Solar Magnetohydrodynamics

Priest, E. R.

doi:10.1007/978-94-009-7958-1

Cited by 1,331 publications

(522 citation statements)

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“…Values of β = 0.01 are often quoted (e.g. Priest 1982). However, near null points the plasma β can become very large, so the (true) plasma β varies through the whole region.…”

Section: Discussionmentioning

confidence: 99%

MHD mode coupling in the neighbourhood of a 2D null point

McLaughlin¹,

Hood²

2006

A&A

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Context. At this time there does not exist a robust set of rules connecting low and high β waves across the β ≈ 1 layer. The work here contributes specifically to what happens when a low β fast wave crosses the β ≈ 1 layer and transforms into high β fast and slow waves. Aims. The nature of fast and slow magnetoacoustic waves is investigated in a finite β plasma in the neighbourhood of a twodimensional null point. Methods. The linearised equations are solved in both polar and cartesian forms with a two-step Lax-Wendroff numerical scheme. Analytical work (e.g. small β expansion and WKB approximation) also complement the work. Results. It is found that when a finite gas pressure is included in magnetic equilibrium containing an X-type null point, a fast wave is attracted towards the null by a refraction effect and that a slow wave is generated as the wave crosses the β ≈ 1 layer. Current accumulation occurs close to the null and along nearby separatrices. The fast wave can now pass through the origin due to the non-zero sound speed, an effect not previously seen in related papers but clear seen for larger values of β. Some of the energy can now leave the region of the null point and there is again generation of a slow wave component (we find that the fraction of the incident wave converted to a slow wave is proportional to β). We conclude that there are two competing phenomena; the refraction effect (due to the variable Alfvén speed) and the contribution from the non-zero sound speed. Conclusions. These experiments illustrate the importance of the magnetic topology and of the location of the β ≈ 1 layer in the system.

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“…Values of β = 0.01 are often quoted (e.g. Priest 1982). However, near null points the plasma β can become very large, so the (true) plasma β varies through the whole region.…”

Section: Discussionmentioning

confidence: 99%

MHD mode coupling in the neighbourhood of a 2D null point

McLaughlin¹,

Hood²

2006

A&A

View full text Add to dashboard Cite

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“…The first problem to consider is the 3D magnetohydrostatic test case proposed by Warburton and Karniadakis [58] as an extension to the 2D solution derived by Priest [59]. In this particular magnetohydrostatic problem the fluid is static (i.e., has zero velocity) and the magnetic field is irrotational.…”

Section: Systematic Grid Convergence Studies For a Magnetohydrostaticmentioning

confidence: 99%

High-order central ENO finite-volume scheme for ideal MHD

Susanto

Ivan

Sterck

et al. 2013

Journal of Computational Physics

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A high-order central essentially non-oscillatory (CENO) finite-volume scheme is developed for the compressible ideal magnetohydrodynamics (MHD) equations solved on threedimensional (3D) cubed-sphere grids. The proposed formulation is an extension to 3D geometries of a recent high-order MHD CENO scheme developed on two-dimensional (2D) grids. The main technical challenge in extending the 2D method to 3D cubed-sphere grids is to properly handle the nonplanar cell faces that arise in cubed-sphere grids. This difficulty is solved by considering general hexahedral cells with trilinear faces, which allow us to compute fluxes, areas and volumes with high-order accuracy by transforming to a reference cubic cell. The 3D CENO scheme is implemented within a flexible multi-block cubed-sphere grid framework to fourth-order accuracy, resulting in a high-order solution method for cubed-sphere grids with unique capabilities in terms of adaptive refinement and parallel scalability. The high-order method is applicable to the solution of general hyperbolic conservation laws with, in principle, arbitrary order. The CENO scheme is based on a hybrid solution reconstruction procedure that provides high-order accuracy in smooth regions, even for smooth extrema, and non-oscillatory transitions at discontinuities. The scheme is applied herein to MHD in combination with a GLM divergence correction technique to control the solenoidal condition for the magnetic field while preserving the high-order accuracy of the numerical procedure. The cubed-sphere simulation framework features a flexible design based on a genuine multi-block implementation, leading to high-order accuracy, flux calculation, adaptivity and parallelism that are fully transparent to the boundaries between the six sectors of the cubedsphere grid. The proposed 3D MHD CENO scheme is shown to achieve uniform fourth-order accuracy on cubed-sphere grids. Parallel domain partitioning and grid adaptivity are achieved on the 3D cubed-sphere grids using a hierarchical block-based division strategy with blocks of equal size. Numerical results to demonstrate the high-order accuracy, robustness and capability of the proposed high-order framework are presented and discussed for several test problems.

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“…In Ref. [8] it was shown that continuum modes oscillating at the Brunt-Väisälä [9] frequency directly impacts the stabilily threshold of the internal kink mode, and that inconsistent treatment of the effect of toroidal rotation on the continuum mode would lead to erroneous results. The mode oscillating at the Brunt-Väisälä frequency is in fact a finite n zonal mode, which arises as one of two roots [10] from a dispersion relation that also defines the geodesic acoustic mode.…”

Section: Introductionmentioning

confidence: 99%

Generalised zonal modes in stationary axisymmetric plasmas

Graves

Wahlberg

2017

Plasma Phys. Control. Fusion

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The MHD model enables derivation and analysis of the rich structure of geodesic acoustic modes (GAMs) and zonal modes in axisymmetric magnetic confined plasmas. The modes are identifiable from a single dispersion relation as two branches of slow magnetosonic continua. The lower frequency branch can be identified as a zonal flow, which in the simplified limit of static plasmas, has vanishing magnetic component. It is shown in this contribution that axisymmetric, and lesser known nonaxisymmetric, zonal modes can be derived from MHD and kinetic models. The work provides a comprehensive derivation of the GAMs and zonal flow continua in static and stationary toroidally rotating plasmas, and investigates the exact solution and structure of a generalised family of zonal modes.

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Solar Magnetohydrodynamics

Cited by 1,331 publications

References 0 publications

MHD mode coupling in the neighbourhood of a 2D null point

MHD mode coupling in the neighbourhood of a 2D null point

High-order central ENO finite-volume scheme for ideal MHD

Generalised zonal modes in stationary axisymmetric plasmas

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