On Ponderomotive Effects Induced by Alfvén Waves in Inhomogeneous 2.5D MHD Plasmas

Thurgood, Jonathan; McLaughlin, James

doi:10.1007/s11207-013-0298-4

Cited by 22 publications

(32 citation statements)

References 34 publications

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“…All perturbations to variables in theB 0 -andĈ-directions are of O(α 2 ) and smaller, indicating that behaviour detailed in the following paragraphs is nonlinear and that the Alfvén wave is linearly decoupled from the magnetoacoustic waves (as first discussed in Thurgood & McLaughlin 2013a). Figure 3 shows the field-aligned perturbations in |v B |, where we find a nonlinear O(α 2 /2) disturbance that is everywhere cospatial to the Alfvén wave in v A .…”

Section: Proper Null =mentioning

confidence: 58%

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3D Alfvén wave behaviour about proper and improper magnetic null points

Thurgood¹,

McLaughlin²

2013

A&A

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Context. Magnetohydrodynamic (MHD) waves and magnetic null points are both prevalent in many astrophysical plasmas, including the solar atmosphere. Interaction between waves and null points has been implicated as a possible mechanism for localised heating events. Aims. Here we investigate the transient behaviour of the Alfvén wave about fully 3D proper and improper magnetic null points. Methods. We introduce an Alfvén wave into the vicinity of both proper and improper null points by numerically solving the ideal, β = 0 MHD equations using the LARE3D code. A magnetic fieldline and flux-based coordinate system permits the isolation of resulting wave modes and the analysis of their interaction. Results. We find that the Alfvén wave propagates throughout the region and accumulates near the fan-plane, causing current build up. For different values of null point eccentricity, the qualitative behaviour changes only by the imposition of anisotropic pulse dilation, owing to the differing rates at which fieldlines diverge from the spine. For all eccentricities, we find that the fast and Alfvén waves are linearly decoupled. During the driving phase, an independently propagating fast wave is nonlinearly generated owing to the ponderomotive force. Subsequently, no further excitation of fast waves occurs. Conclusions. We find that the key aspects of the theory of Alfvén waves about 2D null points extends intuitively to the fully 3D case; i.e. the wave propagates along fieldlines and thus accumulates at predictable parts of the topology. We also highlight that unlike in the 2D case, in 3D Alfvén-wave pulses are always toroidal, and thus any aspects of 2D Alfvén-wave-null models that are pulse-geometry specific must be reconsidered in 3D.

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Section: Proper Null =mentioning

confidence: 58%

“…Equation (6) can be derived from Eqs. (2) using the process detailed in Thurgood & McLaughlin (2013a) and is the nondimensionalised equivalent to their Eq. (12).…”

Section: Proper Null =mentioning

confidence: 99%

3D Alfvén wave behaviour about proper and improper magnetic null points

Thurgood¹,

McLaughlin²

2013

A&A

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“…This disturbance is not an independently propagating wave (in β = 0 such motion is prohibited), but a direct consequence of the longitudinal component of the ponderomotive force, which is induced, sustained and carried by the propagating Alfvén wave. This is the specific manifestation of the longitudinal daughter disturbance, a general feature of nonlinear Alfvén waves and a common manifestation of the ponderomotive force (see Thurgood & McLaughlin 2013 for a detailed discussion). Now we consider the fast-mode velocity component v ⊥ , shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…A large body of work regarding the ponderomotive A&A 555, A86 (2013) effects of waves in various MHD scenarios has demonstrated that nonlinear Alfvén waves can generate magnetoacoustic waves as they propagate through regions of inhomogeneous Alfvén speed (such as, e.g., Nakariakov et al 1997Nakariakov et al , 1998Verwichte et al 1999;Botha et al 2000;Tsiklauri et al 2001;McLaughlin et al 2011a;Thurgood & McLaughlin 2013). The specific nature of ponderomotive mode conversion is dependent upon the gradients in the amplitude of the pulse and gradients in the Alfvén-speed profile.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Alfvén wave dynamics at a 2D magnetic null point: ponderomotive force

Thurgood

McLaughlin

2013

A&A

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Context. In the linear, β = 0 MHD regime, the transient properties of magnetohydrodynamic (MHD) waves in the vicinity of 2D null points are well known. The waves are decoupled and accumulate at predictable parts of the magnetic topology: fast waves accumulate at the null point; whereas Alfvén waves cannot cross the separatricies. However, in nonlinear MHD mode conversion can occur at regions of inhomogeneous Alfvén speed, suggesting that the decoupled nature of waves may not extend to the nonlinear regime. Aims. We investigate the behaviour of low-amplitude Alfvén waves about a 2D magnetic null point in nonlinear, β = 0 MHD. Methods. We numerically simulate the introduction of low-amplitude Alfvén waves into the vicinity of a magnetic null point using the nonlinear LARE2D code. Results. Unlike in the linear regime, we find that the Alfvén wave sustains cospatial daughter disturbances, manifest in the transverse and longitudinal fluid velocity, owing to the action of nonlinear magnetic pressure gradients (viz. the ponderomotive force). These disturbances are dependent on the Alfvén wave and do not interact with the medium to excite magnetoacoustic waves, although the transverse daughter becomes focused at the null point. Additionally, an independently propagating fast magnetoacoustic wave is generated during the early stages, which transports some of the initial Alfvén wave energy towards the null point. Subsequently, despite undergoing dispersion and phase-mixing due to gradients in the Alfvén-speed profile (∇c A 0) there is no further nonlinear generation of fast waves. Conclusions. We find that Alfvén waves at 2D cold null points behave largely as in the linear regime, however they sustain transverse and longitudinal disturbances -effects absent in the linear regime -due to nonlinear magnetic pressure gradients.

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Behaviour of Magnetoacoustic Waves in the Neighbourhood of a Two-Dimensional Null Point: Initially Cylindrically Symmetric Perturbations

McLaughlin

2016

J Astrophys Astron

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The propagation of magnetoacoustic waves in the neighbourhood of a 2D null point is investigated for both β = 0 and β = 0 plasmas. Previous work has shown that the Alfvén speed, here v A ∝ r, plays a vital role in such systems and so a natural choice is to switch to polar coordinates. For β = 0 plasma, we derive an analytical solution for the behaviour of the fast magnetoacoustic wave in terms of the Klein-Gordon equation. We also solve the system with a semi-analytical WKB approximation which shows that the β = 0 wave focuses on the null and contracts around it but, due to exponential decay, never reaches the null in a finite time. For the β = 0 plasma, we solve the system numerically and find the behaviour to be similar to that of the β = 0 system at large radii, but completely different close to the null. We show that for an initially cylindrically-symmetric fast magnetoacoustic wave perturbation, there is a decrease in wave speed along the separatrices and so the perturbation starts to take on a quasi-diamond shape; with the corners located along the separatrices. This is due to the growth in pressure gradients that reach a maximum along the separatrices, which in turn reduces the acceleration of the fast wave along the separatrices leading to a deformation of the wave morphology.

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On Ponderomotive Effects Induced by Alfvén Waves in Inhomogeneous 2.5D MHD Plasmas

Cited by 22 publications

References 34 publications

3D Alfvén wave behaviour about proper and improper magnetic null points

3D Alfvén wave behaviour about proper and improper magnetic null points

Nonlinear Alfvén wave dynamics at a 2D magnetic null point: ponderomotive force

Behaviour of Magnetoacoustic Waves in the Neighbourhood of a Two-Dimensional Null Point: Initially Cylindrically Symmetric Perturbations

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