of fusion reactors and a great challenge in computational science due to multiple spatio-temporal scales related to electromagnetic ion and electron dynamics. The simulation becomes further challenging in non-axisymmetric plasmas. In finite beta plasmas, magnetic perturbation appears and influences some key mechanisms of turbulent transport, which include linear instability and zonal flow production. Linear analysis shows that the ion-temperature gradient (ITG) instability, which is essentially an electrostatic instability, is unstable at low beta and its growth rate is reduced by magnetic field line bending at finite beta. On the other hand, the kinetic ballooning mode (KBM), which is an electromagnetic instability, is destabilized at high beta. In addition, trapped electron modes (TEMs), electron temperature gradient (ETG) modes, and micro-tearing modes (MTMs) can be destabilized. These instabilities are classified into two categories: ballooning parity and tearing parity modes. These parities are mixed by nonlinear interactions, so that, for instance, the ITG mode excites tearing parity modes. In the nonlinear evolution, the zonal flow shear acts to regulate the ITG driven turbulence at low beta. On the other hand, at finite beta, interplay between the turbulence and zonal flows becomes complicated because the production of zonal flow is influenced by the finite beta effects. When the zonal flows are too weak, turbulence continues to grow beyond a physically relevant level of saturation in finite-beta tokamaks. Nonlinear mode coupling to stable modes can play a role in the saturation of finite beta ITG mode and KBM. Since there is a quadratic conserved quantity, evaluating nonlinear transfer of the conserved quantity from unstable modes to stable modes is useful for understanding the saturation mechanism of turbulence