Session JO4: MFE Simulation and Modeling

Multiphysics Analysis of a Non-Resonant Internal Mode in NSTX

One class of tearing modes in the National Spherical Torus eXperiment (NSTX) occurs without any evidence of the usual triggering modes. Using several components of the SWIM framework [1], we have performed extensive linear and nonlinear MHD and hybrid MHD-kinetic analyses showing that these may be accounted for by a non-resonant mode with toroidal mode number $n=$1 that develops at moderate normalized \textit{$\beta $}$_{N}$ when the shear is low and the central safety factor $q_{0}$ is close to but greater than one. This mode, which is related to previously identified ``infernal'' modes [2], will saturate and persist, and can develop poloidal mode number $m=$2 magnetic islands in agreement with experiments. Our analysis includes a free-boundary transport simulation of an entire discharge showing that, with reasonable assumptions, we can predict the time of mode onset. Implications for ITER hybrid and AT regimes will be discussed. \\[4pt] [1] See web site http://cswim.org. \\[0pt] [2] J. Manickam, et al., \textit{Nucl. Fus}. \textbf{27}, 1461 (1987).   

Analysis Tools for Fusion Simulations

In this talk, we highlight two analysis tools for evaluating fusion simulations. The first tool is for interactively exploring the topology of the magnetic field using a Poincar\'{e} map. Unlike traditional Poincar\'{e} maps that rely on a dense set of puncture points to form a contiguous representation of the magnetic surface we use a sparse set of connected puncture points. The puncture points are connected based on a rational approximation of the safety factor. The resulting analysis not only allows for the visualization of magnetic surfaces using a minimal number of puncture points but also identifies features such as magnetic islands. The second tool is for performing query based analysis on simulations utilizing particles. To assist in the analysis of simulation codes that utilize millions to billions of particles we have developed analysis tools that combine parallel coordinates plots combine with accelerated index searches. Parallel coordinate plots allow one to identify trends within multivariate data while accelerated index searches allows one to quickly perform range based queries on a large number of multivariate entries.   

MHD spectral analysis of the resistive wall mode in a rotating plasma

The new approach of constructing the full complex ideal MHD spectrum of stationary plasma flows (Goedbloed, PoP 16, 122110 \& 122111, 2009), based on selfadjointness of the generalized force operator and the Doppler-Coriolis shift operator, is generalized to include the dissipation of resistive wall modes. The method consists of first constructing the solution path in the complex omega-plane, determined by energy conservation for the one-sided boundary value problem (open system), and next finding the eigenvalues on that path, determined by imposing the remaining boundary condition. With this split of the eigenvalue problem, the problem is perfectly suited for parallel computation. The lack of self-adjointness of the generalized force operator for the dissipative problem is accounted for by the energy dissipation in the resistive wall. The resulting different new topologies of the one-dimensional solutions paths in the complex omega-plane are analyzed and shown to yield a characterization of the different stabilizing and destabilizing effects operating in the resistive wall problem. The aim of this research is to find parameter regimes of relative stability with respect to the resistive wall mode, incorporating both toroidal and poloidal plasma flows.   

Chaotic Neo-Classical Transport and Damping

A novel {\it chaotic} form of Neo-Classical Transport has now been characterized experimentally and theoretically, as distinct from the traditional {\it collisional} NCT. Experimentally, an electrostatic or magnetic trapping separatrix is applied to pure electron plasma columns, and this separatrix is given controlled $\cos (m \theta )$ variations (ruffles). Equilibrium plasma drift rotation across the ruffles then causes dissipative separatrix crossings, giving enhanced particle transport and wave damping. Similar chaotic separatrix effects occur from wave-induced separatrix $\theta$-ruffles and temporal variations. For spatially separated trapping regions (``superbanana'' regime), traditional NCT scales with collisionality $\nu$ as $\nu^{1/2} B^{- 1/2}$, whereas the chaotic NCT scales as $\nu^0 B^{-1}$. Fortunately, the chaotic particle transport has a distinctive $\sin^2 ( \alpha )$ signature, where $\alpha$ is the angle between the $\theta$-ruffle and the global $\theta$-asymmetry (error field) which drives the transport. Quantitative correspondence with theory has now been obtained for particle transport, diocotron (drift) wave damping, and dissipative wave-wave couplings; also observed is chaotic damping of higher frequency Langmuir waves. This chaotic separatrix dissipation may occur in low-collisionality stellarator and tokamak plasmas also.   

Equilibrium nonlinearity and combined stabilizing effects of magnetic field and plasma flow

The nonlinear ``cat-eyes" and counter-rotating-vortices hydrodynamic solutions are extended to the magnetohydrodynamic equilibrium equation with incompressible flow of arbitrary direction [1,2]. The extended solutions cover a variety of equilibria because four surface quantities remain free. Unlike to linear equilibria, the flow has a strong impact on isobaric surfaces by forming pressure islands located within the equilibrium vortices even for values of $\beta$ (defined as the ratio of the thermal pressure over the external magnetic-field pressure) on the order of 0.01. Also, the axial (``toroidal") current density is appreciably modified by the flow. Furthermore, a magnetic-field-aligned flow of ITER relevance, i.e for Alfv\'en Mach numbers of the order of 0.01, and the flow shear in combination with the variation of the magnetic field perpendicular to the magnetic surfaces have significant stabilizing effects potentially related to the equilibrium nonlinearity. The stable region is enhanced by an external axial magnetic field. \\[0pt] [1] G. N. Throumoulopoulos, H. Tasso and G. Poulipoulis, J. Phys. A: Math. Theor. {\bf 42}, 335501 (2009).\newline [2] G. N. Throumoulopoulos, H. Tasso, Phys. Plasmas {\bf 17}, 032508 (2010).   

Simulation study of toroidal flow generation by ICRF heating using GNET code

The toroidal flow generation by the ICRF heating is investigated in the tokamak plasma applying GNET code, in which the drift kinetic equation is solved in 5D phase-space. We assume a tokamak plasma similar to the Alcator C-mod plasma as a first step. We obtain a steady state distribution of energetic minority ions and the flux surface averaged toroidal flow is evaluated. It is found that a co-directional toroidal flow is generated outside of the RF wave power absorption region. The dominant part of toroidal flow does not depend on the sign of $k_{\parallel}$. When we change the sign of the toroidal current we obtain a reversal of the toroidal flow velocity, which is consistent with the experimental observations. We consider the toroidal precession motion of energetic tail ions accelerated by the ICRF heating. The magnetic shear and the poloidal magnetic drift increases a net toroidal drift motion during one bounce of banana motion. We estimate the toroidal flow by these toroidal precession motion and the results are compared with the simulation ones.   

Radial transfer effects for poloidal rotation

Radial transfer of energy or momentum is the principal agent responsible for radial structures of Geodesic Acoustic Modes (GAMs) or stationary Zonal Flows (ZF) generated by the turbulence. For the GAM, following a physical approach, it is possible to find useful expressions for the individual components of the Poynting flux or radial group velocity allowing predictions where a mathematical full analysis is unfeasible. Striking differences between up-down symmetric flux surfaces and asymmetric ones have been found. For divertor geometries, e.g., the direction of the propagation depends on the sign of the ion grad-B drift with respect to the X-point, reminiscent of a sensitive determinant of the H-mode threshold. In nonlocal turbulence computations it becomes obvious that the linear energy transfer terms can be completely overwhelmed by the action of the turbulence. In contrast, stationary ZFs are governed by the turbulent radial transfer of momentum. For sufficiently large systems, the Reynolds stress becomes a deterministic functional of the flows, which can be empirically determined from the stress response in computational turbulence studies. The functional allows predictions even on flow/turbulence states not readily obtainable from small amplitude noise, such as certain transport bifurcations or meta-stable states.   

Understanding electron transport mechanism in collisionless trapped electron mode turbulence

A prominent candidate for the electron heat transport in tokamaks is collisionless trapped electron mode (CTEM) turbulence. Our large scale simulations using gyrokinetic toroidal code (GTC) finds that electron heat transport can be non-diffusive in CTEM turbulence. Radial correlation analysis shows the existence of mesoscale eddy although the turbulence eddies are predominantly microscopic due to the zonal flow shearing. The radial profile of the electron heat conductivity is found to roughly follow the global profile of fluctuation intensity, while the ion transport tracks local fluctuation intensity. This suggests a non-diffusive component in the electron heat transport, which arises from the ballistic radial drift of trapped electrons due to a combination of the presence of the mesoscale eddies and the weak detuning of the toroidal precessional resonance. However, the ion radial excursion is not affected by the mesoscale eddies due to the parallel decorrelation. A careful study of the radial transport of the trapped electrons confirms the non-diffusive feature, which can be quantitatively modeled by a quasilinear theory.   

Gyrokinetic simulation study on ion temperature gradient modes and zonal flows in Large Helical Device experiments

Ion temperature gradient (ITG) modes and zonal flows in the Large Helical Device (LHD) experiments are studied by gyrokinetic simulation. In recent LHD experiments, the high ion temperature of $>$ 4 keV is achieved by injection of neutral beams, and microturbulence spatial profiles were measured. The measured fluctuations most likely propagate to the ion diamagnetic direction in plasma frame and their amplitudes increase with growth of the temperature gradient, of which results show the characteristics of ITG turbulence. In order to investigate the ITG modes and zonal flows in the LHD experiment, we performed gyrokinetic simulation in the corresponding equilibrium field by means of the GKV-X code which incorporates full geometrical effects of non-axisymmetric field configuration. From the calculation, the growth rate of the ITG mode peaks at r=0.65a where the temperature gradient is most away from its critical value. The obtained results show agreements with the measurements in the experiments. It is also found that the zonal flows are slightly enhanced in inner radial region.   

Perturbed Density Patterns during Microwave and Plasma Interaction in a Rectangular Waveguide

The interaction of electromagnetic waves and plasma has been an active and interesting field of research due to its diverse applications in controlled fusion applications (ITER), particle acceleration, frequency upshifting, resonance absorption, etc. In our recent study, we have observed interesting structures of the perturbed density due to the effect of microwave ponderomotive force when the fundamental TE$_{10}$ mode encounters a plasma in a waveguide. Now in the present investigation, we examine the microwave and plasma interaction in a rectangular waveguide when the two fundamental TE$_{10}$ modes superpose and encounter a plasma in another waveguide of the same size. Here, we explore the importance of phase difference between these two modes. Moreover, in view of the possible applications of high intensity microwaves to ITER, we study the effects of different parameters on the plasma density profile as well on the wavelength of the microwave. For this, we not only consider the homogeneous plasma but initial density is also taken to be linearly varying in the propagation direction and Gaussian distribution along the waveguide width. For each case, we have also analyzed the perturbed plasma density profile for the different temperature of the electrons in the plasma, which gives some interesting results.   

Impurity Turbulent Transport Studies using Gyro-Fluid Models

We study particle turbulent transport using a set of three-component (electric potential $\phi$, hydrogenic density $\delta n_i$ and impurity density $\delta n_z$) gyro-fluid equations. Linear eigenmode analysis shows that at least three modes exist in this slab impurity model, with one stable mode, one unstable mode and a third intersting mode with zero frequency. Quasilinear particle flux for hydrogenic(impurity) gas is calculated from the out-of-phase $\phi$ and $\delta n_i$($\delta n_z$) fluctuations. The results agree with experimental observation of particle transport dependence on density gradient length. We also conduct 2D nonlinear gyro-fluid simulations with DTRANS code. Comparison between heavy impurities (eg. Argon) and light impurities (eg. Boron) show that heavy impurities have strong influence on the transport dynamics while light impurities are acting more like passive tracers. Turbulence growth from initial plasma states without hydrogenic plasma waves ($\delta n_i =\phi=0$) and only a tiny injection of the impurity make clear the role of the impurity injection for drift wave dynamics.   

Beta $>$ 1 Penning Discharge Fusion Device

A cold target (fibre(s) or dust, R. Jones, Ind. J. Phys, 55B, 397, 1981 and Ind. J. Phys, 57B, 378, 1983) is heated by high voltage (Megavolt) pulsed power in Penning geometry. The plasma is thermalized by nonclassical processes and electron space charge ion heating (R. Jones, Il Nuovo Cimento, 40B, \#2, 261, 1977) and heat is confined by both electrostatic and magnetic insulation while plasma pressure is supported by (wall) inertia (beta $>$ 1). (R. Jones, BAPS, 37, \#6, 1474, 1992) More effort needs to be devoted (worldwide) to the study of wall confined plasmas.   

Quantum Macrophysics for Turbulence Concepts in High Temperature Plasma Systems

A quantum statistical theory of equilibrium states within the operator algebraic framework allows a reformulation of classical thermodynamics in terms of the restriction of the equilibrium states to macroscopic observables. This provides a radically different treatment from traditional statistical thermodynamics since it is based on the theory of finite systems and cannot support different equilibrium states under the same external macroscopic constraints. In this context, the classical thermodynamical characterization of phase transitions by singularities in the reduced pressure coincides with the quantum statistical one given by the existence of different equilibrium states with the same values of the thermodynamic variable conjugate to the dominant extensive variable. We use this formulation to explore the transition to turbulence as a phase transition of the second kind and the implications of this use in the prediction of turbulent transport parameters.