Magnetohydrodynamic Equilibrium States Research Articles

Saturated ideal kink/peeling formations described as three-dimensional magnetohydrodynamic tokamak equilibrium states

Free boundary magnetohydrodynamic equilibrium states with spontaneous three dimensional deformations of the plasma-vacuum interface are computed for the first time. The structures obtained have the appearance of saturated ideal external kink/peeling modes. High edge pressure gradients yield toroidal mode number n = 1 corrugations for a high edge bootstrap current and larger n distortions when this current is small. Deformations in the plasma boundary region induce a nonaxisymmetric Pfirsch-Schlüter current driving a field-aligned current ribbon consistent with reported experimental observations. A variation in the 3D equilibrium confirms that the n = 1 mode is a kink/peeling structure. We surmise that our calculated equilibrium structures constitute a viable model for the edge harmonic oscillations and outer modes associated with a quiescent H-mode operation in shaped tokamak plasmas.

A 3-D MHD equilibrium description of nonlinearly saturated ideal external kink/peeling structures in tokamaks

Novel free boundary magnetohydrodynamic equilibrium states with spontaneous three-dimensional (3-D) deformations of the plasma–vacuum interface are computed. The structures obtained look like saturated ideal external kink/peeling modes. Large edge pressure gradients yield toroidal mode number $n=1$ distortions when the edge bootstrap current is large and higher $n$ corrugations when this current is small. Linear ideal MHD stability analyses confirm the nonlinear saturated ideal kink equilibrium states produced and we can identify the Pfirsch–Schlüter current as the main linear instability driving mechanism when the edge pressure gradient is large. The dominant non-axisymmetric component of this Pfirsch–Schlüter current drives a near resonant helical parallel current density ribbon that aligns with the near vanishing magnetic shear region caused by the edge bootstrap current. This current ribbon is a manifestation of the outer mode previously found on JET (Solano 2010). We claim that the equilibrium corrugations describe structures that are commonly observed in quiescent H-mode tokamak discharges.

Bifurcated helical core equilibrium states in tokamaks

Tokamaks with weak to moderate reversed central shear in which the minimum inverse rotational transform (safety factor) qmin is in the neighbourhood of unity can trigger bifurcated magnetohydrodynamic equilibrium states, one of which is similar to a saturated ideal internal kink mode. Peaked prescribed pressure profiles reproduce the ‘snake’ structures observed in many tokamaks which has led to a novel explanation of the snake as a bifurcated equilibrium state. Snake equilibrium structures are computed in simulations of the tokamak à configuration variable (TCV), DIII-D and mega amp spherical torus (MAST) tokamaks. The internal helical deformations only weakly modulate the plasma–vacuum interface which is more sensitive to ripple and resonant magnetic perturbations. On the other hand, the external perturbations do not alter the helical core deformation in a significant manner. The confinement of fast particles in MAST simulations deteriorate with the amplitude of the helical core distortion. These three-dimensional bifurcated solutions constitute a paradigm shift that motivates the applications of tools developed for stellarator research in tokamak physics investigations.

Bootstrap Current Simulations with Experimental LHD Plasma Density and Temperature Profiles, Energy Scattering and Finite Orbit Width

Bootstrap current calculations with the neoclassical SPBSC and VENUS+δf codes have been performed on experimental Large Helical Device (LHD, NIFS, Japan) configurations with different magnetic axis positions and simplified plasma density and temperature profiles. In this paper, we use experimentally obtained electron density and temperature profiles for the LHD discharges #61863 and #82582 to compute the corresponding magnetohydrodynamic equilibrium states and collisional frequency. An improved collisional operator has been implemented into the VENUS+δf code. The comparison between the measured LHD bootstrap current and that expected from neoclassical simulations is discussed.

Magnetohydrodynamic properties of nominally axisymmetric systems with 3D helical core

Magnetohydrodynamic equilibrium states with a three-dimensional helical core are computed to model the MAST spherical tokamak and the RFX-mod reversed field pinch. The boundary is fixed as axisymmetric. The MAST equilibrium state has the appearance of an internal kink mode and is obtained under conditions of weak reversed central shear. The RFX-mod equilibrium state has seven-fold periodicity. An ideal magnetohydrodynamic stability analysis reveals that the reversal of the core magnetic shear can stabilize a periodicity-breaking mode that is dominantly m/n = 1/8 strongly coupled to a m/n = 2/15 component, as long as the central rotational transform does not exceed the value of 8.

Tokamak Magnetohydrodynamic Equilibrium States with Axisymmetric Boundary and a 3D Helical Core

Magnetohydrodynamic (MHD) equilibrium states with imposed axisymmetric boundary are computed in which a spontaneous bifurcation develops to produce an internal three-dimensional (3D) configuration with a helical structure in addition to the standard axisymmetric system. Equilibrium states with similar MHD energy levels are shown to develop very different geometric structures. The helical equilibrium states resemble saturated internal kink mode structures.

Variational principles and Lyapunov stability analysis for compressible cylindrical plasma flows with arbitrary cross-section

The equilibrium and stability properties of ideal compressible magnetohydrodynamic (MHD) flows are investigated. The domain is taken to be cylindrical with arbitrary cross-section. Variational principles for plasma equilibria with mass flow are formulated, where we associate the cylindrical MHD equilibrium states to critical points of a conserved Lyapunov functional. This functional consists of the sum of the total energy, the mass, the circulation along field lines (cross-helicity), the momentum and the magnetic helicity. Lyapunov stability conditions for compressible cylindrical ideal MHD flows with arbitrary cross-section are determined.

Theoretical study of onset conditions for solar eruptive processes

We apply the model of quasistatic equilibrium sequences to describe the time development of magnetic field structures in the plasma of the solar corona, and to determine onset points of a dynamical evolution. The representation of the magnetic field by Euler potentials provides a realistic modeling of the photospheric boundary conditions. We present a numerical method suited for the computation of magnetohydrodynamic equilibrium states and for analysing their stability against perturbations within ideal MHD. Pressure and magnetic footpoint displacement can be prescribed separately as boundary conditions. We consider magnetic arcade structures typical for large two-ribbon flares. Our results indicate that a finite pressure gradient seems to be essential for the existence of onset points. Furthermore, it is shown that magnetic shear destabilizes for intermediate values, but can have a stabilizing effect for a large amount of shear.

Magnetohydrodynamic Stability of Spheromak Plasma in Toroidal Flux Conserver with Rectangular Cross Section. II. Application of Mercier Criterion

The magnetohydrodynamic equilibrium states by Hill's vortex model and by the Coulomb-wave-function model are proved to be unstable. New MHD equilibrium configurations are determined by using another model for which d p /dψ=0 on the magnetic axis. Here p is the pressure and ψ is the flux function. The values of the safety factor on the magnetic axis, q axis , are evaluated for these configurations. The MHD stability of these equilibrium states is investigated by the Mercier criterion. The values of the maximum beta ratio β max are evaluated for this model. The optimized pressure distributions are determined by use of the Mercier criterion and the values of β max are also evaluated for these pressure distributions. The values of β max are shown to be at most 12%, if the condition q axis <1 is required.