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

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

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

Relationships between the Prediction of Linear MHD Stability Criteria and the Experiment in LHD

We analyze the relationship between the experimentally observed pressure gradients at resonant rational surfaces and the theoretically predicted ideal magnetohydrodynamics (MHD) unstable region of global modes in the large helical device (LHD). According to the stability analysis of the ideal MHD modes with a low toroidal mode number, we find that the ideal MHD mode gives a constraint on the operational regime of the pressure gradients in the core. In the edge, a clear saturation of the pressure gradients due to the ideal MHD instability has not been observed up to the high beta regime around 3% as the volume-averaged toridal beta value, where global ideal MHD modes are predictedto be unstable

Effects of Current Profile on Global Ideal MHD Stability in a Compact Quasi-Axisymmetric Stellarator

The global ideal magnetohydrodynamic (MHD) stability for a proposed compact quasi-axisymmetric stellarator CHS-qa has been investigated taking the effect of bootstrap current into account. Assuming experimentally achievable density and temperature profiles, the stability properties of global low-n modes have been studied by using threedimensionalnumerical codes based on fixed boundary MHD equilibria including self-consistent bootstrap current for the CHS-qa reference configuration. Consequently it has been shown that values of edge rotational transform play a crucial role in triggering external kink instability. Concerning a lot of other possibilities in experimental practice to change the total parallel current, we have also studied equilibria with increased or decreased parallel current, but fixed profile. The onset of external kink modes depends on rotational transform or current profile, and we found a stable equilibrium in spite of the edge rotational transform above 0.5. The results imply the possibility of stabilizing external kink modes through current and/or pressure profile control in high beta equilibria

Impact of Energetic Ion Driven Global Modes on Toroidal Plasma Confinements

Excitation of energetic-ion-driven Alfv6n eigenmodes (AEs) and their impact on energetic ion confinement are widely and intensively studied in helical devices such as CHS and LHD as well as major tokamaks. The excitation of AEs sensitively depends on the parameter space defined by the averaged beam beta and the velocity ratio V6nlV6 (V611 : injected beam ion velocity, Va: Alfv6n velocity). In LHD, these two relevant parameters are widely scanned without suffering from current disruptions. So far, toroidicity induced AE (TAE), global AE (GAE) and energetic particle mode (EPM) or resonant TAE (R-TAE) were identified during tangential neutral beam injection (NBI) in CHS and LHD. Moreover, a new coherent mode with the frequency by about 8 times higher than the TAE frequency was observed in NBI heated plasmas of LHD at low magnetic field (<0.6T). This mode may be induced by helical field components of the confinement field. Nonlinear phenomena of bursting amplitude modulation and fast frequency chirping are clearly seen for TAEs and EPMs in CHS and LHD. EPMs in CHS and bursting TAEs in LHD enhance radial transport of energetic ions in certain plasma conditions

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

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