Stability of a linear pinch

Suydam, B. R.

doi:10.1016/0891-3919(58)90108-6

Cited by 23 publications

(29 citation statements)

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“…In the theoretical analysis of magnetohydrodynamic (MHD) waves, the effects of a curved loop axis are usually omitted. The stability of straight tubes with twisted magnetic field has been investigated by e.g., Shafranov (1957), Kruskal et al (1958), and Suydam (1958). The role of line tying conditions in the context of coronal loops has been studied by e.g., Raadu (1972) while the effect of gas pressure on the kink instability has been analysed by e.g., Giachetti et al (1977).…”

Section: Introductionmentioning

confidence: 99%

Transverse kink oscillations in the presence of twist

Terradas

Goossens

2012

A&A

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Context. Magnetic twist is thought to play an important role in coronal loops. The effects of magnetic twist on stable magnetohydrodynamic (MHD) waves is poorly understood because they are seldom studied for relevant cases. Aims. The goal of this work is to study the fingerprints of magnetic twist on stable transverse kink oscillations. Methods. We numerically calculated the eigenmodes of propagating and standing MHD waves for a model of a loop with magnetic twist. The azimuthal component of the magnetic field was assumed to be small in comparison to the longitudinal component. We did not consider resonantly damped modes or kink instabilities in our analysis. Results. For a nonconstant twist the frequencies of the MHD wave modes are split, which has important consequences for standing waves. This is different from the degenerated situation for equilibrium models with constant twist, which are characterised by an azimuthal component of the magnetic field that linearly increases with the radial coordinate. Conclusions. In the presence of twist standing kink solutions are characterised by a change in polarisation of the transverse displacement along the tube. For weak twist, and in the thin tube approximation, the frequency of standing modes is unaltered and the tube oscillates at the kink speed of the corresponding straight tube. The change in polarisation is linearly proportional to the degree of twist. This has implications with regard to observations of kink modes, since the detection of this variation in polarisation can be used as an indirect method to estimate the twist in oscillating loops.

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Section: Introductionmentioning

confidence: 99%

Transverse kink oscillations in the presence of twist

Terradas

Goossens

2012

A&A

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“…For cylindrical (1D) diffuse linear plasma columns, the theory of MHD stability is well established and can be found in textbook descriptions [22,21]. Details of the internal magnetic field variation determine many analytic stability results, while the pressure variation also appears in the established Suydam criterion for interchange/fluting modes [75]. The latter are connected to clustering sequences of discrete modes towards the edges of the MHD continua (frequency ranges ω(r) of slow and Alfvén frequencies), which extend to marginal frequency ω 2 = 0 when mB θ /r + kB z vanishes internal to the plasma column.…”

Section: Internal and External Kinks For Diffuse Plasma Columnsmentioning

confidence: 99%

Ideal MHD instabilities for coronal mass ejections: interacting current channels and particle acceleration

Keppens¹,

Guo²,

Makwana³

et al. 2019

Rev. Mod. Plasma Phys.

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We review and discuss insights on ideal magnetohydrodynamic (MHD) instabilities that can play a role in destabilizing solar coronal flux rope structures. For single flux ropes, failed or actual eruptions may result from internal or external kink evolutions, or from torus unstable configurations. We highlight recent findings from 3D magnetic field reconstructions and simulations where kink and torus instabilities play a prominent role.For interacting current systems, we critically discuss different routes to coronal dynamics and global eruptions, due to current channel coalescence or to tilt-kink scenarios. These scenarios involve the presence of two nearby current channels and are clearly distinct from the popular kink or torus instability. Since the solar corona is pervaded with myriads of magnetic loops -creating 2 Rony Keppens * et al.interacting flux ropes typified by parallel or antiparallel current channels as exemplified in various recent observational studies -coalescence or tilt-kink evolutions must be very common for destabilizing adjacent flux rope systems. Since they also evolve on ideal MHD timescales, they may well drive many sympathetic eruptions witnessed in the solar corona. Moreover, they necessarily lead to thin current sheets that are liable to reconnection. We review findings from 2D and 3D MHD simulations for tilt and coalescence evolutions, as well as on particle acceleration aspects derived from computed charged particle motions in tilt-kink disruptions and coalescing flux ropes. The latter were recently studied in two-way coupled kinetic-fluid models, where the complete phase-space information of reconnection is incorporated.

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“…where  and P in the flow-velocity equation (1) are the mass density and a viscous stress tensor, respectively. The equation for temperature (3) includes a conductive heat-flux density q, and  is the adiabatic index, which is typically set to 5/3.…”

Section: Nonlinear and Linear Mhd Equationsmentioning

confidence: 99%

“…In the absence of resistive dissipation, i.e. ideal MHD, the threshold for linear instability lies at a finite amount of "bad" magnetic curvature [1,2]. Bending of magnetic field-lines provides a restoring force, but it vanishes for resonant helical perturbations that align wavefronts with magnetic field (B) over entire surfaces of closed field-lines.…”

Section: Introductionmentioning

confidence: 99%

Stabilization of numerical interchange in spectral-element magnetohydrodynamics

Sovinec¹

2016

Journal of Computational Physics

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Auxiliary numerical projections of the divergence of flow velocity and vorticity parallel to magnetic field are developed and tested for the purpose of suppressing unphysical interchange instability in magnetohydrodynamic simulations. The numerical instability arises with equal-order C 0 finite-and spectral-element expansions of the flow velocity, magnetic field, and pressure and is sensitive to behavior at the limit of resolution. The auxiliary projections are motivated by physical field-line bending, and coercive responses to the projections are added to the flow-velocity equation. Their incomplete expansions are limited to the highest-order orthogonal polynomial in at least one coordinate of the spectral elements. Cylindrical eigenmode computations show that the projections induce convergence from the stable side with first-order ideal-MHD equations during h-refinement and p-refinement. Hyperbolic and parabolic projections and responses are compared, together with different methods for avoiding magnetic divergence error. The projections are also shown to be effective in linear and nonlinear time-dependent computations with the NIMROD code [C. R. Sovinec, et al., J. Comput. Phys. 195 (2004) 355-386], provided that the projections introduce numerical dissipation.2 filtering of incompressible fluid simulations [7], to a penalty method for MHD eigenvalue computations [4], and to finite/spectral element stabilization techniques [for example, 8-11].Our interest is nonlinear time-dependent simulation of nonideal MHD for magnetic confinement. This model admits viscosity that can stabilize localized interchange and facilitate computations. However, dissipation of dynamics perpendicular to magnetic field is weak in high-temperature plasma, and adding enough conventional viscosity to stabilize numerical interchange can distort dynamics. In principle, it is possible to address numerical interchange with sufficiently fine meshing for physical levels of viscosity. However, resonances that are susceptible to interchange can exist across the entire region of closed magnetic flux, and computing with globally fine resolution is computationally challenging and inefficient. The many resonances that occur in a region of bad magnetic curvature would also foil attempts to stabilize selected modes with spatially localized viscous dissipation.The numerical representation of interchange was first studied in the context of ideal-MHD eigenvalue computation for static equilibria. The fundamental dependent fields are the components of the displacement vector, and perturbations in pressure and magnetic field are eliminated analytically prior to discretization. The resulting force operator is a second-order differential operator in space, and it is self-adjoint [12]. Finite-element methods (FEM) for this problem benefit from distinct expansions for the flux-normal, parallel, and "cross" components of the displacement vector, and integration by parts leaves only first-order derivatives of basis and test functions. To conform with analytical ...

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Stability of a linear pinch

Cited by 23 publications

References 0 publications

Transverse kink oscillations in the presence of twist

Transverse kink oscillations in the presence of twist

Ideal MHD instabilities for coronal mass ejections: interacting current channels and particle acceleration

Stabilization of numerical interchange in spectral-element magnetohydrodynamics

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