Global Magnetohydrodynamic Modes Research Articles

Stability of global magnetohydrodynamic modes in the L-5 compact torsatron

Global magnetohydrodynamic (MHD) modes in free-boundary plasma equilibrium configurations of the L-5 six-period compact torsatron (project of the Prokhorov General Physics Institute, Russian Academy of Sciences; G. M. Batanov et al., Plasma Dev. Operat. 11, 161 (2003)) have been investigated using the CAS3D code. It is shown that global internal ideal MHD modes can be found reliably only in Mercier unstable plasmas. In all cases under study, they are intrinsically ballooning in nature, i.e., the disturbance at the inner side of the torus is significantly lower in value than that at the outer side. Besides internal modes localized near low-order rational magnetic surfaces, external modes that are localized near the free plasma boundary and are not associated with any rational magnetic surface inside the plasma (the so-called peeling modes) have been found. In contrast to a tokamak with the same aspect ratio, in which pressure-gradient edge-localized modes are ballooning in nature, the peeling modes in the 3D currentless magnetic configuration investigated in the present work are quasi-cylindrical in the flux coordinate system. The problem of plasma boundary destruction under the action of magnetic fields generated by plasma currents is also briefly discussed.

Elastic or magnetic? A toy model for global magnetar oscillations with implications for quasi-periodic oscillations during flares

Abstract We use a simple toy-model to discuss global magnetohydrodynamic modes of a neutron star, taking into account the magnetic coupling between the elastic crust and the fluid core. Our results suggest that the notion of pure torsional crust modes is not useful for the coupled system. All modes excite Alfvén waves in the core. However, we also show that the modes that are most likely to be excited by a fractured crust, e.g. during a magnetar flare, are such that the crust and the core oscillate in concert. For our simple model, the frequencies of these modes are similar to the ‘pure crustal’ frequencies. In addition, our model provides a natural explanation for the presence of lower frequency (<30 Hz) quasi-periodic oscillations seen in the 2004 December giant flare of SGR 1806–20.

A kinetic magnetohydrodynamic energy integral in three dimensional geometry

Recent observations of Alfvén wave excitations in stellarator geometry and their successful description by the global magnetohydrodynamic (MHD) stability code CAS3D (Code for the Analysis of the MHD Stability of 3D Equilibria) [C. Nührenberg, Phys. Plasmas 6, 137 (1998)] have raised the question of to what extent a fast particle population may destabilize such modes. In answering this question a theoretical basis must be developed through which the influence of fast particles upon global MHD modes in realistic three-dimensional geometries can be investigated. As a first step towards this goal, a linearized drift-kinetic equation for electro-magnetic perturbations is derived and solved. It is furthermore shown that a generalized kinetic MHD energy integral exists which is nonlinear with respect to the mode frequencies. This energy integral agrees with previous less general results in their limits.

Measurement of core velocity fluctuations and the dynamo in a reversed-field pinch

Plasma flow velocity fluctuations have been directly measured in the high-temperature magnetically confined plasma in the Madison Symmetric Torus (MST) Reversed-Field Pinch (RFP) [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)]. These measurements show that the flow velocity fluctuations are correlated with magnetic field fluctuations such that the electromotive force 〈ṽ×B̃〉 approximately balances parallel Ohm’s law, E∥+〈ṽ×B̃〉∥=ηJ∥. This initial measurement is subject to limitations of spatial localization and other uncertainties, but is evidence for sustainment of the RFP magnetic field configuration by the magnetohydrodynamic (MHD) dynamo, 〈ṽ×B̃〉. Both the flow velocity and magnetic field fluctuations are the result of global resistive MHD modes of helicity m=1, n=5–10 in the core of MST. Chord-averaged flow velocity fluctuations are measured in the core of MST by recording the Doppler shift of impurity line emission with a specialized high resolution and throughput grating spectrometer. Magnetic field fluctuations are recorded with a large array of small edge pickup coils, which allows spectral decomposition into discrete modes and subsequent correlation with the velocity fluctuation data.

Global three-dimensional MHD simulations of accretion disks and jet formation in AGNS

We present the results of three-dimensional global magnetohydrodynamic (MHD) simulations of a gas torus in active galactic nuclei. When the torus is threaded by large-scale vertical magnetic fields, a magnetically driven jet is ejected from the torus. Since magnetic braking extracts angular momentum from the torus, the surface layer of the torus accretes like an avalanche. Due to the growth of global non-axisymmetric MHD modes, the avalanching flow breaks up into spiral channels and creates a helical structure inside the jet. We found that when the torus is initially threaded by weak toroidal magnetic fields, it evolves toward a quasi-steady state with β = P gas P mag ∼ 10 . As the angular momentum is re-distributed, the torus becomes flattened and the angular momentum distribution approaches that of Keplerian disks.

Global ideal magnetohydrodynamic stability analysis for the configurational space of Wendelstein 7–X

A survey of the magnetohydrodynamic (MHD) stability properties of three-dimensional (3-D) MHD configurations representing the Wendelstein 7–X (W7–X) stellarator experiment [ G. Grieger et al., Plasma Physics and Controlled Nuclear Fusion Research, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 525] was performed with the Code for the Analysis for the Stability of 3-D Equilibria (CAS3D) [C. Schwab, Phys. Fluids B 5, 3195 (1993)] . This study confirms and elaborates previous indications on the structural characteristics of global MHD modes in stellarators. In particular these characteristics pertain to the compressibility of these modes, the equivalence of the decoupled stability problems for the modes with different parities, and the separability of global from fine-scale perturbations within the same mode family. As to the W7–X stellarator experiment, the envisaged configurational class—providing the intended experimental flexibility—appears to offer scenarios of safely stable operation.

The effect of sheared axial flow on the linear stability of the Z-pinch

A linear analysis of the ideal magnetohydrodynamic (MHD) stability of the Z-pinch is presented in which plasma flows are included in the equilibrium. With sheared axial flows it is found that substantial stabilization of internal modes is possible for some equilibrium profiles. For this to occur equilibria with a change in fluid velocity across the pinch radius of about Mach 2 are required. However, this ignores the surrounding vacuum and for the more realistic free boundary modes flows of about Mach 4 are required to stabilize all global MHD modes. This stabilization of MHD modes is not observed for all equilibria however. This fact, combined with the supersonic flow speeds required for stability, make it unlikely that a Z-pinch could in practice be stabilized by the introduction of sheared flow.

Ideal magnetohydrodynamics: Global mode analysis of three-dimensional plasma configurations

The global magnetohydrodynamic (MHD) stability of three-dimensional (3-D) toroidal plasmas, investigated here by the ideal MHD energy principle formulated in magnetic coordinates, is studied by a Finite-Element-Fourier code, the C_ode for the A_nalysis of the S_tability of 3-D equilibria (CAS3D) [Theory of Fusion Plasmas, Varenna 1990 (Editrice Compositori, Bologna, 1990), p. 667]. A first survey of the stability properties of 3-D equilibria clarifies structural characteristics of global MHD modes, such as the existence of separable mode families and the possibility of annihilating all compression terms, i.e., the fluid and the field compression, for the minimizing perturbation.

Experimental exploration of profile control in the Princeton Beta Experiment-Modified (PBX-M) tokamak

The experimental program of the Princeton Beta Experiment-Modified (PBX-M) tokamak [Phys. Fluids B2, 1271 (1990)] is directed toward tailoring plasma profiles to achieve greater stability and confinement and to gain access to the second stability region. Modification of the current density profile has been achieved with lower-hybrid current drive (LHCD), leading to a regime free of global magnetohydrodynamic modes, while raising the value of q(0) above unity. The diffusion of the fast electrons produced by LHCD has been examined using two-dimensional hard x-ray imaging. Ion Bernstein waves (IBW) have been used for ion heating: a preliminary analysis shows that ion heating was spatially localized and in agreement with theoretical calculations. Divertor biasing has modified the electric field inside the last closed surface, resulting in the formation of a transport barrier, which in turn has reduced the threshold power of neutral beam injection (NBI) for H-mode transition by 25%.

Energetic particle effects on global magnetohydrodynamic modes

The effects of energetic particles on magnetohydrodynamic (MHD) type modes are studied using analytical theories and the nonvariational kinetic-MHD stability code (nova-k) [Workshop on Theory of Fusion Plasmas, (Societa Italiana di Fisica, Bologna, 1987), p. 185]. In particular, the problems of (1) the stabilization of ideal MHD internal kink modes and the excitation of resonant ‘‘fishbone’’ internal modes and (2) the alpha particle destabilization of toroidicity-induced Alfvén eigenmodes (TAE) via transit resonances are addressed. Analytical theories are presented to help explain the nova-k results. For energetic trapped particles generated by neutral beam injection or ion cyclotron resonant heating, a stability window for the n=1 internal kink mode in the hot particle beta space exists even in the absence of core ion finite Larmor radius effect. On the other hand, the trapped alpha particles are found to resonantly excite instability of the n=1 internal mode and can lower the critical beta threshold. The circulating alpha particles can strongly destabilize TAE modes via inverse Landau damping associated with the spatial gradient of the alpha-particle pressure.