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This paper formulates the Tokamak Magneto-Hydrodynamics (TMHD), initially outlined by X. Li and L. E. Zakharov [Plasma Science and Technology 17(2), 97-104 (2015)] for proper simulations of macroscopic plasma dynamics. The simplest set of magneto-hydrodynamics equations, sufficient for disruption modeling and extendable to more refined physics, is explained in detail. First, the TMHD introduces to 3-D simulations the Reference Magnetic Coordinates (RMC), which are aligned with the magnetic field in the best possible way. The numerical implementation of RMC is adaptive grids. Being consistent with the high anisotropy of the tokamak plasma, RMC allow simulations at realistic, very high plasma electric conductivity. Second, the TMHD splits the equation of motion into an equilibrium equation and the plasma advancing equation. This resolves the 4 decade old problem of Courant limitations of the time step in existing, plasma inertia driven numerical codes. The splitting allows disruption simulations on a relatively slow time scale in comparison with the fast time of ideal MHD instabilities. A new, efficient numerical scheme is proposed for TMHD. [ABSTRACT FROM AUTHOR]

Magnetic fields are an essential component of a plasma. In many astrophysical, solar, magnetospheric, and laboratory situations the magnetic field in the plasma can be very dynamic and form highly complex structures. One approach to unraveling these structures is to determine the magnetic skeleton of the field, a set of topological features that divide the magnetic field into topologically distinct domains. In general, the features of the magnetic skeleton are difficult to locate, in particular those given by numerical experiments. In this paper, we propose a new set of tools to find the skeleton of general magnetic fields including null points, spines, separatrix surfaces, and separators. This set of tools is found to be considerably better at finding the skeleton than the currently favored methods used in magnetohydrodynamics. [ABSTRACT FROM AUTHOR]

The paper investigates the role of relative motion between the fluid components of a plasma model, which is simulated by concatenation of two anisotropic magnetohydrodynamic (MHD) fluids, on the propagation of low-frequency waves and instabilities. The gyrotropic pressure of both the MHD components is given by generalized polytropic laws that allow the system to reduce to a variety of states. The linearized analysis is carried out and dispersion relation is derived using the normal mode technique. The dispersion relation, which gives numerous earlier results as special cases, is discussed both analytically as well as numerically for parameters appropriate for the space plasma. It is found that the relative motion between the two components, besides modifying the condition for fire-hose instability, causes the concatenated system to exhibit different kinds of relative ordering of the magnitudes of phase speeds of the various MHD modes in the directions parallel and antiparallel to the magnetic field. The relative motion between the components also influences the phase relationship between density and magnetic field fluctuations for the various compressive modes in the background ambient plasma. [ABSTRACT FROM AUTHOR]

The reversal mechanism of a dipole magnetic field generated by dynamo action in a rotating spherical shell is investigated by a three-dimensional nonlinear magnetohydrodynamic simulation as well as a linear stability analysis. The emphasis of the study is on understanding the relationship between dipole reversal and the symmetry properties of the dynamo solution. As a result, first, it is found that there is a threshold of the magnetic Prandtl number, below which the dipole field is never reversed, and above which the reversal occurs at irregular intervals like the paleomagnetic evolution of the geodynamo. Second, it is shown that the dynamo process responsible for the generation of a dipole field (called “a-dynamo” in this paper) consists only of the antimirror symmetric magnetic field and the mirror symmetric velocity field with respect to the equatorial plane. Third, it is found that the components of the opposite symmetry to the a-dynamo grow only during the polarity reversal events and quickly decay afterwards. This indicates that the dipole field reversal and the loss of equatorial symmetry are tightly connected. In fact, it is clearly demonstrated by numerical analyses that the a-dynamo process is linearly unstable for the perturbation of opposite symmetry when the magnetic Prandtl number exceeds the threshold for dipole reversal. Mode coupling between the longitudinal Fourier components plays a crucial role in creating the instability. Based on the above results, it is proposed that symmetry-breaking instability could be the mechanism for dipole field reversal in the geodynamo process. The energy conversion between components of different symmetry is also analyzed in the quasistable polarity phase and in the polarity reversal phase, respectively. [ABSTRACT FROM AUTHOR]

The energy confinement time and maximum achievable pressure are critical figures of merit for any proposed magnetic fusion concept. The present work focuses on these issues for a hard core Z pinch, which is the cylindrical limit of a large aspect ratio levitated dipole configuration. An analysis is presented that theoretically predicts both τE and β for this configuration. The model makes the optimistic assumption that transport is purely classical in the region of the profile that is magnetohydrodynamically (MHD) stable against interchange modes. In the interchange-unstable region use is made of the quasilinear theory described in the accompanying paper [A. Kouznetsov, J. Freidberg, and J. Kesner, Phys. Plasmas 14, 102501 (2007)] which shows that the plasma pressure relaxes to the MHD marginally stable profile while the density evolves to n∝[∮dl/B]-1. Analytic and numerical calculations lead to explicit scaling relations for τE and β which can be tested in future LDX experiments. [ABSTRACT FROM AUTHOR]

The nonlinear evolution of resistive double tearing modes (DTMs) with safety factor values q=1 and q=3 is studied with a reduced cylindrical model of a tokamak plasma. We focus on cases where the resonant surfaces are a small distance apart. Recent numerical studies have shown that in such configurations high-m modes are strongly unstable and may peak around m=mpeak∼10. In this paper, it is first demonstrated that this result agrees with existing linear theory for DTMs. Based on this theory, a semiempirical formula for the dependence of mpeak on the system parameters is proposed. Second, with the use of nonlinear simulations, it is shown that the presence of fast growing high-m modes leads to a rapid turbulent collapse in an annular region, where small magnetic island structures form. Furthermore, consideration is given to the evolution of low-m modes, in particular the global m=1 internal kink, which can undergo nonlinear driving through coupling to fast growing linear high-m DTMs. Factors influencing the details of the dynamics are discussed. These results may be relevant to the understanding of the magnetohydrodynamic activity near the minimum of q and may thus be of interest for studies on stability and confinement of advanced tokamaks. [ABSTRACT FROM AUTHOR]

This paper presents the experimental characterization of pedestal parameters, edge localized mode (ELM) energy, and particle losses from the main plasma and the corresponding ELM energy fluxes on plasma facing components for a series of dedicated experiments in the Joint European Torus (JET). From these experiments, it is demonstrated that the simple hypothesis relating the peeling-ballooning linear instability to ELM energy losses is not valid. Contrary to previous observations at lower triangularities, small energy losses at low collisionality have been obtained in regimes at high plasma triangularity and q95∼4.5, indicating that the edge plasma magnetohydrodynamic stability is linked with the transport mechanisms that lead to the loss of energy by conduction during type I ELMs. Measurements of the ELM energy fluxes on the divertor target show that their time scale is linked to the ion transport along the field and the formation of a high energy sheath, in agreement with kinetic modeling of ELMs. Higher density ELMs, of a convective nature, lead to overall much longer time scales for the ELM energy flux, with more than 80% of the ELM energy flux arriving after the surface divertor temperature has reached its maximum value. On the contrary, for low density ELMs, of a conductive nature, up to 40% of the energy flux arrives at the divertor target before the surface divertor temperature has reached its maximum value. These large and more conductive ELMs may lead to up to ∼50% of the ELM energy reaching the main wall plasma facing components instead of the divertor target. The extrapolation to the International Thermonuclear Experimental Reactor of the obtained results is described and the main uncertainties discussed. [ABSTRACT FROM AUTHOR]

Recently the shallow water magnetohydrodynamic (SMHD) equations have been proposed for describing the dynamics of nearly incompressible conducting fluids for which the evolution is nearly two-dimensional (2D) with magnetohydrostatic equilibrium in the third direction. In the present paper the properties of the SMHD equations as a nonlinear system of hyperbolic conservation laws are described. Characteristics and Riemann invariants are studied for 1D unsteady and 2D steady flow. Simple wave solutions are derived, and the nonlinear character of the wave modes is investigated. The ∇·(h B)=0 constraint and its role in obtaining a regularized Galilean invariant conservation law form of the SMHD equations is discussed. Solutions of the Rankine-Hugoniot relations are classified and their properties are investigated. The derived properties of the wave modes are illustrated by 1D numerical simulation results of SMHD Riemann problems. A Roe-type linearization of the SMHD equations is given which can serve as a building block for accurate shock-capturing numerical schemes. The SMHD equations are presently being used in the study of the dynamics of layers in the solar interior, but they may also be applicable to problems involving the free surface flow of conducting fluids in laboratory and industrial environments. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The 3D instability of the spontaneous fast magnetic reconnection process is studied with magnetohydrodynamics (MHD) simulations, where the 2D model of the spontaneous fast magnetic reconnection is destabilized in three dimension. As well known in many 2D numerical MHD studies, when a 1D current sheet is destabilized with the current-driven anomalous resistivity, the 2D Petschek type fast magnetic reconnection is established. This paper shows that the 2D Petschek type fast magnetic reconnection can be destabilized in three dimension by an initial resistive disturbance which includes a weak fluctuation in the sheet current direction, i.e., along the magnetic neutral line. The resulting 3D fast magnetic reconnection finally becomes intermittent and random through a 3D instability. In addition, it is also shown that the 3D instability is suppressed by the uniform resistivity. It suggests that the 3D instability is caused in the Petschek-type reconnection process which is characterized by a strongly localized magnetic diffusion region and the slow shock acceleration of the plasma jets and is suppressed in the Sweet-Parker type reconnection process. [ABSTRACT FROM AUTHOR]

Magnetohydrodynamic instabilities of high-mode (H-mode) pedestal are investigated in this paper with the inclusion of bootstrap current for equilibrium and rotation for stability. The jointed European torus-like equilibria of H-mode discharges are generated numerically using the VMEC code. It is found that, when the bootstrap current is taken into account, a safety-factor reversal or plateau can be generated near plasma edge. This confirms previous results of numerical equilibrium reconstructions using other types of codes. The n = 1 magnetohydrodynamic instabilities, where n is toroidal mode number, are investigated numerically in this type of equilibria using the AEGIS code. It is found that the infernal type harmonic can prevail at safety-factor reversal or plateau region. The toroidal plasma rotation effect with low Mach number is investigated. The numerical results show that the mode frequency is close to the rotation frequency at pedestal top, when the value of safety factor at plateau is slightly above a rational number. This mode frequency range seems to coincide with the experimentally observed frequencies of n = 1 edge harmonic oscillations (or outer modes) at the quiescent H-mode discharges. [ABSTRACT FROM AUTHOR]